TSTP Solution File: LCL499+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL499+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 13:51:40 EDT 2009
% Result : Theorem 14.2s
% Output : Refutation 14.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 57 ( 26 ~; 25 |; 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 : 34 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(principia_op_and,plain,
op_and,
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157169656,plain,
op_and,
inference(rewrite,[status(thm)],[principia_op_and]),
[] ).
fof(op_and,plain,
! [A,B] :
( ~ op_and
| $equal(not(or(not(A),not(B))),and(A,B)) ),
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157096288,plain,
( ~ op_and
| $equal(not(or(not(A),not(B))),and(A,B)) ),
inference(rewrite,[status(thm)],[op_and]),
[] ).
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/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(156230216,plain,
( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[modus_ponens]),
[] ).
fof(principia_modus_ponens,plain,
modus_ponens,
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157193544,plain,
modus_ponens,
inference(rewrite,[status(thm)],[principia_modus_ponens]),
[] ).
cnf(165686072,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[156230216,157193544]),
[] ).
fof(r3,plain,
! [A,B] :
( ( ~ r3
| is_a_theorem(implies(or(A,B),or(B,A))) )
& ( r3
| ~ is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B)))) ) ),
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(156987992,plain,
( ~ r3
| is_a_theorem(implies(or(A,B),or(B,A))) ),
inference(rewrite,[status(thm)],[r3]),
[] ).
fof(principia_r3,plain,
r3,
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157226808,plain,
r3,
inference(rewrite,[status(thm)],[principia_r3]),
[] ).
cnf(165722096,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[156987992,157226808]),
[] ).
cnf(168213016,plain,
( ~ is_a_theorem(or(A,B))
| is_a_theorem(or(B,A)) ),
inference(resolution,[status(thm)],[165686072,165722096]),
[] ).
fof(op_implies_or,plain,
! [A,B] :
( ~ op_implies_or
| $equal(or(not(A),B),implies(A,B)) ),
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157127800,plain,
( ~ op_implies_or
| $equal(or(not(A),B),implies(A,B)) ),
inference(rewrite,[status(thm)],[op_implies_or]),
[] ).
fof(principia_op_implies_or,plain,
op_implies_or,
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157157504,plain,
op_implies_or,
inference(rewrite,[status(thm)],[principia_op_implies_or]),
[] ).
cnf(165654744,plain,
$equal(or(not(A),B),implies(A,B)),
inference(resolution,[status(thm)],[157127800,157157504]),
[] ).
fof(r1,plain,
! [A] :
( ( ~ r1
| is_a_theorem(implies(or(A,A),A)) )
& ( r1
| ~ is_a_theorem(implies(or(p(A),p(A)),p(A))) ) ),
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(156931160,plain,
( ~ r1
| is_a_theorem(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],[r1]),
[] ).
fof(principia_r1,plain,
r1,
file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157204688,plain,
r1,
inference(rewrite,[status(thm)],[principia_r1]),
[] ).
cnf(165701976,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[156931160,157204688]),
[] ).
cnf(165908000,plain,
is_a_theorem(or(not(or(A,A)),A)),
inference(paramodulation,[status(thm)],[165654744,165701976,theory(equality)]),
[] ).
cnf(172669184,plain,
is_a_theorem(or(A,not(or(A,A)))),
inference(resolution,[status(thm)],[168213016,165908000]),
[] ).
cnf(173077840,plain,
is_a_theorem(implies(A,not(or(not(A),not(A))))),
inference(paramodulation,[status(thm)],[172669184,165654744,theory(equality)]),
[] ).
cnf(311657224,plain,
is_a_theorem(implies(A,and(A,A))),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157169656,157096288,173077840,theory(equality)]),
[] ).
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/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(156183384,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/SystemOnTPTP9980/LCL499+1.p',unknown),
[] ).
cnf(157297952,plain,
~ kn1,
inference(rewrite,[status(thm)],[rosser_kn1]),
[] ).
cnf(165776288,plain,
~ is_a_theorem(implies(p(A),and(p(A),p(A)))),
inference(resolution,[status(thm)],[156183384,157297952]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[311657224,165776288]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 14 seconds
% START OF PROOF SEQUENCE
% fof(principia_op_and,plain,(op_and),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157169656,plain,(op_and),inference(rewrite,[status(thm)],[principia_op_and]),[]).
%
% fof(op_and,plain,(~op_and|$equal(not(or(not(A),not(B))),and(A,B))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157096288,plain,(~op_and|$equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[op_and]),[]).
%
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(156230216,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(principia_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157193544,plain,(modus_ponens),inference(rewrite,[status(thm)],[principia_modus_ponens]),[]).
%
% cnf(165686072,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[156230216,157193544]),[]).
%
% fof(r3,plain,(((~r3|is_a_theorem(implies(or(A,B),or(B,A))))&(r3|~is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B))))))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(156987992,plain,(~r3|is_a_theorem(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[r3]),[]).
%
% fof(principia_r3,plain,(r3),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157226808,plain,(r3),inference(rewrite,[status(thm)],[principia_r3]),[]).
%
% cnf(165722096,plain,(is_a_theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[156987992,157226808]),[]).
%
% cnf(168213016,plain,(~is_a_theorem(or(A,B))|is_a_theorem(or(B,A))),inference(resolution,[status(thm)],[165686072,165722096]),[]).
%
% fof(op_implies_or,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157127800,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_or]),[]).
%
% fof(principia_op_implies_or,plain,(op_implies_or),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157157504,plain,(op_implies_or),inference(rewrite,[status(thm)],[principia_op_implies_or]),[]).
%
% cnf(165654744,plain,($equal(or(not(A),B),implies(A,B))),inference(resolution,[status(thm)],[157127800,157157504]),[]).
%
% fof(r1,plain,(((~r1|is_a_theorem(implies(or(A,A),A)))&(r1|~is_a_theorem(implies(or(p(A),p(A)),p(A)))))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(156931160,plain,(~r1|is_a_theorem(implies(or(A,A),A))),inference(rewrite,[status(thm)],[r1]),[]).
%
% fof(principia_r1,plain,(r1),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157204688,plain,(r1),inference(rewrite,[status(thm)],[principia_r1]),[]).
%
% cnf(165701976,plain,(is_a_theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[156931160,157204688]),[]).
%
% cnf(165908000,plain,(is_a_theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[165654744,165701976,theory(equality)]),[]).
%
% cnf(172669184,plain,(is_a_theorem(or(A,not(or(A,A))))),inference(resolution,[status(thm)],[168213016,165908000]),[]).
%
% cnf(173077840,plain,(is_a_theorem(implies(A,not(or(not(A),not(A)))))),inference(paramodulation,[status(thm)],[172669184,165654744,theory(equality)]),[]).
%
% cnf(311657224,plain,(is_a_theorem(implies(A,and(A,A)))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157169656,157096288,173077840,theory(equality)]),[]).
%
% 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/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(156183384,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/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
%
% cnf(157297952,plain,(~kn1),inference(rewrite,[status(thm)],[rosser_kn1]),[]).
%
% cnf(165776288,plain,(~is_a_theorem(implies(p(A),and(p(A),p(A))))),inference(resolution,[status(thm)],[156183384,157297952]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[311657224,165776288]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------