src/HOL/TPTP/TPTP_Proof_Reconstruction_Test_Units.thy
author wenzelm
Sun, 05 Oct 2014 22:18:40 +0200
changeset 58550 f65911a725ba
parent 56281 03c3d1a7c3b8
child 59720 f893472fff31
permissions -rw-r--r--
more explicit syntax, to avoid misunderstanding of foo-bar as 3 separate arguments;
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(*  Title:      HOL/TPTP/TPTP_Proof_Reconstruction.thy
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    Author:     Nik Sultana, Cambridge University Computer Laboratory
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Unit tests for proof reconstruction module.
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NOTE
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  - Makes use of the PolyML structure.
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*)
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theory TPTP_Proof_Reconstruction_Test
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imports TPTP_Test TPTP_Proof_Reconstruction
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begin
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declare [[ML_exception_trace, ML_print_depth = 200]]
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ML {*
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PolyML.Compiler.maxInlineSize := 0;
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(* FIXME doesn't work with Isabelle?
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   PolyML.Compiler.debug := true *)
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*}
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declare [[
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  tptp_trace_reconstruction = true
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]]
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lemma "! (X1 :: bool) (X2 :: bool) (X3 :: bool) (X4 :: bool) (X5 :: bool). P \<Longrightarrow> ! (X1 :: bool) (X3 :: bool) (X5 :: bool). P"
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apply (tactic {*canonicalise_qtfr_order @{context} 1*})
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oops
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lemma "! (X1 :: bool) (X2 :: bool) (X3 :: bool) (X4 :: bool) (X5 :: bool). P \<Longrightarrow> ! (X1 :: bool) (X3 :: bool) (X5 :: bool). P"
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apply (tactic {*canonicalise_qtfr_order @{context} 1*})
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apply (rule allI)+
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apply (tactic {*nominal_inst_parametermatch_tac @{context} @{thm allE} 1*})+
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oops
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(*Could test bind_tac further with NUM667^1 inode43*)
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(*
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  (* SEU581^2.p_nux *)
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     (* (Annotated_step ("inode1", "bind"), *)
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lemma "\<forall>(SV5\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
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            SV6\<Colon>TPTP_Interpret.ind.
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            (bnd_in (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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              (bnd_powerset bnd_sK1_A) =
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             bnd_in (bnd_dsetconstr SV6 SV5)
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              (bnd_powerset SV6)) =
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            False \<Longrightarrow>
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         (bnd_in (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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           (bnd_powerset bnd_sK1_A) =
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          bnd_in (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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           (bnd_powerset bnd_sK1_A)) =
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         False"
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ML_prf {*
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open TPTP_Syntax;
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open TPTP_Proof;
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val binds =
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[Bind ("SV6", Atom (THF_Atom_term (Term_Func (Uninterpreted "sK1_A", [])))), Bind ("SV5", Quant (Lambda, [("SX0", SOME (Fmla_type (Atom (THF_Atom_term (Term_Func (TypeSymbol Type_Ind, []))))))], Fmla (Interpreted_ExtraLogic Apply, [Atom (THF_Atom_term (Term_Func (Uninterpreted "sK2_SY15", []))), Atom (THF_Atom_term (Term_Var "SX0"))])))]
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(* |> TPTP_Reconstruct.permute *)
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(*
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val binds =
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[Bind ("SV5", Quant (Lambda, [("SX0", SOME (Fmla_type (Atom (THF_Atom_term (Term_Func (TypeSymbol Type_Ind, []))))))], Fmla (Interpreted_ExtraLogic Apply, [Atom (THF_Atom_term (Term_Func (Uninterpreted "sK2_SY15", []))), Atom (THF_Atom_term (Term_Var "SX0"))]))),
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Bind ("SV6", Atom (THF_Atom_term (Term_Func (Uninterpreted "sK1_A", []))))
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]
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*)
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val tec =
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(*
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  map (bind_tac @{context} (hd prob_names)) binds
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  |> FIRST
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*)
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  bind_tac @{context} (hd prob_names) binds
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*}
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apply (tactic {*tec*})
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done
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     (* (Annotated_step ("inode2", "bind"), *)
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lemma "\<forall>(SV7\<Colon>TPTP_Interpret.ind) SV8\<Colon>TPTP_Interpret.ind.
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            (bnd_subset SV8 SV7 =
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             bnd_subset (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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              bnd_sK1_A) =
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            False \<or>
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            bnd_in SV8 (bnd_powerset SV7) = False \<Longrightarrow>
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         (bnd_subset (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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           bnd_sK1_A =
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          bnd_subset (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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           bnd_sK1_A) =
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         False \<or>
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         bnd_in (bnd_dsetconstr bnd_sK1_A bnd_sK2_SY15)
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          (bnd_powerset bnd_sK1_A) =
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         False"
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ML_prf {*
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open TPTP_Syntax;
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open TPTP_Proof;
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val binds =
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[Bind ("SV8", Fmla (Interpreted_ExtraLogic Apply, [Fmla (Interpreted_ExtraLogic Apply, [Atom (THF_Atom_term (Term_Func (Uninterpreted "dsetconstr", []))), Atom (THF_Atom_term (Term_Func (Uninterpreted "sK1_A", [])))]), Quant (Lambda, [("SX0", SOME (Fmla_type (Atom (THF_Atom_term (Term_Func (TypeSymbol Type_Ind, []))))))], Fmla (Interpreted_ExtraLogic Apply, [Atom (THF_Atom_term (Term_Func (Uninterpreted "sK2_SY15", []))), Atom (THF_Atom_term (Term_Var "SX0"))]))])), Bind ("SV7", Atom (THF_Atom_term (Term_Func (Uninterpreted "sK1_A", []))))]
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(* |> TPTP_Reconstruct.permute *)
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val tec =
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(*
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  map (bind_tac @{context} (hd prob_names)) binds
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  |> FIRST
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*)
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  bind_tac @{context} (hd prob_names) binds
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*}
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apply (tactic {*tec*})
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done
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*)
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(*
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from SEU897^5
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lemma "
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\<forall>SV9 SV10 SV11 SV12 SV13 SV14.
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   (((((bnd_sK5_SY14 SV14 SV13 SV12 = SV11) = False \<or>
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       (bnd_sK4_SX0 = SV10 (bnd_sK5_SY14 SV9 SV10 SV11)) =
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       False) \<or>
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      bnd_cR SV14 = False) \<or>
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     (SV12 = SV13 SV14) = False) \<or>
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    bnd_cR SV9 = False) \<or>
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   (SV11 = SV10 SV9) = False \<Longrightarrow>
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\<forall>SV14 SV13 SV12 SV10 SV9.
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   (((((bnd_sK5_SY14 SV14 SV13 SV12 =
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        bnd_sK5_SY14 SV14 SV13 SV12) =
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       False \<or>
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       (bnd_sK4_SX0 =
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        SV10
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         (bnd_sK5_SY14 SV9 SV10
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           (bnd_sK5_SY14 SV14 SV13 SV12))) =
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       False) \<or>
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      bnd_cR SV14 = False) \<or>
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     (SV12 = SV13 SV14) = False) \<or>
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    bnd_cR SV9 = False) \<or>
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   (bnd_sK5_SY14 SV14 SV13 SV12 = SV10 SV9) = False"
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ML_prf {*
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open TPTP_Syntax;
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open TPTP_Proof;
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val binds =
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[Bind ("SV11", Fmla (Interpreted_ExtraLogic Apply, [Fmla (Interpreted_ExtraLogic Apply, [Fmla (Interpreted_ExtraLogic Apply, [Atom (THF_Atom_term (Term_Func (Uninterpreted "sK5_SY14", []))), Atom (THF_Atom_term (Term_Var "SV14"))]), Atom (THF_Atom_term (Term_Var "SV13"))]), Atom (THF_Atom_term (Term_Var "SV12"))]))]
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val tec = bind_tac @{context} (hd prob_names) binds
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*}
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apply (tactic {*tec*})
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done
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*)
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subsection "Interpreting the inferences"
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(*from SET598^5
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lemma "(bnd_sK1_X = (\<lambda>SY17. bnd_sK2_Y SY17 \<and> bnd_sK3_Z SY17) \<longrightarrow>
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   ((\<forall>SY25. bnd_sK1_X SY25 \<longrightarrow> bnd_sK2_Y SY25) \<and>
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    (\<forall>SY26. bnd_sK1_X SY26 \<longrightarrow> bnd_sK3_Z SY26)) \<and>
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   (\<forall>SY27.
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       (\<forall>SY21. SY27 SY21 \<longrightarrow> bnd_sK2_Y SY21) \<and>
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       (\<forall>SY15. SY27 SY15 \<longrightarrow> bnd_sK3_Z SY15) \<longrightarrow>
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       (\<forall>SY30. SY27 SY30 \<longrightarrow> bnd_sK1_X SY30))) =
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  False \<Longrightarrow>
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  (\<not> (bnd_sK1_X = (\<lambda>SY17. bnd_sK2_Y SY17 \<and> bnd_sK3_Z SY17) \<longrightarrow>
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      ((\<forall>SY25. bnd_sK1_X SY25 \<longrightarrow> bnd_sK2_Y SY25) \<and>
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       (\<forall>SY26. bnd_sK1_X SY26 \<longrightarrow> bnd_sK3_Z SY26)) \<and>
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      (\<forall>SY27.
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          (\<forall>SY21. SY27 SY21 \<longrightarrow> bnd_sK2_Y SY21) \<and>
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          (\<forall>SY15. SY27 SY15 \<longrightarrow> bnd_sK3_Z SY15) \<longrightarrow>
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          (\<forall>SY30. SY27 SY30 \<longrightarrow> bnd_sK1_X SY30)))) =
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  True"
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apply (tactic {*polarity_switch_tac @{context}*})
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done
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lemma "
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  (((\<forall>SY25. bnd_sK1_X SY25 \<longrightarrow> bnd_sK2_Y SY25) \<and>
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    (\<forall>SY26. bnd_sK1_X SY26 \<longrightarrow> bnd_sK3_Z SY26)) \<and>
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   (\<forall>SY27.
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       (\<forall>SY21. SY27 SY21 \<longrightarrow> bnd_sK2_Y SY21) \<and>
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       (\<forall>SY15. SY27 SY15 \<longrightarrow> bnd_sK3_Z SY15) \<longrightarrow>
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       (\<forall>SY30. SY27 SY30 \<longrightarrow> bnd_sK1_X SY30)) \<longrightarrow>
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   bnd_sK1_X = (\<lambda>SY17. bnd_sK2_Y SY17 \<and> bnd_sK3_Z SY17)) =
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  False \<Longrightarrow>
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  (\<not> (((\<forall>SY25. bnd_sK1_X SY25 \<longrightarrow> bnd_sK2_Y SY25) \<and>
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       (\<forall>SY26. bnd_sK1_X SY26 \<longrightarrow> bnd_sK3_Z SY26)) \<and>
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      (\<forall>SY27.
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          (\<forall>SY21. SY27 SY21 \<longrightarrow> bnd_sK2_Y SY21) \<and>
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          (\<forall>SY15. SY27 SY15 \<longrightarrow> bnd_sK3_Z SY15) \<longrightarrow>
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          (\<forall>SY30. SY27 SY30 \<longrightarrow> bnd_sK1_X SY30)) \<longrightarrow>
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      bnd_sK1_X = (\<lambda>SY17. bnd_sK2_Y SY17 \<and> bnd_sK3_Z SY17))) =
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  True"
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apply (tactic {*polarity_switch_tac @{context}*})
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done
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*)
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(* beware lack of type annotations
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(* lemma "!!x. (A x = B x) = False ==> (B x = A x) = False" *)
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(* lemma "!!x. (A x = B x) = True ==> (B x = A x) = True" *)
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(* lemma "((A x) = (B x)) = True ==> ((B x) = (A x)) = True" *)
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lemma "(A = B) = True ==> (B = A) = True"
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*)
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lemma "!!x. ((A x :: bool) = B x) = False ==> (B x = A x) = False"
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apply (tactic {*expander_animal @{context} 1*})
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oops
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lemma "(A & B) ==> ~(~A | ~B)"
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by (tactic {*expander_animal @{context} 1*})
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lemma "(A | B) ==> ~(~A & ~B)"
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by (tactic {*expander_animal @{context} 1*})
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lemma "(A | B) | C ==> A | (B | C)"
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by (tactic {*expander_animal @{context} 1*})
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lemma "(~~A) = B ==> A = B"
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by (tactic {*expander_animal @{context} 1*})
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lemma "~ ~ (A = True) ==> A = True"
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by (tactic {*expander_animal @{context} 1*})
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(*This might not be a goal which might realistically arise:
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lemma "((~~A) = B) & (B = (~~A)) ==> ~(~(A = B) | ~(B = A))" *)
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lemma "((~~A) = True) ==> ~(~(A = True) | ~(True = A))"
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apply (tactic {*expander_animal @{context} 1*})+
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apply (rule conjI)
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apply assumption
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apply (rule sym, assumption)
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done
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lemma "A = B ==> ((~~A) = B) & (B = (~~A)) ==> ~(~(A = B) | ~(B = A))"
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by (tactic {*expander_animal @{context} 1*})+
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(*some lemmas assume constants in the signature of PUZ114^5*)
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consts
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  PUZ114_5_bnd_sK1 :: "TPTP_Interpret.ind"
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  PUZ114_5_bnd_sK2 :: "TPTP_Interpret.ind"
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  PUZ114_5_bnd_sK3 :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
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  PUZ114_5_bnd_sK4 :: "(TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool) \<Rightarrow> TPTP_Interpret.ind"
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  PUZ114_5_bnd_sK5 :: "(TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool) \<Rightarrow> TPTP_Interpret.ind"
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  PUZ114_5_bnd_s :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
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  PUZ114_5_bnd_c1 :: TPTP_Interpret.ind
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(*testing logical expansion*)
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lemma "!! SY30. (SY30 PUZ114_5_bnd_c1 PUZ114_5_bnd_c1 \<and>
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       (\<forall>Xj Xk.
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           SY30 Xj Xk \<longrightarrow>
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           SY30 (PUZ114_5_bnd_s (PUZ114_5_bnd_s Xj)) Xk \<and>
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           SY30 (PUZ114_5_bnd_s Xj) (PUZ114_5_bnd_s Xk)) \<longrightarrow>
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       SY30 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2)
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==> (
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       (~ SY30 PUZ114_5_bnd_c1 PUZ114_5_bnd_c1)
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     | (~ (\<forall>Xj Xk.
