# HG changeset patch # User paulson # Date 909046698 -7200 # Node ID 81e1a83ee00265e48838f1b1d8ec7e5fb100e156 # Parent c669e2161b089f190ca80c6ad652a749834e7e5f tidying diff -r c669e2161b08 -r 81e1a83ee002 src/FOL/ex/cla.ML --- a/src/FOL/ex/cla.ML Thu Oct 22 10:57:18 1998 +0200 +++ b/src/FOL/ex/cla.ML Thu Oct 22 10:58:18 1998 +0200 @@ -143,8 +143,7 @@ (*Discussed in Avron, Gentzen-Type Systems, Resolution and Tableaux, JAR 10 (265-281), 1993. Proof is trivial!*) -Goal - "~ ((EX x.~P(x)) & ((EX x. P(x)) | (EX x. P(x) & Q(x))) & ~ (EX x. P(x)))"; +Goal "~ ((EX x.~P(x)) & ((EX x. P(x)) | (EX x. P(x) & Q(x))) & ~ (EX x. P(x)))"; by (Blast_tac 1); result(); @@ -306,8 +305,7 @@ result(); writeln"Problem 36"; -Goal - "(ALL x. EX y. J(x,y)) & \ +Goal "(ALL x. EX y. J(x,y)) & \ \ (ALL x. EX y. G(x,y)) & \ \ (ALL x y. J(x,y) | G(x,y) --> (ALL z. J(y,z) | G(y,z) --> H(x,z))) \ \ --> (ALL x. EX y. H(x,y))"; @@ -324,8 +322,7 @@ result(); writeln"Problem 38"; -Goal - "(ALL x. p(a) & (p(x) --> (EX y. p(y) & r(x,y))) --> \ +Goal "(ALL x. p(a) & (p(x) --> (EX y. p(y) & r(x,y))) --> \ \ (EX z. EX w. p(z) & r(x,w) & r(w,z))) <-> \ \ (ALL x. (~p(a) | p(x) | (EX z. EX w. p(z) & r(x,w) & r(w,z))) & \ \ (~p(a) | ~(EX y. p(y) & r(x,y)) | \ @@ -385,8 +382,7 @@ writeln"Problem 46"; -Goal - "(ALL x. f(x) & (ALL y. f(y) & h(y,x) --> g(y)) --> g(x)) & \ +Goal "(ALL x. f(x) & (ALL y. f(y) & h(y,x) --> g(y)) --> g(x)) & \ \ ((EX x. f(x) & ~g(x)) --> \ \ (EX x. f(x) & ~g(x) & (ALL y. f(y) & ~g(y) --> j(x,y)))) & \ \ (ALL x y. f(x) & f(y) & h(x,y) --> ~j(y,x)) \ @@ -422,16 +418,14 @@ result(); writeln"Problem 51"; -Goal - "(EX z w. ALL x y. P(x,y) <-> (x=z & y=w)) --> \ +Goal "(EX z w. ALL x y. P(x,y) <-> (x=z & y=w)) --> \ \ (EX z. ALL x. EX w. (ALL y. P(x,y) <-> y=w) <-> x=z)"; by (Blast_tac 1); result(); writeln"Problem 52"; (*Almost the same as 51. *) -Goal - "(EX z w. ALL x y. P(x,y) <-> (x=z & y=w)) --> \ +Goal "(EX z w. ALL x y. P(x,y) <-> (x=z & y=w)) --> \ \ (EX w. ALL y. EX z. (ALL x. P(x,y) <-> x=z) <-> y=w)"; by (Blast_tac 1); result(); @@ -439,8 +433,7 @@ writeln"Problem 55"; (*Original, equational version by Len Schubert, via Pelletier *** NOT PROVED -Goal - "(EX x. lives(x) & killed(x,agatha)) & \ +Goal "(EX x. lives(x) & killed(x,agatha)) & \ \ lives(agatha) & lives(butler) & lives(charles) & \ \ (ALL x. lives(x) --> x=agatha | x=butler | x=charles) & \ \ (ALL x