TSTP Solution File: LCL452+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL452+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 13:50:39 EDT 2009
% Result : Theorem 23.2s
% Output : Refutation 23.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 21 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 59 ( 27 ~; 26 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 0 con; 1-2 aty)
% Number of variables : 48 ( 9 sgn 12 !; 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/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(150419768,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/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151389792,plain,
modus_ponens,
inference(rewrite,[status(thm)],[hilbert_modus_ponens]),
[] ).
cnf(154299392,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[150419768,151389792]),
[] ).
fof(implies_1,plain,
! [A,B] :
( ( ~ implies_1
| is_a_theorem(implies(A,implies(B,A))) )
& ( implies_1
| ~ is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B)))) ) ),
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(150546696,plain,
( ~ implies_1
| is_a_theorem(implies(A,implies(B,A))) ),
inference(rewrite,[status(thm)],[implies_1]),
[] ).
fof(hilbert_implies_1,plain,
implies_1,
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(150372192,plain,
implies_1,
inference(rewrite,[status(thm)],[hilbert_implies_1]),
[] ).
cnf(160011272,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolution,[status(thm)],[150546696,150372192]),
[] ).
cnf(164305936,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[154299392,160011272]),
[] ).
fof(op_or,plain,
! [A,B] :
( ~ op_or
| $equal(not(and(not(A),not(B))),or(A,B)) ),
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151274520,plain,
( ~ op_or
| $equal(not(and(not(A),not(B))),or(A,B)) ),
inference(rewrite,[status(thm)],[op_or]),
[] ).
fof(hilbert_op_or,plain,
op_or,
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151353680,plain,
op_or,
inference(rewrite,[status(thm)],[hilbert_op_or]),
[] ).
cnf(159949592,plain,
$equal(not(and(not(A),not(B))),or(A,B)),
inference(resolution,[status(thm)],[151274520,151353680]),
[] ).
fof(op_implies_and,plain,
! [A,B] :
( ~ op_implies_and
| $equal(not(and(A,not(B))),implies(A,B)) ),
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151310152,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/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151365872,plain,
op_implies_and,
inference(rewrite,[status(thm)],[hilbert_op_implies_and]),
[] ).
cnf(159961032,plain,
$equal(not(and(A,not(B))),implies(A,B)),
inference(resolution,[status(thm)],[151310152,151365872]),
[] ).
cnf(161853536,plain,
$equal(or(A,B),implies(not(A),B)),
inference(paramodulation,[status(thm)],[159949592,159961032,theory(equality)]),
[] ).
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/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(150731472,plain,
( ~ or_1
| is_a_theorem(implies(A,or(A,B))) ),
inference(rewrite,[status(thm)],[or_1]),
[] ).
fof(hilbert_or_1,plain,
or_1,
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151484352,plain,
or_1,
inference(rewrite,[status(thm)],[hilbert_or_1]),
[] ).
cnf(160059376,plain,
is_a_theorem(implies(A,or(A,B))),
inference(resolution,[status(thm)],[150731472,151484352]),
[] ).
cnf(162586744,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(paramodulation,[status(thm)],[161853536,160059376,theory(equality)]),
[] ).
cnf(165991320,plain,
is_a_theorem(implies(A,implies(B,implies(not(B),C)))),
inference(resolution,[status(thm)],[164305936,162586744]),
[] ).
cnf(164289608,plain,
( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[154299392,160011272]),
[] ).
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/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151050168,plain,
( cn2
| ~ is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B)))) ),
inference(rewrite,[status(thm)],[cn2]),
[] ).
fof(luka_cn2,plain,
~ cn2,
file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
[] ).
cnf(151582520,plain,
~ cn2,
inference(rewrite,[status(thm)],[luka_cn2]),
[] ).
cnf(160118416,plain,
~ is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B)))),
inference(resolution,[status(thm)],[151050168,151582520]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[165991320,164289608,160118416]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 23 seconds
% START OF PROOF SEQUENCE
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(150419768,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(hilbert_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151389792,plain,(modus_ponens),inference(rewrite,[status(thm)],[hilbert_modus_ponens]),[]).
%
% cnf(154299392,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[150419768,151389792]),[]).
%
% fof(implies_1,plain,(((~implies_1|is_a_theorem(implies(A,implies(B,A))))&(implies_1|~is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B))))))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(150546696,plain,(~implies_1|is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[implies_1]),[]).
%
% fof(hilbert_implies_1,plain,(implies_1),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(150372192,plain,(implies_1),inference(rewrite,[status(thm)],[hilbert_implies_1]),[]).
%
% cnf(160011272,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(resolution,[status(thm)],[150546696,150372192]),[]).
%
% cnf(164305936,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[154299392,160011272]),[]).
%
% fof(op_or,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151274520,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),inference(rewrite,[status(thm)],[op_or]),[]).
%
% fof(hilbert_op_or,plain,(op_or),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151353680,plain,(op_or),inference(rewrite,[status(thm)],[hilbert_op_or]),[]).
%
% cnf(159949592,plain,($equal(not(and(not(A),not(B))),or(A,B))),inference(resolution,[status(thm)],[151274520,151353680]),[]).
%
% fof(op_implies_and,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151310152,plain,(~op_implies_and|$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/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151365872,plain,(op_implies_and),inference(rewrite,[status(thm)],[hilbert_op_implies_and]),[]).
%
% cnf(159961032,plain,($equal(not(and(A,not(B))),implies(A,B))),inference(resolution,[status(thm)],[151310152,151365872]),[]).
%
% cnf(161853536,plain,($equal(or(A,B),implies(not(A),B))),inference(paramodulation,[status(thm)],[159949592,159961032,theory(equality)]),[]).
%
% 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/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(150731472,plain,(~or_1|is_a_theorem(implies(A,or(A,B)))),inference(rewrite,[status(thm)],[or_1]),[]).
%
% fof(hilbert_or_1,plain,(or_1),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151484352,plain,(or_1),inference(rewrite,[status(thm)],[hilbert_or_1]),[]).
%
% cnf(160059376,plain,(is_a_theorem(implies(A,or(A,B)))),inference(resolution,[status(thm)],[150731472,151484352]),[]).
%
% cnf(162586744,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(paramodulation,[status(thm)],[161853536,160059376,theory(equality)]),[]).
%
% cnf(165991320,plain,(is_a_theorem(implies(A,implies(B,implies(not(B),C))))),inference(resolution,[status(thm)],[164305936,162586744]),[]).
%
% cnf(164289608,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[154299392,160011272]),[]).
%
% 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/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151050168,plain,(cn2|~is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B))))),inference(rewrite,[status(thm)],[cn2]),[]).
%
% fof(luka_cn2,plain,(~cn2),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
%
% cnf(151582520,plain,(~cn2),inference(rewrite,[status(thm)],[luka_cn2]),[]).
%
% cnf(160118416,plain,(~is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B))))),inference(resolution,[status(thm)],[151050168,151582520]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[165991320,164289608,160118416]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------