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           SY30 Xj Xk \<longrightarrow>
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           SY30 (PUZ114_5_bnd_s (PUZ114_5_bnd_s Xj)) Xk \<and>
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           SY30 (PUZ114_5_bnd_s Xj) (PUZ114_5_bnd_s Xk)))
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     | SY30 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2
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)"
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by (tactic {*expander_animal @{context} 1*})+
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(*
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extcnf_forall_pos:
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     (! X. L1) | ... | Ln
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 ----------------------------   X' fresh
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  ! X'. (L1[X'/X] | ... | Ln)
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After elimination rule has been applied we'll have a subgoal which looks like this:
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            (! X. L1)
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 ----------------------------   X' fresh
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  ! X'. (L1[X'/X] | ... | Ln)
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and we need to transform it so that, in Isabelle, we go from
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 (! X. L1) ==> ! X'. (L1[X'/X] | ... | Ln)
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to
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 \<And> X'. L1[X'/X] ==> (L1[X'/X] | ... | Ln)
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(where X' is fresh, or renamings are done suitably).*)
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lemma "A | B \<Longrightarrow> A | B | C"
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apply (tactic {*flip_conclusion_tac @{context} 1*})+
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apply (tactic {*break_hypotheses 1*})+
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oops
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consts
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  CSR122_1_bnd_lBill_THFTYPE_i :: TPTP_Interpret.ind
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  CSR122_1_bnd_lMary_THFTYPE_i :: TPTP_Interpret.ind
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  CSR122_1_bnd_lSue_THFTYPE_i :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   283
  CSR122_1_bnd_n2009_THFTYPE_i :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   284
  CSR122_1_bnd_lYearFn_THFTYPE_IiiI :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   285
  CSR122_1_bnd_holdsDuring_THFTYPE_IiooI ::
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   286
    "TPTP_Interpret.ind \<Rightarrow> bool \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   287
  CSR122_1_bnd_likes_THFTYPE_IiioI ::
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   288
    "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   289
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   290
lemma "\<forall>SV2. (CSR122_1_bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
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parents:
diff changeset
   291
                 (CSR122_1_bnd_lYearFn_THFTYPE_IiiI CSR122_1_bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   292
                 (\<not> (\<not> CSR122_1_bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   293
                        CSR122_1_bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   294
                        CSR122_1_bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   295
                     \<not> CSR122_1_bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   296
                        CSR122_1_bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   297
                        CSR122_1_bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   298
                CSR122_1_bnd_holdsDuring_THFTYPE_IiooI SV2 True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   299
               False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   300
         \<forall>SV2. (CSR122_1_bnd_lYearFn_THFTYPE_IiiI CSR122_1_bnd_n2009_THFTYPE_i =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   301
                SV2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   302
               False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   303
               ((\<not> (\<not> CSR122_1_bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   304
                       CSR122_1_bnd_lMary_THFTYPE_i CSR122_1_bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   305
                    \<not> CSR122_1_bnd_likes_THFTYPE_IiioI CSR122_1_bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   306
                       CSR122_1_bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   307
                True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   308
               False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   309
apply (rule allI, erule_tac x = "SV2" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   310
apply (tactic {*extuni_dec_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   311
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   312
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   313
(*SEU882^5*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   314
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   315
lemma
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   316
 "\<forall>(SV2\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   317
        SV1\<Colon>TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   318
        (SV1 SV2 = bnd_sK1_Xy) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   319
        False
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   320
   \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   321
   \<forall>SV2\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   322
            (bnd_sK1_Xy = bnd_sK1_Xy) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   323
            False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   324
ML_prf {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   325
open TPTP_Syntax;
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   326
open TPTP_Proof;
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   327
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   328
val binds =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   329
[Bind ("SV1", Quant (Lambda, [("SX0", SOME (Fmla_type (Atom (THF_Atom_term (Term_Func (TypeSymbol Type_Ind, []))))))], Atom (THF_Atom_term (Term_Func (Uninterpreted "sK1_Xy", [])))))]
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   330
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   331
val tec = bind_tac @{context} (hd prob_names) binds
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   332
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   333
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   334
apply (tactic {*strip_qtfrs
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   335
                (* THEN tec *)*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   336
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   337
apply (tactic {*tec*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   338
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   339
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   340
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   341
lemma "A | B \<Longrightarrow> C1 | A | C2 | B | C3"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   342
apply (erule disjE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   343
apply (tactic {*clause_breaker 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   344
apply (tactic {*clause_breaker 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   345
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   346
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   347
lemma "A \<Longrightarrow> A"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   348
apply (tactic {*clause_breaker 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   349
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   350
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   351
typedecl NUM667_1_bnd_nat
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   352
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   353
  NUM667_1_bnd_less :: "NUM667_1_bnd_nat \<Rightarrow> NUM667_1_bnd_nat \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   354
  NUM667_1_bnd_x :: NUM667_1_bnd_nat
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   355
  NUM667_1_bnd_y :: NUM667_1_bnd_nat
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   356
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   357
(*NUM667^1 node 302 -- dec*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   358
lemma "\<forall>SV12 SV13 SV14 SV9 SV10 SV11.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   359
       ((((NUM667_1_bnd_less SV12 SV13 = NUM667_1_bnd_less SV11 SV10) = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   360
          (SV14 = SV13) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   361
         NUM667_1_bnd_less SV12 SV14 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   362
        NUM667_1_bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   363
       (SV9 = SV11) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   364
       False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   365
       \<forall>SV9 SV14 SV10 SV13 SV11 SV12.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   366
       (((((SV12 = SV11) = False \<or> (SV13 = SV10) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   367
          (SV14 = SV13) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   368
         NUM667_1_bnd_less SV12 SV14 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   369
        NUM667_1_bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   370
       (SV9 = SV11) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   371
       False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   372
apply (tactic {*strip_qtfrs_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   373
apply (tactic {*break_hypotheses 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   374
apply (tactic {*ALLGOALS (TRY o clause_breaker)*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   375
apply (tactic {*extuni_dec_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   376
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   377
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   378
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   379
extuni_dec_n @{context} 2;
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   380
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   381
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   382
(*NUM667^1, node 202*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   383
lemma "\<forall>SV9 SV10 SV11.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   384
       ((((SV9 = SV11) = (NUM667_1_bnd_x = NUM667_1_bnd_y)) = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   385
         NUM667_1_bnd_less SV11 SV10 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   386
        NUM667_1_bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   387
       NUM667_1_bnd_less NUM667_1_bnd_x NUM667_1_bnd_y =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   388
       True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   389
       \<forall>SV10 SV9 SV11.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   390
       ((((SV11 = NUM667_1_bnd_x) = False \<or> (SV9 = NUM667_1_bnd_y) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   391
         NUM667_1_bnd_less SV11 SV10 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   392
        NUM667_1_bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   393
       NUM667_1_bnd_less NUM667_1_bnd_x NUM667_1_bnd_y =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   394
       True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   395
apply (tactic {*strip_qtfrs_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   396
apply (tactic {*break_hypotheses 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   397
apply (tactic {*ALLGOALS (TRY o clause_breaker)*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   398
apply (tactic {*extuni_dec_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   399
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   400
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   401
(*NUM667^1 node 141*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   402
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   403
lemma "((bnd_x = bnd_x) = False \<or> (bnd_y = bnd_z) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   404
         bnd_less bnd_x bnd_y = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   405
         (bnd_y = bnd_z) = False \<or> bnd_less bnd_x bnd_y = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   406
apply (tactic {*strip_qtfrs*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   407
apply (tactic {*break_hypotheses 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   408
apply (tactic {*ALLGOALS (TRY o clause_breaker)*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   409
apply (erule extuni_triv)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   410
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   411
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   412
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   413
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   414
fun full_extcnf_combined_tac ctxt =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   415
  extcnf_combined_tac ctxt NONE
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   416
   [ConstsDiff,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   417
    StripQuantifiers,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   418
    Flip_Conclusion,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   419
    Loop [
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   420
     Close_Branch,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   421
     ConjI,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   422
     King_Cong,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   423
     Break_Hypotheses,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   424
     Existential_Free,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   425
     Existential_Var,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   426
     Universal,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   427
     RemoveRedundantQuantifications],
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   428
    CleanUp [RemoveHypothesesFromSkolemDefs, RemoveDuplicates],
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   429
    AbsorbSkolemDefs]
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   430
   []
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   431
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   432
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   433
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   434
fun nonfull_extcnf_combined_tac ctxt feats =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   435
  extcnf_combined_tac ctxt NONE
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   436
   [ConstsDiff,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   437
    StripQuantifiers,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   438
    InnerLoopOnce (Break_Hypotheses :: feats),
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   439
    AbsorbSkolemDefs]
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   440
   []
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   441
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   442
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   443
consts SEU882_5_bnd_sK1_Xy :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   444
lemma
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   445
  "\<forall>SV2. (SEU882_5_bnd_sK1_Xy = SEU882_5_bnd_sK1_Xy) = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   446
   (SEU882_5_bnd_sK1_Xy = SEU882_5_bnd_sK1_Xy) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   447
(* apply (erule_tac x = "(@X. False)" in allE) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   448
(* apply (tactic {*remove_redundant_quantification 1*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   449
(* apply assumption *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   450
by (tactic {*nonfull_extcnf_combined_tac @{context} [RemoveRedundantQuantifications, Extuni_FlexRigid]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   451
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   452
(*NUM667^1*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   453
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   454
     (* (Annotated_step ("153", "extuni_triv"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   455
lemma "((bnd_y = bnd_x) = False \<or> (bnd_z = bnd_z) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   456
         (bnd_y = bnd_z) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   457
         (bnd_y = bnd_x) = False \<or> (bnd_y = bnd_z) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   458
apply (tactic {*nonfull_extcnf_combined_tac [Extuni_Triv]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   459
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   460
     (* (Annotated_step ("162", "extuni_triv"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   461
lemma "((bnd_y = bnd_x) = False \<or> (bnd_z = bnd_z) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   462
         bnd_less bnd_y bnd_z = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   463
         (bnd_y = bnd_x) = False \<or> bnd_less bnd_y bnd_z = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   464
apply (tactic {*nonfull_extcnf_combined_tac [Extuni_Triv]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   465
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   466
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   467
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   468
(* SEU602^2 *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   469
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   470
  SEU602_2_bnd_sK7_E :: "(TPTP_Interpret.ind \<Rightarrow> bool) \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   471
  SEU602_2_bnd_sK2_SY17 :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   472
  SEU602_2_bnd_in :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   473
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   474
     (* (Annotated_step ("113", "extuni_func"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   475
lemma "\<forall>SV49\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   476
            (SV49 =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   477
             (\<lambda>SY23\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   478
                 \<not> SEU602_2_bnd_in SY23 SEU602_2_bnd_sK2_SY17)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   479
            False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   480
         \<forall>SV49\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   481
            (SV49 (SEU602_2_bnd_sK7_E SV49) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   482
             (\<not> SEU602_2_bnd_in (SEU602_2_bnd_sK7_E SV49) SEU602_2_bnd_sK2_SY17)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   483
            False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   484
(*FIXME this (and similar) tests are getting the "Bad background theory of goal state" error since upgrading to Isabelle2013-2.*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   485
by (tactic {*fn thm =>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   486
  let
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   487
    val ctxt =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   488
      theory_of_thm thm
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   489
      |> Context.Theory
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   490
      |> Context.proof_of
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   491
  in nonfull_extcnf_combined_tac ctxt [Extuni_Func, Existential_Var] thm
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   492
  end*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   493
(*by (tactic {*nonfull_extcnf_combined_tac @{context} [Extuni_Func, Existential_Var]*})*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   494
oops
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   495
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   496
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   497
  SEV405_5_bnd_sK1_SY2 :: "(TPTP_Interpret.ind \<Rightarrow> bool) \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   498
  SEV405_5_bnd_cA :: bool
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   499
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   500
lemma "\<forall>SV1\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   501
            (\<forall>SY2\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   502
                \<not> (\<not> (\<not> SV1 SY2 \<or> SEV405_5_bnd_cA) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   503
                   \<not> (\<not> SEV405_5_bnd_cA \<or> SV1 SY2))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   504
            False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   505
         \<forall>SV1\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   506
            (\<not> (\<not> (\<not> SV1 (SEV405_5_bnd_sK1_SY2 SV1) \<or> SEV405_5_bnd_cA) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   507
                \<not> (\<not> SEV405_5_bnd_cA \<or> SV1 (SEV405_5_bnd_sK1_SY2 SV1)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   508
            False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   509
by (tactic {*nonfull_extcnf_combined_tac @{context} [Existential_Var]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   510
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   511
strip quantifiers -- creating a space of permutations; from shallowest to deepest (iterative deepening)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   512
flip the conclusion -- giving us branch
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   513
apply some collection of rules, in some order, until the space has been explored completely. advantage of not having extcnf_combined: search space is shallow -- particularly if the collection of rules is small.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   514
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   515
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   516
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   517
  SEU581_2_bnd_sK1 :: "TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   518
  SEU581_2_bnd_sK2 :: "TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   519
  SEU581_2_bnd_subset :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> HOL.bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   520
  SEU581_2_bnd_dsetconstr ::  "TPTP_Interpret.ind \<Rightarrow> (TPTP_Interpret.ind \<Rightarrow> HOL.bool) \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   521
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   522
(*testing parameters*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   523
lemma "! X :: TPTP_Interpret.ind . (\<forall>A B. SEU581_2_bnd_in B (SEU581_2_bnd_powerset A) \<longrightarrow> SEU581_2_bnd_subset B A) = True
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   524
\<Longrightarrow> ! X :: TPTP_Interpret.ind . (\<forall>A B. \<not> SEU581_2_bnd_in B (SEU581_2_bnd_powerset A) \<or> SEU581_2_bnd_subset B A) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   525
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   526
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   527
lemma "(A & B) = True ==> (A | B) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   528
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   529
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   530
lemma "(\<not> bnd_subset (bnd_dsetconstr bnd_sK1 bnd_sK2) bnd_sK1) = True \<Longrightarrow> (bnd_subset (bnd_dsetconstr bnd_sK1 bnd_sK2) bnd_sK1) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   531
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   532
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   533
(*testing goals with parameters*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   534
lemma "(\<not> bnd_subset (bnd_dsetconstr bnd_sK1 bnd_sK2) bnd_sK1) = True \<Longrightarrow> ! X. (bnd_subset (bnd_dsetconstr bnd_sK1 bnd_sK2) bnd_sK1) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   535
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   536
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   537
lemma "(A & B) = True ==> (B & A) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   538
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   539
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   540
(*appreciating differences between THEN, REPEAT, and APPEND*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   541
lemma "A & B ==> B & A"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   542
apply (tactic {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   543
  TRY (etac @{thm conjE} 1)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   544
  THEN TRY (rtac @{thm conjI} 1)*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   545
by assumption+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   546
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   547
lemma "A & B ==> B & A"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   548
by (tactic {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   549
  etac @{thm conjE} 1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   550
  THEN rtac @{thm conjI} 1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   551
