TSTP Solution File: LCL459+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL459+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:50:54 EDT 2009
% Result : Theorem 204.7s
% Output : Refutation 204.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 49 ( 22 ~; 21 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 25 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(kn1,plain,
! [A] :
( ( ~ kn1
| is_a_theorem(implies(A,and(A,A))) )
& ( kn1
| ~ is_a_theorem(implies(p(A),and(p(A),p(A)))) ) ),
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(165650856,plain,
( kn1
| ~ is_a_theorem(implies(p(A),and(p(A),p(A)))) ),
inference(rewrite,[status(thm)],[kn1]),
[] ).
fof(rosser_kn1,plain,
~ kn1,
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(166841008,plain,
~ kn1,
inference(rewrite,[status(thm)],[rosser_kn1]),
[] ).
cnf(175367000,plain,
~ is_a_theorem(implies(p(A),and(p(A),p(A)))),
inference(resolution,[status(thm)],[165650856,166841008]),
[] ).
fof(implies_2,plain,
! [A,B] :
( ( ~ implies_2
| is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) )
& ( implies_2
| ~ is_a_theorem(implies(implies(x(A,B),implies(x(A,B),y(A,B))),implies(x(A,B),y(A,B)))) ) ),
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(165851320,plain,
( ~ implies_2
| is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) ),
inference(rewrite,[status(thm)],[implies_2]),
[] ).
fof(hilbert_implies_2,plain,
implies_2,
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(166694880,plain,
implies_2,
inference(rewrite,[status(thm)],[hilbert_implies_2]),
[] ).
cnf(175270376,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolution,[status(thm)],[165851320,166694880]),
[] ).
fof(modus_ponens,plain,
! [A,B] :
( ( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) )
& ( ~ is_a_theorem(y(A,B))
| modus_ponens )
& ( is_a_theorem(x(A,B))
| modus_ponens )
& ( is_a_theorem(implies(x(A,B),y(A,B)))
| modus_ponens ) ),
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(165697688,plain,
( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[modus_ponens]),
[] ).
fof(hilbert_modus_ponens,plain,
modus_ponens,
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(166660944,plain,
modus_ponens,
inference(rewrite,[status(thm)],[hilbert_modus_ponens]),
[] ).
cnf(175229040,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[165697688,166660944]),
[] ).
fof(and_3,plain,
! [A,B] :
( ( ~ and_3
| is_a_theorem(implies(A,implies(B,and(A,B)))) )
& ( and_3
| ~ is_a_theorem(implies(x(A,B),implies(y(A,B),and(x(A,B),y(A,B))))) ) ),
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(165973368,plain,
( ~ and_3
| is_a_theorem(implies(A,implies(B,and(A,B)))) ),
inference(rewrite,[status(thm)],[and_3]),
[] ).
fof(hilbert_and_3,plain,
and_3,
file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),
[] ).
cnf(166743848,plain,
and_3,
inference(rewrite,[status(thm)],[hilbert_and_3]),
[] ).
cnf(175301864,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolution,[status(thm)],[165973368,166743848]),
[] ).
cnf(179832144,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,and(B,C))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[175229040,175301864]),
[] ).
cnf(111294224,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolution,[status(thm)],[175270376,179832144]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[175367000,111294224]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 207 seconds
% START OF PROOF SEQUENCE
% fof(kn1,plain,(((~kn1|is_a_theorem(implies(A,and(A,A))))&(kn1|~is_a_theorem(implies(p(A),and(p(A),p(A))))))),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(165650856,plain,(kn1|~is_a_theorem(implies(p(A),and(p(A),p(A))))),inference(rewrite,[status(thm)],[kn1]),[]).
%
% fof(rosser_kn1,plain,(~kn1),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(166841008,plain,(~kn1),inference(rewrite,[status(thm)],[rosser_kn1]),[]).
%
% cnf(175367000,plain,(~is_a_theorem(implies(p(A),and(p(A),p(A))))),inference(resolution,[status(thm)],[165650856,166841008]),[]).
%
% fof(implies_2,plain,(((~implies_2|is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))))&(implies_2|~is_a_theorem(implies(implies(x(A,B),implies(x(A,B),y(A,B))),implies(x(A,B),y(A,B))))))),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(165851320,plain,(~implies_2|is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))),inference(rewrite,[status(thm)],[implies_2]),[]).
%
% fof(hilbert_implies_2,plain,(implies_2),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(166694880,plain,(implies_2),inference(rewrite,[status(thm)],[hilbert_implies_2]),[]).
%
% cnf(175270376,plain,(is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))),inference(resolution,[status(thm)],[165851320,166694880]),[]).
%
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(165697688,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(hilbert_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(166660944,plain,(modus_ponens),inference(rewrite,[status(thm)],[hilbert_modus_ponens]),[]).
%
% cnf(175229040,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[165697688,166660944]),[]).
%
% fof(and_3,plain,(((~and_3|is_a_theorem(implies(A,implies(B,and(A,B)))))&(and_3|~is_a_theorem(implies(x(A,B),implies(y(A,B),and(x(A,B),y(A,B)))))))),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(165973368,plain,(~and_3|is_a_theorem(implies(A,implies(B,and(A,B))))),inference(rewrite,[status(thm)],[and_3]),[]).
%
% fof(hilbert_and_3,plain,(and_3),file('/tmp/SystemOnTPTP5854/LCL459+1.p',unknown),[]).
%
% cnf(166743848,plain,(and_3),inference(rewrite,[status(thm)],[hilbert_and_3]),[]).
%
% cnf(175301864,plain,(is_a_theorem(implies(A,implies(B,and(A,B))))),inference(resolution,[status(thm)],[165973368,166743848]),[]).
%
% cnf(179832144,plain,(~is_a_theorem(implies(implies(B,implies(C,and(B,C))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[175229040,175301864]),[]).
%
% cnf(111294224,plain,(is_a_theorem(implies(A,and(A,A)))),inference(resolution,[status(thm)],[175270376,179832144]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[175367000,111294224]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------