TSTP Solution File: LCL469+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL469+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 13:51:05 EDT 2009
% Result : Theorem 2.1s
% Output : Refutation 2.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 23 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 59 ( 27 ~; 26 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 45 ( 7 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(156778688,plain,
( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[modus_ponens]),
[] ).
fof(luka_modus_ponens,plain,
modus_ponens,
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157748712,plain,
modus_ponens,
inference(rewrite,[status(thm)],[luka_modus_ponens]),
[] ).
cnf(166212584,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[156778688,157748712]),
[] ).
fof(op_or,plain,
! [A,B] :
( ~ op_or
| $equal(not(and(not(A),not(B))),or(A,B)) ),
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157633440,plain,
( ~ op_or
| $equal(not(and(not(A),not(B))),or(A,B)) ),
inference(rewrite,[status(thm)],[op_or]),
[] ).
fof(luka_op_or,plain,
op_or,
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157712600,plain,
op_or,
inference(rewrite,[status(thm)],[luka_op_or]),
[] ).
cnf(166191976,plain,
$equal(not(and(not(A),not(B))),or(A,B)),
inference(resolution,[status(thm)],[157633440,157712600]),
[] ).
fof(op_implies_and,plain,
! [A,B] :
( ~ op_implies_and
| $equal(not(and(A,not(B))),implies(A,B)) ),
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157669072,plain,
( ~ op_implies_and
| $equal(not(and(A,not(B))),implies(A,B)) ),
inference(rewrite,[status(thm)],[op_implies_and]),
[] ).
fof(hilbert_op_implies_and,plain,
op_implies_and,
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157806840,plain,
op_implies_and,
inference(rewrite,[status(thm)],[hilbert_op_implies_and]),
[] ).
cnf(166263824,plain,
$equal(not(and(A,not(B))),implies(A,B)),
inference(resolution,[status(thm)],[157669072,157806840]),
[] ).
fof(cn2,plain,
! [A,B] :
( ( ~ cn2
| is_a_theorem(implies(A,implies(not(A),B))) )
& ( cn2
| ~ is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B)))) ) ),
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157427480,plain,
( ~ cn2
| is_a_theorem(implies(A,implies(not(A),B))) ),
inference(rewrite,[status(thm)],[cn2]),
[] ).
fof(luka_cn2,plain,
cn2,
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(156730824,plain,
cn2,
inference(rewrite,[status(thm)],[luka_cn2]),
[] ).
cnf(166235984,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(resolution,[status(thm)],[157427480,156730824]),
[] ).
cnf(166436632,plain,
is_a_theorem(implies(B,not(and(not(B),not(A))))),
inference(paramodulation,[status(thm)],[166263824,166235984,theory(equality)]),
[] ).
cnf(167952040,plain,
is_a_theorem(implies(A,or(A,B))),
inference(paramodulation,[status(thm)],[166191976,166436632,theory(equality)]),
[] ).
cnf(169812160,plain,
( ~ is_a_theorem(A)
| is_a_theorem(or(A,B)) ),
inference(resolution,[status(thm)],[166212584,167952040]),
[] ).
cnf(171029824,plain,
is_a_theorem(or(implies(B,or(B,C)),A)),
inference(resolution,[status(thm)],[169812160,167952040]),
[] ).
fof(cn3,plain,
! [A] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(A),A),A)) )
& ( cn3
| ~ is_a_theorem(implies(implies(not(p(A)),p(A)),p(A))) ) ),
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157454888,plain,
( ~ cn3
| is_a_theorem(implies(implies(not(A),A),A)) ),
inference(rewrite,[status(thm)],[cn3]),
[] ).
fof(luka_cn3,plain,
cn3,
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157782840,plain,
cn3,
inference(rewrite,[status(thm)],[luka_cn3]),
[] ).
cnf(166246416,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(resolution,[status(thm)],[157454888,157782840]),
[] ).
cnf(166500392,plain,
is_a_theorem(implies(not(and(not(A),not(A))),A)),
inference(paramodulation,[status(thm)],[166263824,166246416,theory(equality)]),
[] ).
cnf(168054768,plain,
is_a_theorem(implies(or(A,A),A)),
inference(paramodulation,[status(thm)],[166191976,166500392,theory(equality)]),
[] ).
cnf(169850752,plain,
( ~ is_a_theorem(or(A,A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[166212584,168054768]),
[] ).
fof(or_1,plain,
! [A,B] :
( ( ~ or_1
| is_a_theorem(implies(A,or(A,B))) )
& ( or_1
| ~ is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B)))) ) ),
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157072704,plain,
( or_1
| ~ is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B)))) ),
inference(rewrite,[status(thm)],[or_1]),
[] ).
fof(hilbert_or_1,plain,
~ or_1,
file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),
[] ).
cnf(157825496,plain,
~ or_1,
inference(rewrite,[status(thm)],[hilbert_or_1]),
[] ).
cnf(166274024,plain,
~ is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B)))),
inference(resolution,[status(thm)],[157072704,157825496]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[171029824,169850752,166274024]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(156778688,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(luka_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157748712,plain,(modus_ponens),inference(rewrite,[status(thm)],[luka_modus_ponens]),[]).