  THEN REPEAT (atac 1)*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   552
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   553
lemma "A & B ==> B & A"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   554
apply (tactic {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   555
  rtac @{thm conjI} 1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   556
  APPEND etac @{thm conjE} 1*})+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   557
back
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   558
by assumption+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   559
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   560
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   561
  SEU581_2_bnd_sK3 :: "TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   562
  SEU581_2_bnd_sK4 :: "TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   563
  SEU581_2_bnd_sK5 :: "(TPTP_Interpret.ind \<Rightarrow> bool) \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   564
  SEU581_2_bnd_powerset :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   565
  SEU581_2_bnd_in :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   566
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   567
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   568
  bnd_c1 :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   569
  bnd_s :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   570
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   571
lemma "(\<forall>SX0. (\<not> (\<not> SX0 (PUZ114_5_bnd_sK4 SX0) (PUZ114_5_bnd_sK5 SX0) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   572
              \<not> (\<not> SX0 (bnd_s (bnd_s (PUZ114_5_bnd_sK4 SX0)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   573
                    (PUZ114_5_bnd_sK5 SX0) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   574
                 \<not> SX0 (bnd_s (PUZ114_5_bnd_sK4 SX0))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   575
                    (bnd_s (PUZ114_5_bnd_sK5 SX0)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   576
           \<not> SX0 bnd_c1 bnd_c1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   577
          SX0 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   578
   True ==> \<forall>SV1. ((\<not> (\<not> SV1 (PUZ114_5_bnd_sK4 SV1) (PUZ114_5_bnd_sK5 SV1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   579
              \<not> (\<not> SV1 (bnd_s (bnd_s (PUZ114_5_bnd_sK4 SV1)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   580
                    (PUZ114_5_bnd_sK5 SV1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   581
                 \<not> SV1 (bnd_s (PUZ114_5_bnd_sK4 SV1))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   582
                    (bnd_s (PUZ114_5_bnd_sK5 SV1)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   583
           \<not> SV1 bnd_c1 bnd_c1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   584
          SV1 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   585
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   586
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   587
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   588
lemma "(\<not> SEU581_2_bnd_subset (SEU581_2_bnd_dsetconstr SEU581_2_bnd_sK1 SEU581_2_bnd_sK2) SEU581_2_bnd_sK1) = True \<Longrightarrow> (SEU581_2_bnd_subset (SEU581_2_bnd_dsetconstr SEU581_2_bnd_sK1 SEU581_2_bnd_sK2) SEU581_2_bnd_sK1) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   589
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   590
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   591
(*testing repeated application of simulator*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   592
lemma "(\<not> \<not> False) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   593
    SEU581_2_bnd_subset (SEU581_2_bnd_dsetconstr SEU581_2_bnd_sK1 SEU581_2_bnd_sK2) SEU581_2_bnd_sK1 = True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   594
    False = True \<or> False = True \<or> False = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   595
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   596
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   597
(*Testing non-normal conclusion. Ideally we should be able to apply
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   598
  the tactic to arbitrary chains of extcnf steps -- where it's not
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   599
  generally the case that the conclusions are normal.*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   600
lemma "(\<not> \<not> False) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   601
    SEU581_2_bnd_subset (SEU581_2_bnd_dsetconstr SEU581_2_bnd_sK1 SEU581_2_bnd_sK2) SEU581_2_bnd_sK1 = True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   602
    (\<not> False) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   603
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   604
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   605
(*testing repeated application of simulator, involving different extcnf rules*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   606
lemma "(\<not> \<not> (False | False)) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   607
    SEU581_2_bnd_subset (SEU581_2_bnd_dsetconstr SEU581_2_bnd_sK1 SEU581_2_bnd_sK2) SEU581_2_bnd_sK1 = True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   608
    False = True \<or> False = True \<or> False = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   609
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   610
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   611
(*testing logical expansion*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   612
lemma "(\<forall>A B. SEU581_2_bnd_in B (SEU581_2_bnd_powerset A) \<longrightarrow> SEU581_2_bnd_subset B A) = True
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   613
\<Longrightarrow> (\<forall>A B. \<not> SEU581_2_bnd_in B (SEU581_2_bnd_powerset A) \<or> SEU581_2_bnd_subset B A) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   614
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   615
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   616
(*testing extcnf_forall_pos*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   617
lemma "(\<forall>A Xphi. SEU581_2_bnd_in (SEU581_2_bnd_dsetconstr A Xphi) (SEU581_2_bnd_powerset A)) = True \<Longrightarrow> \<forall>SV1. (\<forall>SY14.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   618
             SEU581_2_bnd_in (SEU581_2_bnd_dsetconstr SV1 SY14)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   619
              (SEU581_2_bnd_powerset SV1)) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   620
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   621
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   622
lemma "((\<forall>A Xphi. SEU581_2_bnd_in (SEU581_2_bnd_dsetconstr A Xphi) (SEU581_2_bnd_powerset A)) = True) | ((~ False) = False) \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   623
\<forall>SV1. ((\<forall>SY14. SEU581_2_bnd_in (SEU581_2_bnd_dsetconstr SV1 SY14) (SEU581_2_bnd_powerset SV1)) = True) | ((~ False) = False)"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   624
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   625
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   626
(*testing parameters*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   627
lemma "(\<forall>A B. SEU581_2_bnd_in B (SEU581_2_bnd_powerset A) \<longrightarrow> SEU581_2_bnd_subset B A) = True
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   628
\<Longrightarrow> ! X. (\<forall>A B. \<not> SEU581_2_bnd_in B (SEU581_2_bnd_powerset A) \<or> SEU581_2_bnd_subset B A) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   629
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   630
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   631
lemma "((? A .P1 A) = False) | P2 = True \<Longrightarrow> !X. ((P1 X) = False | P2 = True)"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   632
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   633
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   634
lemma "((!A . (P1a A | P1b A)) = True) | (P2 = True) \<Longrightarrow> !X. (P1a X = True | P1b X = True | P2 = True)"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   635
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   636
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   637
lemma "! Y. (((!A .(P1a A | P1b A)) = True) | P2 = True) \<Longrightarrow> ! Y. (!X. (P1a X = True | P1b X = True | P2 = True))"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   638
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   639
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   640
lemma "! Y. (((!A .(P1a A | P1b A)) = True) | P2 = True) \<Longrightarrow> ! Y. (!X. (P1a X = True | P1b X = True | P2 = True))"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   641
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   642
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   643
lemma "! Y. (((!A .(P1a A | P1b A)) = True) | P2 = True) \<Longrightarrow> ! Y. (!X. (P1a X = True | P1b X = True | P2 = True))"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   644
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   645
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   646
consts dud_bnd_s :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   647
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   648
(*this lemma kills blast*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   649
lemma "(\<not> (\<forall>SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   650
          \<not> PUZ114_5_bnd_sK3 SX0 SX1 \<or> PUZ114_5_bnd_sK3 (dud_bnd_s (dud_bnd_s SX0)) SX1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   651
    \<not> (\<forall>SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   652
          \<not> PUZ114_5_bnd_sK3 SX0 SX1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   653
          PUZ114_5_bnd_sK3 (dud_bnd_s SX0) (dud_bnd_s SX1))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   654
   False \<Longrightarrow> (\<not> (\<forall>SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   655
          \<not> PUZ114_5_bnd_sK3 SX0 SX1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   656
          PUZ114_5_bnd_sK3 (dud_bnd_s SX0) (dud_bnd_s SX1))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   657
   False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   658
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   659
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   660
(*testing logical expansion -- this should be done by blast*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   661
lemma "(\<forall>A B. bnd_in B (bnd_powerset A) \<longrightarrow> SEU581_2_bnd_subset B A) = True
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   662
\<Longrightarrow> (\<forall>A B. \<not> bnd_in B (bnd_powerset A) \<or> SEU581_2_bnd_subset B A) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   663
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   664
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   665
(*testing related to PUZ114^5.p.out*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   666
lemma "\<forall>SV1. ((\<not> (\<not> SV1 (PUZ114_5_bnd_sK4 SV1) (PUZ114_5_bnd_sK5 SV1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   667
                    \<not> (\<not> SV1 (bnd_s (bnd_s (PUZ114_5_bnd_sK4 SV1)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   668
                          (PUZ114_5_bnd_sK5 SV1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   669
                       \<not> SV1 (bnd_s (PUZ114_5_bnd_sK4 SV1))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   670
                          (bnd_s (PUZ114_5_bnd_sK5 SV1))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   671
                True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   672
                (\<not> SV1 bnd_c1 bnd_c1) = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   673
               SV1 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2 = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   674
         \<forall>SV1. (SV1 bnd_c1 bnd_c1 = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   675
                (\<not> (\<not> SV1 (PUZ114_5_bnd_sK4 SV1) (PUZ114_5_bnd_sK5 SV1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   676
                    \<not> (\<not> SV1 (bnd_s (bnd_s (PUZ114_5_bnd_sK4 SV1)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   677
                          (PUZ114_5_bnd_sK5 SV1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   678
                       \<not> SV1 (bnd_s (PUZ114_5_bnd_sK4 SV1))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   679
                          (bnd_s (PUZ114_5_bnd_sK5 SV1))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   680
                True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   681
               SV1 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2 = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   682
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   683
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   684
lemma "\<forall>SV2. (\<forall>SY41.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   685
                   \<not> PUZ114_5_bnd_sK3 SV2 SY41 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   686
                   PUZ114_5_bnd_sK3 (dud_bnd_s (dud_bnd_s SV2)) SY41) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   687
               True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   688
         \<forall>SV4 SV2.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   689
            (\<not> PUZ114_5_bnd_sK3 SV2 SV4 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   690
             PUZ114_5_bnd_sK3 (dud_bnd_s (dud_bnd_s SV2)) SV4) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   691
            True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   692
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   693
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   694
lemma "\<forall>SV3. (\<forall>SY42.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   695
                   \<not> PUZ114_5_bnd_sK3 SV3 SY42 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   696
                   PUZ114_5_bnd_sK3 (dud_bnd_s SV3) (dud_bnd_s SY42)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   697
               True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   698
         \<forall>SV5 SV3.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   699
            (\<not> PUZ114_5_bnd_sK3 SV3 SV5 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   700
             PUZ114_5_bnd_sK3 (dud_bnd_s SV3) (dud_bnd_s SV5)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   701
            True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   702
by (tactic {*full_extcnf_combined_tac @{context}*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   703
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   704
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   705
subsection "unfold_def"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   706
     (* (Annotated_step ("9", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   707
lemma "bnd_kpairiskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   708
             (ALL Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   709
                 bnd_iskpair
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   710
                  (bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   711
                    (bnd_setadjoin (bnd_setadjoin Xx (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   712
                      bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   713
             bnd_kpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   714
             (%Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   715
                 bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   716
                  (bnd_setadjoin (bnd_setadjoin Xx (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   717
                    bnd_emptyset)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   718
             bnd_iskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   719
             (%A. EX Xx. bnd_in Xx (bnd_setunion A) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   720
                         (EX Xy. bnd_in Xy (bnd_setunion A) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   721
                                 A = bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   722
                                      (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   723
                                        (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   724
(bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   725
                                        bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   726
             (~ (ALL SY0 SY1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   727
                    EX SY3.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   728
                       bnd_in SY3
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   729
                        (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   730
                          (bnd_setadjoin (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   731
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   732
                              (bnd_setadjoin SY0 (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   733
                              bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   734
                       (EX SY4.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   735
                           bnd_in SY4
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   736
                            (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   737
                              (bnd_setadjoin (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   738
                                (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   739
                                  (bnd_setadjoin SY0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   740
                                    (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   741
                                  bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   742
                           bnd_setadjoin (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   743
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   744
                              (bnd_setadjoin SY0 (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   745
                              bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   746
                           bnd_setadjoin (bnd_setadjoin SY3 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   747
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   748
                              (bnd_setadjoin SY3 (bnd_setadjoin SY4 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   749
                              bnd_emptyset)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   750
             True
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   751
             ==> (~ (ALL SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   752
                        ~ (ALL SX2.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   753
                              ~ ~ (~ bnd_in SX2
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   754
                                      (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   755
                                        (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   756
(bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   757
(bnd_setadjoin (bnd_setadjoin SX0 (bnd_setadjoin SX1 bnd_emptyset)) bnd_emptyset))) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   758
                                   ~ ~ (ALL SX3.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   759
 ~ ~ (~ bnd_in SX3
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   760
         (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   761
           (bnd_setadjoin (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   762
             (bnd_setadjoin (bnd_setadjoin SX0 (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   763
               bnd_emptyset))) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   764
      bnd_setadjoin (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   765
       (bnd_setadjoin (bnd_setadjoin SX0 (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   766
         bnd_emptyset) ~=
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   767
      bnd_setadjoin (bnd_setadjoin SX2 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   768
       (bnd_setadjoin (bnd_setadjoin SX2 (bnd_setadjoin SX3 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   769
         bnd_emptyset))))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   770
                 True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   771
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   772
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   773
     (* (Annotated_step ("10", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   774
lemma "bnd_kpairiskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   775
             (ALL Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   776
                 bnd_iskpair
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   777
                  (bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   778
                    (bnd_setadjoin (bnd_setadjoin Xx (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   779
                      bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   780
             bnd_kpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   781
             (%Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   782
                 bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   783
                  (bnd_setadjoin (bnd_setadjoin Xx (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   784
                    bnd_emptyset)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   785
             bnd_iskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   786
             (%A. EX Xx. bnd_in Xx (bnd_setunion A) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   787
                         (EX Xy. bnd_in Xy (bnd_setunion A) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   788
                                 A = bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   789
                                      (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   790
                                        (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   791
(bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   792
                                        bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   793
             (ALL SY5 SY6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   794
                 EX SY7.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   795
                    bnd_in SY7
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   796
                     (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   797
                       (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   798
                         (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   799
                           (bnd_setadjoin SY5 (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   800
                           bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   801
                    (EX SY8.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   802
                        bnd_in SY8
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   803
                         (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   804
                           (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   805
                             (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   806
                               (bnd_setadjoin SY5 (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   807
                               bnd_emptyset))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   808
                        bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   809
                         (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   810
                           (bnd_setadjoin SY5 (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   811
                           bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   812
                        bnd_setadjoin (bnd_setadjoin SY7 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   813
                         (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   814
                           (bnd_setadjoin SY7 (bnd_setadjoin SY8 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   815
                           bnd_emptyset))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   816
             True
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   817
             ==> (ALL SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   818
                     ~ (ALL SX2.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   819
                           ~ ~ (~ bnd_in SX2
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   820
                                   (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   821
                                     (bnd_setadjoin (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   822
                                       (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   823
                                         (bnd_setadjoin SX0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   824
 (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   825
                                         bnd_emptyset))) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   826
                                ~ ~ (ALL SX3.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   827
                                        ~ ~ (~ bnd_in SX3