y. killed(x,y) --> hates(x,y)) & \ @@ -472,19 +465,18 @@ \ (ALL x. hates(agatha,x) --> hates(butler,x)) & \ \ (ALL x. ~hates(x,agatha) | ~hates(x,butler) | ~hates(x,charles)) --> \ \ killed(?who,agatha)"; -by (Fast_tac 1); (*MUCH faster than Blast_tac: 8s against 29s*) +by (Fast_tac 1); + (*MUCH faster than Blast_tac: 1.5s against ??s, mostly proof reconstruction*) result(); writeln"Problem 56"; -Goal - "(ALL x. (EX y. P(y) & x=f(y)) --> P(x)) <-> (ALL x. P(x) --> P(f(x)))"; +Goal "(ALL x. (EX y. P(y) & x=f(y)) --> P(x)) <-> (ALL x. P(x) --> P(f(x)))"; by (Blast_tac 1); result(); writeln"Problem 57"; -Goal - "P(f(a,b), f(b,c)) & P(f(b,c), f(a,c)) & \ +Goal "P(f(a,b), f(b,c)) & P(f(b,c), f(a,c)) & \ \ (ALL x y z. P(x,y) & P(y,z) --> P(x,z)) --> P(f(a,b), f(a,c))"; by (Blast_tac 1); result(); @@ -500,14 +492,12 @@ result(); writeln"Problem 60"; -Goal - "ALL x. P(x,f(x)) <-> (EX y. (ALL z. P(z,y) --> P(z,f(x))) & P(x,y))"; +Goal "ALL x. P(x,f(x)) <-> (EX y. (ALL z. P(z,y) --> P(z,f(x))) & P(x,y))"; by (Blast_tac 1); result(); writeln"Problem 62 as corrected in JAR 18 (1997), page 135"; -Goal - "(ALL x. p(a) & (p(x) --> p(f(x))) --> p(f(f(x)))) <-> \ +Goal "(ALL x. p(a) & (p(x) --> p(f(x))) --> p(f(f(x)))) <-> \ \ (ALL x. (~p(a) | p(x) | p(f(f(x)))) & \ \ (~p(a) | ~p(f(x)) | p(f(f(x)))))"; by (Blast_tac 1); @@ -523,8 +513,7 @@ (*From Rudnicki, Obvious Inferences, JAR 3 (1987), 383-393. It does seem obvious!*) -Goal - "(ALL x. F(x) & ~G(x) --> (EX y. H(x,y) & J(y))) & \ +Goal "(ALL x. F(x) & ~G(x) --> (EX y. H(x,y) & J(y))) & \ \ (EX x. K(x) & F(x) & (ALL y. H(x,y) --> K(y))) & \ \ (ALL x. K(x) --> ~G(x)) --> (EX x. K(x) --> ~G(x))"; by (Fast_tac 1); @@ -532,8 +521,7 @@ (*Halting problem: Formulation of Li Dafa (AAR Newsletter 27, Oct 1994.) author U. Egly*) -Goal - "((EX x. A(x) & (ALL y. C(y) --> (ALL z. D(x,y,z)))) --> \ +Goal "((EX x. A(x) & (ALL y. C(y) --> (ALL z. D(x,y,z)))) --> \ \ (EX w. C(w) & (ALL y. C(y) --> (ALL z. D(w,y,z))))) \ \ & \ \ (ALL w. C(w) & (ALL u. C(u) --> (ALL v. D(w,u,v))) --> \ @@ -555,8 +543,7 @@ (*Halting problem II: credited to M. Bruschi by Li Dafa in JAR 18(1), p.105*) -Goal - "((EX x. A(x) & (ALL y. C(y) --> (ALL z. D(x,y,z)))) --> \ +Goal "((EX x. A(x) & (ALL y. C(y) --> (ALL z. D(x,y,z)))) --> \ \ (EX w. C(w) & (ALL y. C(y) --> (ALL z. D(w,y,z))))) \ \ & \ \ (ALL w. C(w) & (ALL u. C(u) --> (ALL v. D(w,u,v))) --> \