%
% cnf(166212584,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[156778688,157748712]),[]).
%
% fof(op_or,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157633440,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),inference(rewrite,[status(thm)],[op_or]),[]).
%
% fof(luka_op_or,plain,(op_or),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157712600,plain,(op_or),inference(rewrite,[status(thm)],[luka_op_or]),[]).
%
% cnf(166191976,plain,($equal(not(and(not(A),not(B))),or(A,B))),inference(resolution,[status(thm)],[157633440,157712600]),[]).
%
% fof(op_implies_and,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157669072,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_and]),[]).
%
% fof(hilbert_op_implies_and,plain,(op_implies_and),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157806840,plain,(op_implies_and),inference(rewrite,[status(thm)],[hilbert_op_implies_and]),[]).
%
% cnf(166263824,plain,($equal(not(and(A,not(B))),implies(A,B))),inference(resolution,[status(thm)],[157669072,157806840]),[]).
%
% fof(cn2,plain,(((~cn2|is_a_theorem(implies(A,implies(not(A),B))))&(cn2|~is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B))))))),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157427480,plain,(~cn2|is_a_theorem(implies(A,implies(not(A),B)))),inference(rewrite,[status(thm)],[cn2]),[]).
%
% fof(luka_cn2,plain,(cn2),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(156730824,plain,(cn2),inference(rewrite,[status(thm)],[luka_cn2]),[]).
%
% cnf(166235984,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(resolution,[status(thm)],[157427480,156730824]),[]).
%
% cnf(166436632,plain,(is_a_theorem(implies(B,not(and(not(B),not(A)))))),inference(paramodulation,[status(thm)],[166263824,166235984,theory(equality)]),[]).
%
% cnf(167952040,plain,(is_a_theorem(implies(A,or(A,B)))),inference(paramodulation,[status(thm)],[166191976,166436632,theory(equality)]),[]).
%
% cnf(169812160,plain,(~is_a_theorem(A)|is_a_theorem(or(A,B))),inference(resolution,[status(thm)],[166212584,167952040]),[]).
%
% cnf(171029824,plain,(is_a_theorem(or(implies(B,or(B,C)),A))),inference(resolution,[status(thm)],[169812160,167952040]),[]).
%
% fof(cn3,plain,(((~cn3|is_a_theorem(implies(implies(not(A),A),A)))&(cn3|~is_a_theorem(implies(implies(not(p(A)),p(A)),p(A)))))),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157454888,plain,(~cn3|is_a_theorem(implies(implies(not(A),A),A))),inference(rewrite,[status(thm)],[cn3]),[]).
%
% fof(luka_cn3,plain,(cn3),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157782840,plain,(cn3),inference(rewrite,[status(thm)],[luka_cn3]),[]).
%
% cnf(166246416,plain,(is_a_theorem(implies(implies(not(A),A),A))),inference(resolution,[status(thm)],[157454888,157782840]),[]).
%
% cnf(166500392,plain,(is_a_theorem(implies(not(and(not(A),not(A))),A))),inference(paramodulation,[status(thm)],[166263824,166246416,theory(equality)]),[]).
%
% cnf(168054768,plain,(is_a_theorem(implies(or(A,A),A))),inference(paramodulation,[status(thm)],[166191976,166500392,theory(equality)]),[]).
%
% cnf(169850752,plain,(~is_a_theorem(or(A,A))|is_a_theorem(A)),inference(resolution,[status(thm)],[166212584,168054768]),[]).
%
% fof(or_1,plain,(((~or_1|is_a_theorem(implies(A,or(A,B))))&(or_1|~is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B))))))),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157072704,plain,(or_1|~is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B))))),inference(rewrite,[status(thm)],[or_1]),[]).
%
% fof(hilbert_or_1,plain,(~or_1),file('/tmp/SystemOnTPTP4980/LCL469+1.p',unknown),[]).
%
% cnf(157825496,plain,(~or_1),inference(rewrite,[status(thm)],[hilbert_or_1]),[]).
%
% cnf(166274024,plain,(~is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B))))),inference(resolution,[status(thm)],[157072704,157825496]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171029824,169850752,166274024]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------