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   828
      (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   829
        (bnd_setadjoin (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   830
          (bnd_setadjoin (bnd_setadjoin SX0 (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   831
            bnd_emptyset))) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   832
   bnd_setadjoin (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   833
    (bnd_setadjoin (bnd_setadjoin SX0 (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   834
      bnd_emptyset) ~=
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   835
   bnd_setadjoin (bnd_setadjoin SX2 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   836
    (bnd_setadjoin (bnd_setadjoin SX2 (bnd_setadjoin SX3 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   837
      bnd_emptyset)))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   838
                 True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   839
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   840
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   841
     (* (Annotated_step ("12", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   842
lemma "bnd_cCKB6_BLACK =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   843
         (\<lambda>Xu Xv.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   844
             \<forall>Xw. Xw bnd_c1 bnd_c1 \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   845
                  (\<forall>Xj Xk.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   846
                      Xw Xj Xk \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   847
                      Xw (bnd_s (bnd_s Xj)) Xk \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   848
                      Xw (bnd_s Xj) (bnd_s Xk)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   849
                  Xw Xu Xv) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   850
         ((((\<forall>SY36 SY37.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   851
                \<not> PUZ114_5_bnd_sK3 SY36 SY37 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   852
                PUZ114_5_bnd_sK3 (bnd_s (bnd_s SY36)) SY37) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   853
            (\<forall>SY38 SY39.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   854
                \<not> PUZ114_5_bnd_sK3 SY38 SY39 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   855
                PUZ114_5_bnd_sK3 (bnd_s SY38) (bnd_s SY39))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   856
           PUZ114_5_bnd_sK3 bnd_c1 bnd_c1) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   857
          \<not> PUZ114_5_bnd_sK3 (bnd_s (bnd_s (bnd_s PUZ114_5_bnd_sK1)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   858
             (bnd_s PUZ114_5_bnd_sK2)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   859
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   860
         (\<not> (\<not> \<not> (\<not> \<not> (\<not> (\<forall>SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   861
                             \<not> PUZ114_5_bnd_sK3 SX0 SX1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   862
                             PUZ114_5_bnd_sK3 (bnd_s (bnd_s SX0)) SX1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   863
                       \<not> (\<forall>SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   864
                             \<not> PUZ114_5_bnd_sK3 SX0 SX1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   865
                             PUZ114_5_bnd_sK3 (bnd_s SX0) (bnd_s SX1))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   866
                  \<not> PUZ114_5_bnd_sK3 bnd_c1 bnd_c1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   867
             \<not> \<not> PUZ114_5_bnd_sK3 (bnd_s (bnd_s (bnd_s PUZ114_5_bnd_sK1)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   868
                  (bnd_s PUZ114_5_bnd_sK2))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   869
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   870
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   871
apply (erule conjE)+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   872
apply (erule subst)+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   873
apply (tactic {*log_expander 1*})+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   874
apply (rule refl)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   875
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   876
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   877
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   878
     (* (Annotated_step ("13", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   879
lemma "bnd_cCKB6_BLACK =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   880
         (\<lambda>Xu Xv.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   881
             \<forall>Xw. Xw bnd_c1 bnd_c1 \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   882
                  (\<forall>Xj Xk.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   883
                      Xw Xj Xk \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   884
                      Xw (bnd_s (bnd_s Xj)) Xk \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   885
                      Xw (bnd_s Xj) (bnd_s Xk)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   886
                  Xw Xu Xv) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   887
         (\<forall>SY30.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   888
             (SY30 (PUZ114_5_bnd_sK4 SY30) (PUZ114_5_bnd_sK5 SY30) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   889
              (\<not> SY30 (bnd_s (bnd_s (PUZ114_5_bnd_sK4 SY30)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   890
                  (PUZ114_5_bnd_sK5 SY30) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   891
               \<not> SY30 (bnd_s (PUZ114_5_bnd_sK4 SY30))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   892
                  (bnd_s (PUZ114_5_bnd_sK5 SY30))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   893
              \<not> SY30 bnd_c1 bnd_c1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   894
             SY30 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   895
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   896
         (\<forall>SX0. (\<not> (\<not> SX0 (PUZ114_5_bnd_sK4 SX0) (PUZ114_5_bnd_sK5 SX0) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   897
                    \<not> (\<not> SX0 (bnd_s (bnd_s (PUZ114_5_bnd_sK4 SX0)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   898
                          (PUZ114_5_bnd_sK5 SX0) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   899
                       \<not> SX0 (bnd_s (PUZ114_5_bnd_sK4 SX0))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   900
                          (bnd_s (PUZ114_5_bnd_sK5 SX0)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   901
                 \<not> SX0 bnd_c1 bnd_c1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   902
                SX0 PUZ114_5_bnd_sK1 PUZ114_5_bnd_sK2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   903
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   904
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   905
apply (erule conjE)+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   906
apply (tactic {*expander_animal 1*})+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   907
apply assumption
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   908
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   909
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   910
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   911
(*FIXME move this heuristic elsewhere*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   912
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   913
(*Other than the list (which must not be empty) this function
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   914
  expects a parameter indicating the smallest integer.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   915
  (Using Int.minInt isn't always viable).*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   916
fun max_int_floored min l =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   917
  if null l then raise List.Empty
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   918
  else fold (curry Int.max) l min;
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   919
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   920
val _ = @{assert} (max_int_floored ~101002 [1]  = 1)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   921
val _ = @{assert} (max_int_floored 0 [1, 3, 5] = 5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   922
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   923
fun max_index_floored min l =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   924
  let
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   925
    val max = max_int_floored min l
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   926
  in find_index (pair max #> op =) l end
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   927
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   928
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   929
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   930
max_index_floored 0 [1, 3, 5]
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   931
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   932
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   933
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   934
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   935
Given argument ([h_1, ..., h_n], conc),
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   936
obtained from term of form
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   937
  h_1 ==> ... ==> h_n ==> conclusion,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   938
this function indicates which h_i is biggest,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   939
or NONE if h_n = 0.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   940
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   941
fun biggest_hypothesis (hypos, _) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   942
  if null hypos then NONE
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   943
  else
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   944
    map size_of_term hypos
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   945
    |> max_index_floored 0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   946
    |> SOME
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   947
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   948
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   949
ML {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   950
fun biggest_hyp_first_tac i = fn st =>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   951
  let
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   952
    val results = TERMFUN biggest_hypothesis (SOME i) st
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   953
val _ = tracing ("result=" ^ PolyML.makestring results)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   954
  in
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   955
    if null results then no_tac st
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   956
    else
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   957
      let
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   958
        val result = the_single results
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   959
      in
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   960
        case result of
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   961
            NONE => no_tac st
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   962
          | SOME n =>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   963
              if n > 0 then rotate_tac n i st else no_tac st
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   964
      end
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   965
  end
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   966
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   967
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   968
     (* (Annotated_step ("6", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   969
lemma  "(\<not> (\<exists>U :: TPTP_Interpret.ind \<Rightarrow> bool. \<forall>V. U V = SEV405_5_bnd_cA)) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   970
         (\<not> \<not> (\<forall>SX0 :: TPTP_Interpret.ind \<Rightarrow> bool. \<not> (\<forall>SX1. \<not> (\<not> (\<not> SX0 SX1 \<or> SEV405_5_bnd_cA) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   971
 \<not> (\<not> SEV405_5_bnd_cA \<or> SX0 SX1))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   972
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   973
(* by (tactic {*unfold_def_tac []*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   974
oops
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   975
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   976
subsection "Using leo2_tac"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   977
(*these require PUZ114^5's proof to be loaded
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   978
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   979
ML {*leo2_tac @{context} (hd prob_names) "50"*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   980
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   981
ML {*leo2_tac @{context} (hd prob_names) "4"*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   982
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   983
ML {*leo2_tac @{context} (hd prob_names) "9"*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   984
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   985
     (* (Annotated_step ("9", "extcnf_combined"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   986
lemma "(\<forall>SY30.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   987
             SY30 bnd_c1 bnd_c1 \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   988
             (\<forall>Xj Xk.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   989
                 SY30 Xj Xk \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   990
                 SY30 (bnd_s (bnd_s Xj)) Xk \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   991
                 SY30 (bnd_s Xj) (bnd_s Xk)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   992
             SY30 bnd_sK1 bnd_sK2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   993
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   994
         (\<forall>SY30.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   995
             (SY30 (bnd_sK4 SY30) (bnd_sK5 SY30) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   996
              (\<not> SY30 (bnd_s (bnd_s (bnd_sK4 SY30)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   997
                  (bnd_sK5 SY30) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   998
               \<not> SY30 (bnd_s (bnd_sK4 SY30))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
   999
                  (bnd_s (bnd_sK5 SY30))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1000
              \<not> SY30 bnd_c1 bnd_c1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1001
             SY30 bnd_sK1 bnd_sK2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1002
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1003
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "9") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1004
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1005
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1006
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1007
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1008
typedecl GEG007_1_bnd_reg
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1009
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1010
  GEG007_1_bnd_sK7_SX2 :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> GEG007_1_bnd_reg"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1011
  GEG007_1_bnd_sK6_SX2 :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> GEG007_1_bnd_reg"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1012
  GEG007_1_bnd_a :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1013
  GEG007_1_bnd_catalunya  :: "GEG007_1_bnd_reg"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1014
  GEG007_1_bnd_spain :: "GEG007_1_bnd_reg"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1015
  GEG007_1_bnd_c :: "GEG007_1_bnd_reg \<Rightarrow> GEG007_1_bnd_reg \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1016
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1017
     (* (Annotated_step ("147", "extcnf_forall_neg"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1018
lemma "\<forall>SV13 SV6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1019
            (\<forall>SX2. \<not> GEG007_1_bnd_c SX2 GEG007_1_bnd_spain \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1020
                   GEG007_1_bnd_c SX2 GEG007_1_bnd_catalunya) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1021
            False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1022
            GEG007_1_bnd_a SV6 SV13 = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1023
         \<forall>SV6 SV13.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1024
            (\<not> GEG007_1_bnd_c (GEG007_1_bnd_sK7_SX2 SV13 SV6) GEG007_1_bnd_spain \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1025
             GEG007_1_bnd_c (GEG007_1_bnd_sK7_SX2 SV13 SV6) GEG007_1_bnd_catalunya) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1026
            False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1027
            GEG007_1_bnd_a SV6 SV13 = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1028
by (tactic {*nonfull_extcnf_combined_tac @{context} [Existential_Var]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1029
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1030
     (* (Annotated_step ("116", "extcnf_forall_neg"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1031
lemma "\<forall>SV13 SV6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1032
            (\<forall>SX2. \<not> \<not> (\<not> \<not> (\<not> GEG007_1_bnd_c SX2 GEG007_1_bnd_catalunya \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1033
                             \<not> \<not> \<not> (\<forall>SX3.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1034
       \<not> \<not> (\<not> (\<forall>SX4. \<not> GEG007_1_bnd_c SX4 SX3 \<or> GEG007_1_bnd_c SX4 SX2) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1035
            \<not> (\<forall>SX4. \<not> GEG007_1_bnd_c SX4 SX3 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1036
                     GEG007_1_bnd_c SX4 GEG007_1_bnd_catalunya)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1037
                        \<not> \<not> (\<not> GEG007_1_bnd_c SX2 GEG007_1_bnd_spain \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1038
                             \<not> \<not> \<not> (\<forall>SX3.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1039
       \<not> \<not> (\<not> (\<forall>SX4. \<not> GEG007_1_bnd_c SX4 SX3 \<or> GEG007_1_bnd_c SX4 SX2) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1040
            \<not> (\<forall>SX4. \<not> GEG007_1_bnd_c SX4 SX3 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1041
                     GEG007_1_bnd_c SX4 GEG007_1_bnd_spain)))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1042
            False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1043
            GEG007_1_bnd_a SV6 SV13 = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1044
         \<forall>SV6 SV13.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1045
            (\<not> \<not> (\<not> \<not> (\<not> GEG007_1_bnd_c (GEG007_1_bnd_sK6_SX2 SV13 SV6)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1046
                          GEG007_1_bnd_catalunya \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1047
                       \<not> \<not> \<not> (\<forall>SY68.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1048
 \<not> \<not> (\<not> (\<forall>SY69.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1049
            \<not> GEG007_1_bnd_c SY69 SY68 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1050
            GEG007_1_bnd_c SY69 (GEG007_1_bnd_sK6_SX2 SV13 SV6)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1051
      \<not> (\<forall>SX4. \<not> GEG007_1_bnd_c SX4 SY68 \<or> GEG007_1_bnd_c SX4 GEG007_1_bnd_catalunya)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1052
                  \<not> \<not> (\<not> GEG007_1_bnd_c (GEG007_1_bnd_sK6_SX2 SV13 SV6)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1053
                          GEG007_1_bnd_spain \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1054
                       \<not> \<not> \<not> (\<forall>SY71.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1055
 \<not> \<not> (\<not> (\<forall>SY72.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1056
            \<not> GEG007_1_bnd_c SY72 SY71 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1057
            GEG007_1_bnd_c SY72 (GEG007_1_bnd_sK6_SX2 SV13 SV6)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1058
      \<not> (\<forall>SX4. \<not> GEG007_1_bnd_c SX4 SY71 \<or> GEG007_1_bnd_c SX4 GEG007_1_bnd_spain)))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1059
            False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1060
            GEG007_1_bnd_a SV6 SV13 = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1061
by (tactic {*nonfull_extcnf_combined_tac @{context} [Existential_Var]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1062
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1063
consts PUZ107_5_bnd_sK1_SX0 ::
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1064
  "TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1065
      \<Rightarrow> TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1066
        \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1067
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1068
lemma "\<forall>(SV4\<Colon>TPTP_Interpret.ind) (SV8\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1069
   (SV6\<Colon>TPTP_Interpret.ind) (SV2\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1070
   (SV3\<Colon>TPTP_Interpret.ind) SV1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1071
   ((SV1 \<noteq> SV3) = False \<or> PUZ107_5_bnd_sK1_SX0 SV1 SV2 SV6 SV8 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1072
   PUZ107_5_bnd_sK1_SX0 SV3 SV4 SV6 SV8 = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1073
\<forall>(SV4\<Colon>TPTP_Interpret.ind) (SV8\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1074
   (SV6\<Colon>TPTP_Interpret.ind) (SV2\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1075
   (SV3\<Colon>TPTP_Interpret.ind) SV1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1076
   ((SV1 = SV3) = True \<or> PUZ107_5_bnd_sK1_SX0 SV1 SV2 SV6 SV8 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1077
   PUZ107_5_bnd_sK1_SX0 SV3 SV4 SV6 SV8 = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1078
by (tactic {*nonfull_extcnf_combined_tac @{context} [Not_neg]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1079
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1080
lemma "
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1081
\<forall>(SV8\<Colon>TPTP_Interpret.ind) (SV6\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1082
   (SV4\<Colon>TPTP_Interpret.ind) (SV2\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1083
   (SV3\<Colon>TPTP_Interpret.ind) SV1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1084
   ((SV1 \<noteq> SV3 \<or> SV2 \<noteq> SV4) = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1085
    PUZ107_5_bnd_sK1_SX0 SV1 SV2 SV6 SV8 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1086
   PUZ107_5_bnd_sK1_SX0 SV3 SV4 SV6 SV8 = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1087
\<forall>(SV4\<Colon>TPTP_Interpret.ind) (SV8\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1088
   (SV6\<Colon>TPTP_Interpret.ind) (SV2\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1089
   (SV3\<Colon>TPTP_Interpret.ind) SV1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1090
   ((SV1 \<noteq> SV3) = False \<or> PUZ107_5_bnd_sK1_SX0 SV1 SV2 SV6 SV8 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1091
   PUZ107_5_bnd_sK1_SX0 SV3 SV4 SV6 SV8 = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1092
by (tactic {*nonfull_extcnf_combined_tac @{context} [Or_neg]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1093
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1094
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1095
  NUM016_5_bnd_a :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1096
  NUM016_5_bnd_prime :: "TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1097
  NUM016_5_bnd_factorial_plus_one :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1098
  NUM016_5_bnd_prime_divisor :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1099
  NUM016_5_bnd_divides :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1100
  NUM016_5_bnd_less :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1101
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1102
     (* (Annotated_step ("6", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1103
lemma "((((((((((((\<forall>X\<Colon>TPTP_Interpret.ind. \<not> NUM016_5_bnd_less X X) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1104
                    (\<forall>(X\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1105
                        Y\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1106
                        \<not> NUM016_5_bnd_less X Y \<or> \<not> NUM016_5_bnd_less Y X)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1107
                   (\<forall>X\<Colon>TPTP_Interpret.ind. NUM016_5_bnd_divides X X)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1108
                  (\<forall>(X\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1109
