%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS109+1 : TPTP v3.4.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:27:43 EDT 2009
% Result : Unsatisfiable 0.0s
% Output : Refutation 0.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 127 ( 57 ~; 56 |; 14 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 48 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_7,plain,
! [A,B,C] :
( ~ rf(A,B)
| ~ rf(A,C)
| $equal(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163790800,plain,
( ~ rf(A,B)
| ~ rf(A,C)
| $equal(C,B) ),
inference(rewrite,[status(thm)],[axiom_7]),
[] ).
fof(axiom_2,plain,
! [A,C] :
( ( rf(A,y_nn_1(A))
| ~ cunsatisfiable(A) )
& ( ca_ax2(y_nn_1(A))
| ~ cunsatisfiable(A) )
& ( cpxcomp(A)
| ~ cunsatisfiable(A) )
& ( cunsatisfiable(A)
| ~ cpxcomp(A)
| ~ rf(A,C)
| ~ ca_ax2(C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163658424,plain,
( rf(A,y_nn_1(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
fof(axiom_13,plain,
cunsatisfiable(i2003_11_14_17_21_08508),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163865040,plain,
cunsatisfiable(i2003_11_14_17_21_08508),
inference(rewrite,[status(thm)],[axiom_13]),
[] ).
cnf(169162392,plain,
rf(i2003_11_14_17_21_08508,y_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[163658424,163865040]),
[] ).
cnf(169304592,plain,
( ~ rf(i2003_11_14_17_21_08508,A)
| $equal(A,y_nn_1(i2003_11_14_17_21_08508)) ),
inference(resolution,[status(thm)],[163790800,169162392]),
[] ).
fof(axiom_14,plain,
! [A,B] :
( ~ rs(A,B)
| rf(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163870576,plain,
( ~ rs(A,B)
| rf(A,B) ),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
fof(axiom_6,plain,
! [A,C] :
( ( cp(y_nn_1(A))
| ~ ca_vx3(A) )
& ( rs(A,y_nn_1(A))
| ~ ca_vx3(A) )
& ( ca_vx3(A)
| ~ rs(A,C)
| ~ cp(C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163775640,plain,
( rs(A,y_nn_1(A))
| ~ ca_vx3(A) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
fof(axiom_5,plain,
! [A,C,B] :
( ( ~ rinvf(A,C)
| ca_vx3(C)
| ~ ca_ax2(A) )
& ( ~ rinvs(A,B)
| cp(B)
| ~ ca_ax2(A) )
& ( ~ ca_vx3(y(A,B,C))
| ~ cp(y_nn_1(A,B,C))
| ca_ax2(A) )
& ( rinvf(A,y(A,B,C))
| ~ cp(y_nn_1(A,B,C))
| ca_ax2(A) )
& ( ~ ca_vx3(y(A,B,C))
| rinvs(A,y_nn_1(A,B,C))
| ca_ax2(A) )
& ( rinvf(A,y(A,B,C))
| rinvs(A,y_nn_1(A,B,C))
| ca_ax2(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163755584,plain,
( ~ rinvf(A,C)
| ca_vx3(C)
| ~ ca_ax2(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(163651200,plain,
( ca_ax2(y_nn_1(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(169147248,plain,
ca_ax2(y_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[163651200,163865040]),
[] ).
cnf(169259392,plain,
( ~ rinvf(y_nn_1(i2003_11_14_17_21_08508),B)
| ca_vx3(B) ),
inference(resolution,[status(thm)],[163755584,169147248]),
[] ).
fof(axiom_9,plain,
! [A,B] :
( ( ~ rinvf(A,B)
| rf(B,A) )
& ( rinvf(A,B)
| ~ rf(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163809416,plain,
( rinvf(A,B)
| ~ rf(B,A) ),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(169269648,plain,
rinvf(y_nn_1(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[163809416,169162392]),
[] ).
cnf(169429704,plain,
ca_vx3(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[169259392,169269648]),
[] ).
cnf(169471736,plain,
rs(i2003_11_14_17_21_08508,y_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[163775640,169429704]),
[] ).
