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