                      (Y\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1110
                      Z\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1111
                      (\<not> NUM016_5_bnd_divides X Y \<or> \<not> NUM016_5_bnd_divides Y Z) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1112
                      NUM016_5_bnd_divides X Z)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1113
                 (\<forall>(X\<Colon>TPTP_Interpret.ind) Y\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1114
                     \<not> NUM016_5_bnd_divides X Y \<or> \<not> NUM016_5_bnd_less Y X)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1115
                (\<forall>X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1116
                    NUM016_5_bnd_less X (NUM016_5_bnd_factorial_plus_one X))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1117
               (\<forall>(X\<Colon>TPTP_Interpret.ind) Y\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1118
                   \<not> NUM016_5_bnd_divides X (NUM016_5_bnd_factorial_plus_one Y) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1119
                   NUM016_5_bnd_less Y X)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1120
              (\<forall>X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1121
                  NUM016_5_bnd_prime X \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1122
                  NUM016_5_bnd_divides (NUM016_5_bnd_prime_divisor X) X)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1123
             (\<forall>X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1124
                 NUM016_5_bnd_prime X \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1125
                 NUM016_5_bnd_prime (NUM016_5_bnd_prime_divisor X))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1126
            (\<forall>X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1127
                NUM016_5_bnd_prime X \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1128
                NUM016_5_bnd_less (NUM016_5_bnd_prime_divisor X) X)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1129
           NUM016_5_bnd_prime NUM016_5_bnd_a) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1130
          (\<forall>X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1131
              (\<not> NUM016_5_bnd_prime X \<or> \<not> NUM016_5_bnd_less NUM016_5_bnd_a X) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1132
              NUM016_5_bnd_less (NUM016_5_bnd_factorial_plus_one NUM016_5_bnd_a) X)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1133
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1134
         (\<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> \<not> (\<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1135
     \<not> NUM016_5_bnd_less SX0 SX0) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1136
                               \<not> (\<forall>(SX0\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1137
     SX1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1138
     \<not> NUM016_5_bnd_less SX0 SX1 \<or> \<not> NUM016_5_bnd_less SX1 SX0)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1139
                          \<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1140
NUM016_5_bnd_divides SX0 SX0)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1141
                     \<not> (\<forall>(SX0\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1142
                           (SX1\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1143
                           SX2\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1144
                           (\<not> NUM016_5_bnd_divides SX0 SX1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1145
                            \<not> NUM016_5_bnd_divides SX1 SX2) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1146
                           NUM016_5_bnd_divides SX0 SX2)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1147
                \<not> (\<forall>(SX0\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1148
                      SX1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1149
                      \<not> NUM016_5_bnd_divides SX0 SX1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1150
                      \<not> NUM016_5_bnd_less SX1 SX0)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1151
           \<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1152
                 NUM016_5_bnd_less SX0 (NUM016_5_bnd_factorial_plus_one SX0))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1153
      \<not> (\<forall>(SX0\<Colon>TPTP_Interpret.ind) SX1\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1154
            \<not> NUM016_5_bnd_divides SX0 (NUM016_5_bnd_factorial_plus_one SX1) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1155
            NUM016_5_bnd_less SX1 SX0)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1156
 \<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1157
       NUM016_5_bnd_prime SX0 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1158
       NUM016_5_bnd_divides (NUM016_5_bnd_prime_divisor SX0) SX0)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1159
                            \<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1160
  NUM016_5_bnd_prime SX0 \<or> NUM016_5_bnd_prime (NUM016_5_bnd_prime_divisor SX0))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1161
                       \<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1162
                             NUM016_5_bnd_prime SX0 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1163
                             NUM016_5_bnd_less (NUM016_5_bnd_prime_divisor SX0)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1164
                              SX0)) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1165
                  \<not> NUM016_5_bnd_prime NUM016_5_bnd_a) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1166
             \<not> (\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1167
                   (\<not> NUM016_5_bnd_prime SX0 \<or> \<not> NUM016_5_bnd_less NUM016_5_bnd_a SX0) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1168
                   NUM016_5_bnd_less (NUM016_5_bnd_factorial_plus_one NUM016_5_bnd_a)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1169
                    SX0))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1170
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1171
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1172
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1173
     (* (Annotated_step ("3", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1174
lemma "(~ ((((((((((((ALL X. ~ bnd_less X X) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1175
                           (ALL X Y. ~ bnd_less X Y | ~ bnd_less Y X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1176
                          (ALL X. bnd_divides X X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1177
                         (ALL X Y Z.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1178
                             (~ bnd_divides X Y | ~ bnd_divides Y Z) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1179
                             bnd_divides X Z)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1180
                        (ALL X Y. ~ bnd_divides X Y | ~ bnd_less Y X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1181
                       (ALL X. bnd_less X (bnd_factorial_plus_one X))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1182
                      (ALL X Y.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1183
                          ~ bnd_divides X (bnd_factorial_plus_one Y) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1184
                          bnd_less Y X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1185
                     (ALL X. bnd_prime X | bnd_divides (bnd_prime_divisor X) X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1186
                    (ALL X. bnd_prime X | bnd_prime (bnd_prime_divisor X))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1187
                   (ALL X. bnd_prime X | bnd_less (bnd_prime_divisor X) X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1188
                  bnd_prime bnd_a) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1189
                 (ALL X. (~ bnd_prime X | ~ bnd_less bnd_a X) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1190
                         bnd_less (bnd_factorial_plus_one bnd_a) X))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1191
             False
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1192
             ==> (~ ((((((((((((ALL X. ~ bnd_less X X) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1193
                               (ALL X Y. ~ bnd_less X Y | ~ bnd_less Y X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1194
                              (ALL X. bnd_divides X X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1195
                             (ALL X Y Z.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1196
                                 (~ bnd_divides X Y | ~ bnd_divides Y Z) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1197
                                 bnd_divides X Z)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1198
                            (ALL X Y. ~ bnd_divides X Y | ~ bnd_less Y X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1199
                           (ALL X. bnd_less X (bnd_factorial_plus_one X))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1200
                          (ALL X Y.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1201
                              ~ bnd_divides X (bnd_factorial_plus_one Y) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1202
                              bnd_less Y X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1203
                         (ALL X. bnd_prime X |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1204
                                 bnd_divides (bnd_prime_divisor X) X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1205
                        (ALL X. bnd_prime X | bnd_prime (bnd_prime_divisor X))) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1206
                       (ALL X. bnd_prime X | bnd_less (bnd_prime_divisor X) X)) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1207
                      bnd_prime bnd_a) &
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1208
                     (ALL X. (~ bnd_prime X | ~ bnd_less bnd_a X) |
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1209
                             bnd_less (bnd_factorial_plus_one bnd_a) X))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1210
                 False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1211
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1212
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1213
(* SET062^6.p.out
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1214
      [[(Annotated_step ("3", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1215
lemma "(\<forall>Z3. False \<longrightarrow> bnd_cA Z3) = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1216
         (\<forall>Z3. False \<longrightarrow> bnd_cA Z3) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1217
by (tactic {*unfold_def_tac @{context} []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1218
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1219
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1220
(* SEU559^2.p.out *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1221
   (* [[(Annotated_step ("3", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1222
lemma "bnd_subset = (\<lambda>A B. \<forall>Xx. bnd_in Xx A \<longrightarrow> bnd_in Xx B) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1223
         (\<forall>A B. (\<forall>Xx. bnd_in Xx A \<longrightarrow> bnd_in Xx B) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1224
                bnd_subset A B) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1225
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1226
         (\<forall>SY0 SY1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1227
             (\<forall>Xx. bnd_in Xx SY0 \<longrightarrow> bnd_in Xx SY1) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1228
             (\<forall>SY5. bnd_in SY5 SY0 \<longrightarrow> bnd_in SY5 SY1)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1229
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1230
by (tactic {*unfold_def_tac [@{thm bnd_subset_def}]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1231
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1232
(* SEU559^2.p.out
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1233
    [[(Annotated_step ("6", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1234
lemma "(\<not> (\<exists>Xx. \<forall>Xy. Xx \<longrightarrow> Xy)) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1235
         (\<not> \<not> (\<forall>SX0. \<not> (\<forall>SX1. \<not> SX0 \<or> SX1))) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1236
by (tactic {*unfold_def_tac []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1237
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1238
(* SEU502^2.p.out
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1239
    [[(Annotated_step ("3", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1240
lemma "bnd_emptysetE =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1241
         (\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1242
         (bnd_emptysetE \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1243
          (\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> False)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1244
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1245
         ((\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1246
          (\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> False)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1247
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1248
by (tactic {*unfold_def_tac [@{thm bnd_emptysetE_def}]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1249
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1250
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1251
typedecl AGT037_2_bnd_mu
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1252
consts
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1253
  AGT037_2_bnd_sK1_SX0 :: TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1254
  AGT037_2_bnd_cola :: AGT037_2_bnd_mu
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1255
  AGT037_2_bnd_jan :: AGT037_2_bnd_mu
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1256
  AGT037_2_bnd_possibly_likes :: "AGT037_2_bnd_mu \<Rightarrow> AGT037_2_bnd_mu \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1257
  AGT037_2_bnd_sK5_SY68 ::
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1258
    "TPTP_Interpret.ind
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1259
     \<Rightarrow> AGT037_2_bnd_mu
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1260
       \<Rightarrow> AGT037_2_bnd_mu
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1261
         \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1262
  AGT037_2_bnd_likes :: "AGT037_2_bnd_mu \<Rightarrow> AGT037_2_bnd_mu \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1263
  AGT037_2_bnd_very_much_likes :: "AGT037_2_bnd_mu \<Rightarrow> AGT037_2_bnd_mu \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1264
  AGT037_2_bnd_a1 :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1265
  AGT037_2_bnd_a2 :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1266
  AGT037_2_bnd_a3 :: "TPTP_Interpret.ind \<Rightarrow> TPTP_Interpret.ind \<Rightarrow> bool"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1267
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1268
(*test that nullary skolem terms are OK*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1269
     (* (Annotated_step ("79", "extcnf_forall_neg"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1270
lemma "(\<forall>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1271
             AGT037_2_bnd_possibly_likes AGT037_2_bnd_jan AGT037_2_bnd_cola SX0) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1272
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1273
         AGT037_2_bnd_possibly_likes AGT037_2_bnd_jan AGT037_2_bnd_cola AGT037_2_bnd_sK1_SX0 =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1274
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1275
by (tactic {*nonfull_extcnf_combined_tac @{context} [Existential_Var]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1276
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1277
     (* (Annotated_step ("202", "extcnf_forall_neg"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1278
lemma "\<forall>(SV13\<Colon>TPTP_Interpret.ind) (SV39\<Colon>AGT037_2_bnd_mu) (SV29\<Colon>AGT037_2_bnd_mu)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1279
            SV45\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1280
            ((((\<forall>SY68\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1281
                   \<not> AGT037_2_bnd_a1 SV45 SY68 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1282
                   AGT037_2_bnd_likes SV29 SV39 SY68) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1283
               False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1284
               (\<not> (\<forall>SY69\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1285
                      \<not> AGT037_2_bnd_a2 SV45 SY69 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1286
                      AGT037_2_bnd_likes SV29 SV39 SY69)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1287
               True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1288
              AGT037_2_bnd_likes SV29 SV39 SV45 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1289
             AGT037_2_bnd_very_much_likes SV29 SV39 SV45 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1290
            AGT037_2_bnd_a3 SV13 SV45 = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1291
         \<forall>(SV29\<Colon>AGT037_2_bnd_mu) (SV39\<Colon>AGT037_2_bnd_mu) (SV13\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1292
            SV45\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1293
            ((((\<not> AGT037_2_bnd_a1 SV45
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1294
                   (AGT037_2_bnd_sK5_SY68 SV13 SV39 SV29 SV45) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1295
                AGT037_2_bnd_likes SV29 SV39
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1296
                 (AGT037_2_bnd_sK5_SY68 SV13 SV39 SV29 SV45)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1297
               False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1298
               (\<not> (\<forall>SY69\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1299
                      \<not> AGT037_2_bnd_a2 SV45 SY69 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1300
                      AGT037_2_bnd_likes SV29 SV39 SY69)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1301
               True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1302
              AGT037_2_bnd_likes SV29 SV39 SV45 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1303
             AGT037_2_bnd_very_much_likes SV29 SV39 SV45 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1304
            AGT037_2_bnd_a3 SV13 SV45 = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1305
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1306
apply (rule allI)+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1307
apply (erule_tac x = "SV13" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1308
apply (erule_tac x = "SV39" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1309
apply (erule_tac x = "SV29" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1310
apply (erule_tac x = "SV45" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1311
apply (erule disjE)+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1312
defer
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1313
apply (tactic {*clause_breaker 1*})+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1314
apply (drule_tac sk = "bnd_sK5_SY68 SV13 SV39 SV29 SV45" in leo2_skolemise)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1315
defer
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1316
apply (tactic {*clause_breaker 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1317
apply (tactic {*nonfull_extcnf_combined_tac []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1318
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1319
by (tactic {*nonfull_extcnf_combined_tac @{context} [Existential_Var]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1320
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1321
(*(*NUM667^1*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1322
lemma "\<forall>SV12 SV13 SV14 SV9 SV10 SV11.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1323
   ((((bnd_less SV12 SV13 = bnd_less SV11 SV10) = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1324
      (SV14 = SV13) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1325
     bnd_less SV12 SV14 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1326
    bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1327
   (SV9 = SV11) = False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1328
\<forall>SV9 SV14 SV10 SV11 SV13 SV12.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1329
   ((((bnd_less SV12 SV13 = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1330
       bnd_less SV11 SV10 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1331
      (SV14 = SV13) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1332
     bnd_less SV12 SV14 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1333
    bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1334
   (SV9 = SV11) = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1335
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1336
apply (tactic {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1337
  extcnf_combined_tac NONE
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1338
   [ConstsDiff,
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1339
    StripQuantifiers]
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1340
   []*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1341
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1342
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1343
apply (rule allI)+
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1344
apply (erule_tac x = "SV12" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1345
apply (erule_tac x = "SV13" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1346
apply (erule_tac x = "SV14" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1347
apply (erule_tac x = "SV9" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1348
apply (erule_tac x = "SV10" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1349
apply (erule_tac x = "SV11" in allE)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1350
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1351
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "300") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1352
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1353
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1354
(*NUM667^1 node 302 -- dec*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1355
lemma "\<forall>SV12 SV13 SV14 SV9 SV10 SV11.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1356
       ((((bnd_less SV12 SV13 = bnd_less SV11 SV10) = False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1357
          (SV14 = SV13) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1358
         bnd_less SV12 SV14 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1359
        bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1360
       (SV9 = SV11) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1361
       False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1362
       \<forall>SV9 SV14 SV10 SV13 SV11 SV12.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1363
       (((((SV12 = SV11) = False \<or> (SV13 = SV10) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1364
          (SV14 = SV13) = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1365
         bnd_less SV12 SV14 = False) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1366
        bnd_less SV9 SV10 = True) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1367
       (SV9 = SV11) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1368
       False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1369
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "302") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1370
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1371
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1372
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1373
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1374
(*CSR122^2*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1375
     (* (Annotated_step ("23", "extuni_bool2"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1376
lemma "(bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1377
           (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1378
           (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1379
                  bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1380
               \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1381
                  bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1382
          bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1383
           bnd_lBill_THFTYPE_i) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1384
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1385
         bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1386
          (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1387
          (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1388
                 bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1389
              \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1390
                 bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1391
         True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1392
         bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1393
          bnd_lBill_THFTYPE_i =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1394
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1395
(* apply (erule extuni_bool2) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1396
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1397
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "23") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1398
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1399
     (* (Annotated_step ("24", "extuni_bool1"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1400
lemma "(bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1401
           (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1402
           (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1403
                  bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1404
               \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1405
                  bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1406
          bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1407
           bnd_lBill_THFTYPE_i) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1408
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1409
         bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1410
          (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1411
          (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1412
                 bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1413
              \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1414
                 bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1415
         False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1416
         bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1417
          bnd_lBill_THFTYPE_i =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1418
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1419
(* apply (erule extuni_bool1) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1420
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1421
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "24") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1422
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1423
     (* (Annotated_step ("25", "extuni_bool2"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1424
lemma "(bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1425
           (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1426
           (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1427
                  bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1428
               \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1429
                  bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1430
          bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1431
           bnd_lBill_THFTYPE_i) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1432
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1433
         bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1434
          (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1435
          (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1436
                 bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1437
              \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1438
                 bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1439
         True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1440
         bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1441
          bnd_lBill_THFTYPE_i =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1442
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1443
(* apply (erule extuni_bool2) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1444
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1445
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "25") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1446
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1447
     (* (Annotated_step ("26", "extuni_bool1"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1448
lemma "\<forall>SV2. (bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1449
                 (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1450
                 (\<not> (\<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1451
                        bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1452
                        bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1453
                     \<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1454
                        bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1455
                        bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1456
                bnd_holdsDuring_THFTYPE_IiooI SV2 True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1457
               False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1458
         \<forall>SV2. bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1459
                (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1460
                (\<not> (\<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1461
                       bnd_lMary_THFTYPE_i bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1462
                    \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1463
                       bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1464
               False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1465
               bnd_holdsDuring_THFTYPE_IiooI SV2 True = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1466
(* apply (rule allI, erule allE) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1467
(* apply (erule extuni_bool1) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1468
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1469
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "26") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1470
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1471
     (* (Annotated_step ("27", "extuni_bool2"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1472
lemma "\<forall>SV2. (bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1473
                 (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1474
                 (\<not> (\<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1475
                        bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1476
                        bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1477
                     \<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1478
                        bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1479
                        bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1480
                bnd_holdsDuring_THFTYPE_IiooI SV2 True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1481
               False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1482
         \<forall>SV2. bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1483
                (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1484
                (\<not> (\<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1485
                       bnd_lMary_THFTYPE_i bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1486
                    \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1487
                       bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1488
               True \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1489
               bnd_holdsDuring_THFTYPE_IiooI SV2 True = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1490
(* apply (rule allI, erule allE) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1491
(* apply (erule extuni_bool2) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1492
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1493
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "27") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1494
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1495
     (* (Annotated_step ("30", "extuni_bool1"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1496
lemma "((\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1497
                 bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1498
              \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1499
                 bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1500
          True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1501
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1502
         (\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1503
                bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1504
             \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1505
                bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1506
         False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1507
         True = False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1508
(* apply (erule extuni_bool1) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1509
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1510
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "30") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1511
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1512
     (* (Annotated_step ("29", "extuni_bind"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1513
lemma "(bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1514
          bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1515
         False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1516
         ((\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1517
                 bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1518
              \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1519
                 bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1520
          True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1521
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1522
         ((\<not> (\<not> bnd_likes_THFTYPE_IiioI bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1523
                 bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1524
              \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1525
                 bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1526
          True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1527
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1528
(* apply (tactic {*break_hypotheses 1*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1529
(* apply (erule extuni_bind) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1530
(* apply (tactic {*clause_breaker 1*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1531
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1532
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "29") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1533
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1534
     (* (Annotated_step ("28", "extuni_dec"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1535
lemma "\<forall>SV2. (bnd_holdsDuring_THFTYPE_IiooI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1536
                 (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1537
                 (\<not> (\<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1538
                        bnd_lMary_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1539
                        bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1540
                     \<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1541
                        bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1542
                        bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1543
                bnd_holdsDuring_THFTYPE_IiooI SV2 True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1544
               False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1545
         \<forall>SV2. (bnd_lYearFn_THFTYPE_IiiI bnd_n2009_THFTYPE_i =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1546
                SV2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1547
               False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1548
               ((\<not> (\<not> bnd_likes_THFTYPE_IiioI
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1549
                       bnd_lMary_THFTYPE_i bnd_lBill_THFTYPE_i \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1550
                    \<not> bnd_likes_THFTYPE_IiioI bnd_lSue_THFTYPE_i
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1551
                       bnd_lBill_THFTYPE_i)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1552
                True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1553
               False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1554
(* apply (rule allI) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1555
(* apply (erule_tac x = "SV2" in allE) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1556
(* apply (erule extuni_dec_2) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1557
(* done *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1558
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "28") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1559
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1560
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1561
(* QUA002^1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1562
   (* [[(Annotated_step ("49", "extuni_dec"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1563
lemma "((bnd_sK3_E = bnd_sK1_X1 \<or> bnd_sK3_E = bnd_sK2_X2) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1564
          (bnd_sK3_E = bnd_sK2_X2 \<or> bnd_sK3_E = bnd_sK1_X1)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1565
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1566
         ((bnd_sK3_E = bnd_sK2_X2) = (bnd_sK3_E = bnd_sK2_X2)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1567
         False \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1568
         ((bnd_sK3_E = bnd_sK1_X1) = (bnd_sK3_E = bnd_sK1_X1)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1569
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1570
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "49") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1571
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1572
     (* (Annotated_step ("20", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1573
lemma "(bnd_addition bnd_sK1_X1 bnd_sK2_X2 \<noteq>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1574
          bnd_addition bnd_sK2_X2 bnd_sK1_X1) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1575
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1576
         (bnd_sup
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1577
           (\<lambda>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1578
               SX0 = bnd_sK1_X1 \<or> SX0 = bnd_sK2_X2) \<noteq>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1579
          bnd_sup
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1580
           (\<lambda>SX0\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1581
               SX0 = bnd_sK2_X2 \<or> SX0 = bnd_sK1_X1)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1582
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1583
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "20") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1584
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1585
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1586
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1587
(*SEU620^2*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1588
     (* (Annotated_step ("11", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1589
lemma "bnd_kpairiskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1590
         (\<forall>Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1591
             bnd_iskpair
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1592
              (bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1593
                (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1594
                  (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1595
                    (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1596
                  bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1597
         bnd_kpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1598
         (\<lambda>Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1599
             bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1600
              (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1601
                (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1602
                  (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1603
                bnd_emptyset)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1604
         bnd_iskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1605
         (\<lambda>A. \<exists>Xx. bnd_in Xx (bnd_setunion A) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1606
                   (\<exists>Xy. bnd_in Xy (bnd_setunion A) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1607
                         A =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1608
                         bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1609
                          (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1610
                          (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1611
                            (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1612
                              (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1613
                            bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1614
         (\<forall>SY5 SY6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1615
             (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1616
               (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1617
                 (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1618
                   (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1619
                 bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1620
              bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1621
               (bnd_setadjoin (bnd_sK3 SY6 SY5) bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1622
               (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1623
                 (bnd_setadjoin (bnd_sK3 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1624
                   (bnd_setadjoin (bnd_sK4 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1625
                     bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1626
                 bnd_emptyset) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1627
              bnd_in (bnd_sK4 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1628
               (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1629
                 (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1630
                   (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1631
                     (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1632
                       (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1633
                     bnd_emptyset)))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1634
             bnd_in (bnd_sK3 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1635
              (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1636
                (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1637
                  (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1638
                    (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1639
                      (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1640
                    bnd_emptyset)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1641
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1642
         (\<forall>SX0 SX1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1643
             \<not> (\<not> \<not> (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1644
                      (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1645
                      (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1646
                        (bnd_setadjoin SX0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1647
                          (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1648
                        bnd_emptyset) \<noteq>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1649
                     bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1650
                      (bnd_setadjoin (bnd_sK3 SX1 SX0)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1651
                        bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1652
                      (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1653
                        (bnd_setadjoin (bnd_sK3 SX1 SX0)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1654
                          (bnd_setadjoin (bnd_sK4 SX1 SX0)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1655
                            bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1656
                        bnd_emptyset) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1657
                     \<not> bnd_in (bnd_sK4 SX1 SX0)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1658
                        (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1659
                          (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1660
                            (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1661
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1662
                              (bnd_setadjoin SX0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1663
(bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1664
                              bnd_emptyset)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1665
                \<not> bnd_in (bnd_sK3 SX1 SX0)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1666
                   (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1667
                     (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1668
                       (bnd_setadjoin SX0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1669
                       (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1670
                         (bnd_setadjoin SX0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1671
                           (bnd_setadjoin SX1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1672
                         bnd_emptyset))))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1673
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1674
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "11") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1675
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1676
     (* (Annotated_step ("3", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1677
lemma "bnd_kpairiskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1678
         (\<forall>Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1679
             bnd_iskpair
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1680
              (bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1681
                (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1682
                  (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1683
                    (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1684
                  bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1685
         bnd_kpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1686
         (\<lambda>Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1687
             bnd_setadjoin (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1688
              (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1689
                (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1690
                  (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1691
                bnd_emptyset)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1692
         bnd_iskpair =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1693
         (\<lambda>A. \<exists>Xx. bnd_in Xx (bnd_setunion A) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1694
                   (\<exists>Xy. bnd_in Xy (bnd_setunion A) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1695
                         A =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1696
                         bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1697
                          (bnd_setadjoin Xx bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1698
                          (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1699
                            (bnd_setadjoin Xx
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1700
                              (bnd_setadjoin Xy bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1701
                            bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1702
         (bnd_kpairiskpair \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1703
          (\<forall>Xx Xy. bnd_iskpair (bnd_kpair Xx Xy))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1704
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1705
         ((\<forall>SY5 SY6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1706
              \<exists>SY7. bnd_in SY7
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1707
                     (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1708
                       (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1709
                         (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1710
                         (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1711
                           (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1712
                             (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1713
                           bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1714
                    (\<exists>SY8. bnd_in SY8
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1715
                            (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1716
                              (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1717
(bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1718
(bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1719
  (bnd_setadjoin SY5 (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1720
  bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1721
                           bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1722
                            (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1723
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1724
                              (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1725
(bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1726
                              bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1727
                           bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1728
                            (bnd_setadjoin SY7 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1729
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1730
                              (bnd_setadjoin SY7
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1731
(bnd_setadjoin SY8 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1732
                              bnd_emptyset))) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1733
          (\<forall>SY0 SY1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1734
              \<exists>SY3. bnd_in SY3
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1735
                     (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1736
                       (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1737
                         (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1738
                         (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1739
                           (bnd_setadjoin SY0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1740
                             (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1741
                           bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1742
                    (\<exists>SY4. bnd_in SY4
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1743
                            (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1744
                              (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1745
(bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1746
(bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1747
  (bnd_setadjoin SY0 (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1748
  bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1749
                           bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1750
                            (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1751
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1752
                              (bnd_setadjoin SY0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1753
(bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1754
                              bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1755
                           bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1756
                            (bnd_setadjoin SY3 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1757
                            (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1758
                              (bnd_setadjoin SY3
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1759
(bnd_setadjoin SY4 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1760
                              bnd_emptyset)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1761
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1762
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "3") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1763
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1764
     (* (Annotated_step ("8", "extcnf_combined"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1765
lemma "(\<forall>SY5 SY6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1766
             \<exists>SY7. bnd_in SY7
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1767
                    (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1768
                      (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1769
                        (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1770
                        (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1771
                          (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1772
                            (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1773
                          bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1774
                   (\<exists>SY8. bnd_in SY8
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1775
                           (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1776
                             (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1777
                               (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1778
                               (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1779
 (bnd_setadjoin SY5 (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1780
 bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1781
                          bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1782
                           (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1783
                           (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1784
                             (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1785
                               (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1786
                             bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1787
                          bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1788
                           (bnd_setadjoin SY7 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1789
                           (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1790
                             (bnd_setadjoin SY7
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1791
                               (bnd_setadjoin SY8 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1792
                             bnd_emptyset))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1793
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1794
         (\<forall>SY5 SY6.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1795
             (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1796
               (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1797
                 (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1798
                   (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1799
                 bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1800
              bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1801
               (bnd_setadjoin (bnd_sK3 SY6 SY5) bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1802
               (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1803
                 (bnd_setadjoin (bnd_sK3 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1804
                   (bnd_setadjoin (bnd_sK4 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1805
                     bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1806
                 bnd_emptyset) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1807
              bnd_in (bnd_sK4 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1808
               (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1809
                 (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1810
                   (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1811
                     (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1812
                       (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1813
                     bnd_emptyset)))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1814
             bnd_in (bnd_sK3 SY6 SY5)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1815
              (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1816
                (bnd_setadjoin (bnd_setadjoin SY5 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1817
                  (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1818
                    (bnd_setadjoin SY5
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1819
                      (bnd_setadjoin SY6 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1820
                    bnd_emptyset)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1821
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1822
by (tactic {*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1823
HEADGOAL (extcnf_combined_tac Full false (hd prob_names))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1824
*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1825
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1826
     (* (Annotated_step ("7", "extcnf_combined"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1827
lemma "(\<not> (\<forall>SY0 SY1.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1828
                \<exists>SY3. bnd_in SY3
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1829
                       (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1830
                         (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1831
                           (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1832
                           (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1833
                             (bnd_setadjoin SY0
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1834
                               (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1835
                             bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1836
                      (\<exists>SY4. bnd_in SY4
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1837
                              (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1838
(bnd_setadjoin (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1839
  (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1840
    (bnd_setadjoin SY0 (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1841
    bnd_emptyset))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1842
                             bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1843
                              (bnd_setadjoin SY0 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1844
                              (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1845
(bnd_setadjoin SY0 (bnd_setadjoin SY1 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1846
bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1847
                             bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1848
                              (bnd_setadjoin SY3 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1849
                              (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1850
(bnd_setadjoin SY3 (bnd_setadjoin SY4 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1851
bnd_emptyset)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1852
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1853
         (\<forall>SY24.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1854
             (\<forall>SY25.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1855
                 bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1856
                  (bnd_setadjoin bnd_sK1 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1857
                  (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1858
                    (bnd_setadjoin bnd_sK1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1859
                      (bnd_setadjoin bnd_sK2 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1860
                    bnd_emptyset) \<noteq>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1861
                 bnd_setadjoin (bnd_setadjoin SY24 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1862
                  (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1863
                    (bnd_setadjoin SY24
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1864
                      (bnd_setadjoin SY25 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1865
                    bnd_emptyset) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1866
                 \<not> bnd_in SY25
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1867
                    (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1868
                      (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1869
                        (bnd_setadjoin bnd_sK1 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1870
                        (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1871
                          (bnd_setadjoin bnd_sK1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1872
                            (bnd_setadjoin bnd_sK2
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1873
                              bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1874
                          bnd_emptyset)))) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1875
             \<not> bnd_in SY24
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1876
                (bnd_setunion
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1877
                  (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1878
                    (bnd_setadjoin bnd_sK1 bnd_emptyset)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1879
                    (bnd_setadjoin
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1880
                      (bnd_setadjoin bnd_sK1
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1881
                        (bnd_setadjoin bnd_sK2 bnd_emptyset))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1882
                      bnd_emptyset)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1883
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1884
by (tactic {*HEADGOAL (extcnf_combined_tac Full false (hd prob_names))*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1885
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1886
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1887
(*PUZ081^2*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1888
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1889
     (* (Annotated_step ("9", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1890
lemma "bnd_says bnd_mel
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1891
          (\<not> bnd_knave bnd_zoey \<and> \<not> bnd_knave bnd_mel) \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1892
         bnd_says bnd_mel
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1893
          (\<not> bnd_knave bnd_zoey \<and> \<not> bnd_knave bnd_mel) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1894
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1895
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "9") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1896
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1897
     (* (Annotated_step ("10", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1898
lemma "bnd_says bnd_zoey (bnd_knave bnd_mel) \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1899
         bnd_says bnd_zoey (bnd_knave bnd_mel) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1900
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "10") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1901
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1902
     (* (Annotated_step ("11", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1903
lemma "\<forall>P S. bnd_knave P \<and> bnd_says P S \<longrightarrow> \<not> S \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1904
         (\<forall>P S. bnd_knave P \<and> bnd_says P S \<longrightarrow> \<not> S) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1905
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "11") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1906
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1907
     (* (Annotated_step ("12", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1908
lemma "\<forall>P S. bnd_knight P \<and> bnd_says P S \<longrightarrow> S \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1909
         (\<forall>P S. bnd_knight P \<and> bnd_says P S \<longrightarrow> S) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1910
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "12") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1911
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1912
     (* (Annotated_step ("13", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1913
lemma "\<forall>P. bnd_knight P \<noteq> bnd_knave P \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1914
         (\<forall>P. bnd_knight P \<noteq> bnd_knave P) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1915
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "13") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1916
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1917
     (* (Annotated_step ("15", "extcnf_combined"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1918
lemma "(\<not> (\<exists>TZ TM. TZ bnd_zoey \<and> TM bnd_mel)) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1919
         ((\<forall>TM. \<not> TM bnd_mel) \<or> (\<forall>TZ. \<not> TZ bnd_zoey)) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1920
by (tactic {*extcnf_combined_tac Full false (hd prob_names) 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1921
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1922
     (* (Annotated_step ("18", "extcnf_combined"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1923
lemma "(\<forall>P. bnd_knight P \<noteq> bnd_knave P) = True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1924
         ((\<forall>P. \<not> bnd_knave P \<or> \<not> bnd_knight P) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1925
          (\<forall>P. bnd_knave P \<or> bnd_knight P)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1926
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1927
by (tactic {*extcnf_combined_tac Full false (hd prob_names) 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1928
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1929
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1930
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1931
(*from SEU667^2.p.out*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1932
     (* (Annotated_step ("10", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1933
lemma "bnd_dpsetconstrSub =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1934
         (\<forall>A B Xphi.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1935
             bnd_subset (bnd_dpsetconstr A B Xphi)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1936
              (bnd_cartprod A B)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1937
         bnd_dpsetconstr =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1938
         (\<lambda>A B Xphi.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1939
             bnd_dsetconstr (bnd_cartprod A B)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1940
              (\<lambda>Xu. \<exists>Xx. bnd_in Xx A \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1941
                         (\<exists>Xy. (bnd_in Xy B \<and> Xphi Xx Xy) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1942
                               Xu = bnd_kpair Xx Xy))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1943
         bnd_breln = (\<lambda>A B C. bnd_subset C (bnd_cartprod A B)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1944
         (\<not> bnd_subset
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1945
             (bnd_dsetconstr (bnd_cartprod bnd_sK1 bnd_sK2)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1946
               (\<lambda>SY66.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1947
                   \<exists>SY67.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1948
                      bnd_in SY67 bnd_sK1 \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1949
                      (\<exists>SY68.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1950
                          (bnd_in SY68 bnd_sK2 \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1951
                           bnd_sK3 SY67 SY68) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1952
                          SY66 = bnd_kpair SY67 SY68)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1953
             (bnd_cartprod bnd_sK1 bnd_sK2)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1954
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1955
         (\<not> bnd_subset
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1956
             (bnd_dsetconstr (bnd_cartprod bnd_sK1 bnd_sK2)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1957
               (\<lambda>SX0. \<not> (\<forall>SX1. \<not> \<not> (\<not> bnd_in SX1 bnd_sK1 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1958
    \<not> \<not> (\<forall>SX2. \<not> \<not> (\<not> \<not> (\<not> bnd_in SX2 bnd_sK2 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1959
                         \<not> bnd_sK3 SX1 SX2) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1960
                    SX0 \<noteq> bnd_kpair SX1 SX2))))))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1961
             (bnd_cartprod bnd_sK1 bnd_sK2)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1962
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1963
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "10") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1964
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1965
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1966
     (* (Annotated_step ("11", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1967
lemma "bnd_dpsetconstrSub =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1968
         (\<forall>A B Xphi.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1969
             bnd_subset (bnd_dpsetconstr A B Xphi)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1970
              (bnd_cartprod A B)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1971
         bnd_dpsetconstr =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1972
         (\<lambda>A B Xphi.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1973
             bnd_dsetconstr (bnd_cartprod A B)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1974
              (\<lambda>Xu. \<exists>Xx. bnd_in Xx A \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1975
                         (\<exists>Xy. (bnd_in Xy B \<and> Xphi Xx Xy) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1976
                               Xu = bnd_kpair Xx Xy))) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1977
         bnd_breln = (\<lambda>A B C. bnd_subset C (bnd_cartprod A B)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1978
         (\<forall>SY21 SY22 SY23.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1979
             bnd_subset
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1980
              (bnd_dsetconstr (bnd_cartprod SY21 SY22)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1981
                (\<lambda>SY35.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1982
                    \<exists>SY36.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1983
                       bnd_in SY36 SY21 \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1984
                       (\<exists>SY37.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1985
                           (bnd_in SY37 SY22 \<and> SY23 SY36 SY37) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1986
                           SY35 = bnd_kpair SY36 SY37)))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1987
              (bnd_cartprod SY21 SY22)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1988
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1989
         (\<forall>SX0 SX1 SX2.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1990
             bnd_subset
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1991
              (bnd_dsetconstr (bnd_cartprod SX0 SX1)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1992
                (\<lambda>SX3. \<not> (\<forall>SX4. \<not> \<not> (\<not> bnd_in SX4 SX0 \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1993
     \<not> \<not> (\<forall>SX5. \<not> \<not> (\<not> \<not> (\<not> bnd_in SX5 SX1 \<or> \<not> SX2 SX4 SX5) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1994
                     SX3 \<noteq> bnd_kpair SX4 SX5))))))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1995
              (bnd_cartprod SX0 SX1)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1996
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1997
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "11") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1998
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  1999
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2000
(*
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2001
(*from ALG001^5*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2002
      (* (Annotated_step ("4", "extcnf_forall_neg"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2003
lemma "(\<forall>(Xh1 :: bnd_g \<Rightarrow> bnd_b) (Xh2 :: bnd_b \<Rightarrow> bnd_a) (Xf1 :: bnd_g \<Rightarrow> bnd_g \<Rightarrow> bnd_g) (Xf2 :: bnd_b \<Rightarrow> bnd_b \<Rightarrow> bnd_b) (Xf3 :: bnd_a \<Rightarrow> bnd_a \<Rightarrow> bnd_a).
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2004
             (\<forall>Xx Xy. Xh1 (Xf1 Xx Xy) = Xf2 (Xh1 Xx) (Xh1 Xy)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2005
             (\<forall>Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2006
                 Xh2 (Xf2 Xx Xy) = Xf3 (Xh2 Xx) (Xh2 Xy)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2007
             (\<forall>Xx Xy.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2008
                 Xh2 (Xh1 (Xf1 Xx Xy)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2009
                 Xf3 (Xh2 (Xh1 Xx)) (Xh2 (Xh1 Xy)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2010
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2011
         ((\<forall>SY35 SY36.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2012
              bnd_sK1 (bnd_sK3 SY35 SY36) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2013
              bnd_sK4 (bnd_sK1 SY35) (bnd_sK1 SY36)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2014
          (\<forall>SY31 SY32.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2015
              bnd_sK2 (bnd_sK4 SY31 SY32) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2016
              bnd_sK5 (bnd_sK2 SY31) (bnd_sK2 SY32)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2017
          (\<forall>SY39 SY40.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2018
              bnd_sK2 (bnd_sK1 (bnd_sK3 SY39 SY40)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2019
              bnd_sK5 (bnd_sK2 (bnd_sK1 SY39))
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2020
               (bnd_sK2 (bnd_sK1 SY40)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2021
         False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2022
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "4") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2023
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2024
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2025
(*SYN044^4*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2026
(*
56281
03c3d1a7c3b8 proper configuration option "ML_print_depth";
wenzelm
parents: 56265
diff changeset
  2027
declare [[ML_print_depth = 1400]]
55596
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2028
(* the_tactics *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2029
*}
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2030
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2031
     (* (Annotated_step ("12", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2032
lemma "bnd_mor =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2033
         (\<lambda>(X\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2034
             (Y\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) U\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2035
             X U \<or> Y U) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2036
         bnd_mnot =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2037
         (\<lambda>(X\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) U\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2038
             \<not> X U) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2039
         bnd_mimplies =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2040
         (\<lambda>U\<Colon>TPTP_Interpret.ind \<Rightarrow> bool. bnd_mor (bnd_mnot U)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2041
         bnd_mbox_s4 =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2042
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2043
             \<forall>Y\<Colon>TPTP_Interpret.ind. bnd_irel X Y \<longrightarrow> P Y) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2044
         bnd_mand =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2045
         (\<lambda>(X\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2046
             (Y\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) U\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2047
             X U \<and> Y U) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2048
         bnd_ixor =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2049
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2050
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2051
             bnd_inot (bnd_iequiv P Q)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2052
         bnd_ivalid = All \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2053
         bnd_itrue = (\<lambda>W\<Colon>TPTP_Interpret.ind. True) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2054
         bnd_isatisfiable = Ex \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2055
         bnd_ior =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2056
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2057
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2058
             bnd_mor (bnd_mbox_s4 P) (bnd_mbox_s4 Q)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2059
         bnd_inot =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2060
         (\<lambda>P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2061
             bnd_mnot (bnd_mbox_s4 P)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2062
         bnd_iinvalid =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2063
         (\<lambda>Phi\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2064
             \<forall>W\<Colon>TPTP_Interpret.ind. \<not> Phi W) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2065
         bnd_iimplies =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2066
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2067
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2068
             bnd_mimplies (bnd_mbox_s4 P) (bnd_mbox_s4 Q)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2069
         bnd_iimplied =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2070
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2071
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool. bnd_iimplies Q P) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2072
         bnd_ifalse = bnd_inot bnd_itrue \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2073
         bnd_iequiv =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2074
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2075
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2076
             bnd_iand (bnd_iimplies P Q) (bnd_iimplies Q P)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2077
         bnd_icountersatisfiable =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2078
         (\<lambda>Phi\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2079
             \<exists>W\<Colon>TPTP_Interpret.ind. \<not> Phi W) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2080
         bnd_iatom = (\<lambda>P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool. P) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2081
         bnd_iand = bnd_mand \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2082
         (\<forall>(X\<Colon>TPTP_Interpret.ind) (Y\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2083
             Z\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2084
             bnd_irel X Y \<and> bnd_irel Y Z \<longrightarrow> bnd_irel X Z) \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2085
         (\<forall>(X\<Colon>TPTP_Interpret.ind) (Y\<Colon>TPTP_Interpret.ind)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2086
             Z\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2087
             bnd_irel X Y \<and> bnd_irel Y Z \<longrightarrow> bnd_irel X Z) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2088
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2089
(* by (tactic {*tectoc @{context}*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2090
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "12") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2091
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2092
     (* (Annotated_step ("11", "unfold_def"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2093
lemma "bnd_mor =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2094
         (\<lambda>(X\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2095
             (Y\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) U\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2096
             X U \<or> Y U) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2097
         bnd_mnot =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2098
         (\<lambda>(X\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) U\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2099
             \<not> X U) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2100
         bnd_mimplies =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2101
         (\<lambda>U\<Colon>TPTP_Interpret.ind \<Rightarrow> bool. bnd_mor (bnd_mnot U)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2102
         bnd_mbox_s4 =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2103
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) X\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2104
             \<forall>Y\<Colon>TPTP_Interpret.ind. bnd_irel X Y \<longrightarrow> P Y) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2105
         bnd_mand =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2106
         (\<lambda>(X\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2107
             (Y\<Colon>TPTP_Interpret.ind \<Rightarrow> bool) U\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2108
             X U \<and> Y U) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2109
         bnd_ixor =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2110
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2111
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2112
             bnd_inot (bnd_iequiv P Q)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2113
         bnd_ivalid = All \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2114
         bnd_itrue = (\<lambda>W\<Colon>TPTP_Interpret.ind. True) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2115
         bnd_isatisfiable = Ex \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2116
         bnd_ior =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2117
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2118
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2119
             bnd_mor (bnd_mbox_s4 P) (bnd_mbox_s4 Q)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2120
         bnd_inot =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2121
         (\<lambda>P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2122
             bnd_mnot (bnd_mbox_s4 P)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2123
         bnd_iinvalid =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2124
         (\<lambda>Phi\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2125
             \<forall>W\<Colon>TPTP_Interpret.ind. \<not> Phi W) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2126
         bnd_iimplies =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2127
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2128
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2129
             bnd_mimplies (bnd_mbox_s4 P) (bnd_mbox_s4 Q)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2130
         bnd_iimplied =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2131
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2132
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool. bnd_iimplies Q P) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2133
         bnd_ifalse = bnd_inot bnd_itrue \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2134
         bnd_iequiv =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2135
         (\<lambda>(P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2136
             Q\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2137
             bnd_iand (bnd_iimplies P Q) (bnd_iimplies Q P)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2138
         bnd_icountersatisfiable =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2139
         (\<lambda>Phi\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2140
             \<exists>W\<Colon>TPTP_Interpret.ind. \<not> Phi W) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2141
         bnd_iatom = (\<lambda>P\<Colon>TPTP_Interpret.ind \<Rightarrow> bool. P) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2142
         bnd_iand = bnd_mand \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2143
         bnd_ivalid
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2144
          (bnd_iimplies (bnd_iatom bnd_q) (bnd_iatom bnd_r)) \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2145
         (\<forall>SY161\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2146
             \<not> (\<forall>SY162\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2147
                   bnd_irel SY161 SY162 \<longrightarrow> bnd_q SY162) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2148
             (\<forall>SY163\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2149
                 bnd_irel SY161 SY163 \<longrightarrow> bnd_r SY163)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2150
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2151
(* by (tactic {*tectoc @{context}*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2152
by (tactic {*rtac (leo2_tac @{context} (hd prob_names) "11") 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2153
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2154
lemma "
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2155
(\<forall>SY136.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2156
    \<not> (\<forall>SY137. bnd_irel SY136 SY137 \<longrightarrow> bnd_r SY137) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2157
    (\<forall>SY138.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2158
        bnd_irel SY136 SY138 \<longrightarrow> bnd_p SY138 \<and> bnd_q SY138)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2159
True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2160
(\<forall>SY136.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2161
    bnd_irel SY136 (bnd_sK5 SY136) \<and> \<not> bnd_r (bnd_sK5 SY136) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2162
    (\<forall>SY138. \<not> bnd_irel SY136 SY138 \<or> bnd_p SY138) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2163
    (\<forall>SY138. \<not> bnd_irel SY136 SY138 \<or> bnd_q SY138)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2164
True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2165
by (tactic {*HEADGOAL (extcnf_combined_tac Full false (hd prob_names))*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2166
*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2167
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2168
     (* (Annotated_step ("11", "extcnf_forall_neg"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2169
lemma "\<forall>SV1\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2170
            (\<forall>SY2\<Colon>TPTP_Interpret.ind.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2171
                \<not> (\<not> (\<not> SV1 SY2 \<or> SEV405_5_bnd_cA) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2172
                   \<not> (\<not> SEV405_5_bnd_cA \<or> SV1 SY2))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2173
            False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2174
         \<forall>SV1\<Colon>TPTP_Interpret.ind \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2175
            (\<not> (\<not> (\<not> SV1 (SEV405_5_bnd_sK1_SY2 SV1) \<or> SEV405_5_bnd_cA) \<or>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2176
                \<not> (\<not> SEV405_5_bnd_cA \<or> SV1 (SEV405_5_bnd_sK1_SY2 SV1)))) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2177
            False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2178
(* apply (tactic {*full_extcnf_combined_tac*}) *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2179
by (tactic {*nonfull_extcnf_combined_tac @{context} [Existential_Var]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2180
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2181
     (* (Annotated_step ("13", "extcnf_forall_pos"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2182
lemma "(\<forall>SY31 SY32.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2183
             bnd_sK2 (bnd_sK4 SY31 SY32) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2184
             bnd_sK5 (bnd_sK2 SY31) (bnd_sK2 SY32)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2185
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2186
         \<forall>SV1. (\<forall>SY42.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2187
                   bnd_sK2 (bnd_sK4 SV1 SY42) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2188
                   bnd_sK5 (bnd_sK2 SV1) (bnd_sK2 SY42)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2189
               True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2190
by (tactic {*nonfull_extcnf_combined_tac @{context} [Universal]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2191
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2192
     (* (Annotated_step ("14", "extcnf_forall_pos"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2193
lemma "(\<forall>SY35 SY36.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2194
             bnd_sK1 (bnd_sK3 SY35 SY36) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2195
             bnd_sK4 (bnd_sK1 SY35) (bnd_sK1 SY36)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2196
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2197
         \<forall>SV2. (\<forall>SY43.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2198
                   bnd_sK1 (bnd_sK3 SV2 SY43) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2199
                   bnd_sK4 (bnd_sK1 SV2) (bnd_sK1 SY43)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2200
               True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2201
by (tactic {*nonfull_extcnf_combined_tac @{context} [Universal]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2202
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2203
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2204
(*from SYO198^5.p.out*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2205
   (* [[(Annotated_step ("11", "extcnf_forall_special_pos"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2206
lemma "(\<forall>SX0\<Colon>bool \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2207
             \<not> \<not> (\<not> SX0 bnd_sK1_Xx \<or> \<not> SX0 bnd_sK2_Xy)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2208
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2209
         (\<not> \<not> (\<not> True \<or> \<not> True)) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2210
apply (tactic {*extcnf_forall_special_pos_tac 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2211
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2212
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2213
     (* (Annotated_step ("13", "extcnf_forall_special_pos"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2214
lemma "(\<forall>SX0\<Colon>bool \<Rightarrow> bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2215
             \<not> \<not> (\<not> SX0 bnd_sK1_Xx \<or> \<not> SX0 bnd_sK2_Xy)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2216
         True \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2217
         (\<not> \<not> (\<not> bnd_sK1_Xx \<or> \<not> bnd_sK2_Xy)) = True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2218
apply (tactic {*extcnf_forall_special_pos_tac 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2219
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2220
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2221
   (* [[(Annotated_step ("8", "polarity_switch"), *)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2222
lemma "(\<forall>(Xx\<Colon>bool) (Xy\<Colon>bool) Xz\<Colon>bool. True \<and> True \<longrightarrow> True) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2223
         False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2224
         (\<not> (\<forall>(Xx\<Colon>bool) (Xy\<Colon>bool) Xz\<Colon>bool.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2225
                True \<and> True \<longrightarrow> True)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2226
         True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2227
apply (tactic {*nonfull_extcnf_combined_tac @{context} [Polarity_switch]*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2228
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2229
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2230
lemma "((\<forall>SY22 SY23 SY24.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2231
       bnd_sK1_RRR SY22 SY23 \<and> bnd_sK1_RRR SY23 SY24 \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2232
       bnd_sK1_RRR SY22 SY24) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2233
   (\<forall>SY25.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2234
       (\<forall>SY26. SY25 SY26 \<longrightarrow> bnd_sK1_RRR SY26 (bnd_sK2_U SY25)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2235
       (\<forall>SY27.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2236
           (\<forall>SY28. SY25 SY28 \<longrightarrow> bnd_sK1_RRR SY28 SY27) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2237
           bnd_sK1_RRR (bnd_sK2_U SY25) SY27)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2238
   (\<forall>SY29. \<exists>SY30. \<forall>SY31. SY29 SY31 \<longrightarrow> bnd_sK1_RRR SY31 SY30)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2239
  False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2240
  (\<forall>SY25.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2241
      (\<forall>SY26. SY25 SY26 \<longrightarrow> bnd_sK1_RRR SY26 (bnd_sK2_U SY25)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2242
      (\<forall>SY27.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2243
          (\<forall>SY28. SY25 SY28 \<longrightarrow> bnd_sK1_RRR SY28 SY27) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2244
          bnd_sK1_RRR (bnd_sK2_U SY25) SY27)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2245
  True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2246
apply (tactic {*standard_cnf_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2247
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2248
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2249
lemma "((\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2250
   (\<forall>Xx Xy. bnd_in Xx (bnd_setadjoin Xx Xy)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2251
   (\<forall>A B. A = B \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2252
          (\<forall>Xx Xy. Xx = Xy \<longrightarrow> bnd_in Xx A = bnd_in Xy B)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2253
   (\<forall>SY0. bnd_in SY0 bnd_omega \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2254
          bnd_setadjoin SY0 SY0 \<noteq> bnd_emptyset)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2255
  False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2256
 (\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2257
  True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2258
apply (tactic {*standard_cnf_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2259
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2260
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2261
lemma "((\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2262
   (\<forall>Xx Xy. bnd_in Xx (bnd_setadjoin Xx Xy)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2263
   (\<forall>A B. A = B \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2264
          (\<forall>Xx Xy. Xx = Xy \<longrightarrow> bnd_in Xx A = bnd_in Xy B)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2265
   (\<forall>SY0. bnd_in SY0 bnd_omega \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2266
          bnd_setadjoin SY0 SY0 \<noteq> bnd_emptyset)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2267
  False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2268
  (\<forall>Xx Xy. bnd_in Xx (bnd_setadjoin Xx Xy)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2269
  True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2270
apply (tactic {*standard_cnf_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2271
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2272
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2273
lemma "((\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2274
   (\<forall>Xx Xy. bnd_in Xx (bnd_setadjoin Xx Xy)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2275
   (\<forall>A B. A = B \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2276
          (\<forall>Xx Xy. Xx = Xy \<longrightarrow> bnd_in Xx A = bnd_in Xy B)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2277
   (\<forall>SY0. bnd_in SY0 bnd_omega \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2278
          bnd_setadjoin SY0 SY0 \<noteq> bnd_emptyset)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2279
  False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2280
  (\<forall>A B. A = B \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2281
         (\<forall>Xx Xy. Xx = Xy \<longrightarrow> bnd_in Xx A = bnd_in Xy B)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2282
  True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2283
apply (tactic {*standard_cnf_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2284
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2285
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2286
lemma "((\<forall>Xx. bnd_in Xx bnd_emptyset \<longrightarrow> (\<forall>Xphi. Xphi)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2287
   (\<forall>Xx Xy. bnd_in Xx (bnd_setadjoin Xx Xy)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2288
   (\<forall>A B. A = B \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2289
          (\<forall>Xx Xy. Xx = Xy \<longrightarrow> bnd_in Xx A = bnd_in Xy B)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2290
   (\<forall>SY0. bnd_in SY0 bnd_omega \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2291
          bnd_setadjoin SY0 SY0 \<noteq> bnd_emptyset)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2292
  False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2293
  (\<forall>SY0. bnd_in SY0 bnd_omega \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2294
         bnd_setadjoin SY0 SY0 \<noteq> bnd_emptyset) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2295
  False"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2296
apply (tactic {*standard_cnf_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2297
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2298
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2299
(*nested conjunctions*)
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2300
lemma "((((\<forall>Xx. bnd_cP bnd_e Xx = Xx) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2301
     (\<forall>Xy. bnd_cP Xy bnd_e = Xy)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2302
    (\<forall>Xz. bnd_cP Xz Xz = bnd_e)) \<and>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2303
   (\<forall>Xx Xy Xz.
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2304
       bnd_cP (bnd_cP Xx Xy) Xz = bnd_cP Xx (bnd_cP Xy Xz)) \<longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2305
   (\<forall>Xa Xb. bnd_cP Xa Xb = bnd_cP Xb Xa)) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2306
  False \<Longrightarrow>
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2307
  (\<forall>Xx. bnd_cP bnd_e Xx = Xx) =
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2308
  True"
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2309
apply (tactic {*standard_cnf_tac @{context} 1*})
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2310
done
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2311
928b9f677165 reconstruction framework for LEO-II's TPTP proofs;
sultana
parents:
diff changeset
  2312
end