cnf(169563224,plain,
rf(i2003_11_14_17_21_08508,y_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[163870576,169471736]),
[] ).
cnf(169659048,plain,
$equal(y_nn_1(i2003_11_14_17_21_08508),y_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[169304592,169563224]),
[] ).
fof(ca_Ax2_substitution_1,plain,
! [B,A] :
( ~ $equal(B,A)
| ~ ca_ax2(A)
| ca_ax2(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163420632,plain,
( ~ $equal(B,A)
| ~ ca_ax2(A)
| ca_ax2(B) ),
inference(rewrite,[status(thm)],[ca_Ax2_substitution_1]),
[] ).
cnf(163742792,plain,
( ~ rinvs(A,B)
| cp(B)
| ~ ca_ax2(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
fof(axiom_3,plain,
! [A,B] :
( ( ~ cp(A)
| ~ ra_px1(A,B) )
& ( cp(A)
| ra_px1(A,y(A,B)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163676960,plain,
( ~ cp(A)
| ~ ra_px1(A,B) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
fof(axiom_4,plain,
! [A,C] :
( ( ~ cpxcomp(A)
| ra_px1(A,y0_nn_1(A)) )
& ( cpxcomp(A)
| ~ ra_px1(A,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163693344,plain,
( ~ cpxcomp(A)
| ra_px1(A,y0_nn_1(A)) ),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
cnf(163639776,plain,
( cpxcomp(A)
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(167930096,plain,
cpxcomp(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[163639776,163865040]),
[] ).
cnf(169197088,plain,
ra_px1(i2003_11_14_17_21_08508,y0_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[163693344,167930096]),
[] ).
cnf(169325560,plain,
~ cp(i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[163676960,169197088]),
[] ).
cnf(169403440,plain,
( ~ rinvs(A,i2003_11_14_17_21_08508)
| ~ ca_ax2(A) ),
inference(resolution,[status(thm)],[163742792,169325560]),
[] ).
fof(axiom_11,plain,
! [A,B] :
( ( ~ rinvs(A,B)
| rs(B,A) )
& ( rinvs(A,B)
| ~ rs(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),
[] ).
cnf(163843184,plain,
( rinvs(A,B)
| ~ rs(B,A) ),
inference(rewrite,[status(thm)],[axiom_11]),
[] ).
cnf(169555248,plain,
rinvs(y_nn_1(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolution,[status(thm)],[163843184,169471736]),
[] ).
cnf(169631632,plain,
~ ca_ax2(y_nn_1(i2003_11_14_17_21_08508)),
inference(resolution,[status(thm)],[169403440,169555248]),
[] ).
cnf(169739120,plain,
( ~ $equal(y_nn_1(i2003_11_14_17_21_08508),A)
| ~ ca_ax2(A) ),
inference(resolution,[status(thm)],[163420632,169631632]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[169659048,169739120,169147248]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(axiom_7,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163790800,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),inference(rewrite,[status(thm)],[axiom_7]),[]).
%
% fof(axiom_2,plain,(((rf(A,y_nn_1(A))|~cunsatisfiable(A))&(ca_ax2(y_nn_1(A))|~cunsatisfiable(A))&(cpxcomp(A)|~cunsatisfiable(A))&(cunsatisfiable(A)|~cpxcomp(A)|~rf(A,C)|~ca_ax2(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163658424,plain,(rf(A,y_nn_1(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% fof(axiom_13,plain,(cunsatisfiable(i2003_11_14_17_21_08508)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163865040,plain,(cunsatisfiable(i2003_11_14_17_21_08508)),inference(rewrite,[status(thm)],[axiom_13]),[]).
%
% cnf(169162392,plain,(rf(i2003_11_14_17_21_08508,y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[163658424,163865040]),[]).
%
% cnf(169304592,plain,(~rf(i2003_11_14_17_21_08508,A)|$equal(A,y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[163790800,169162392]),[]).
%
% fof(axiom_14,plain,(~rs(A,B)|rf(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163870576,plain,(~rs(A,B)|rf(A,B)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% fof(axiom_6,plain,(((cp(y_nn_1(A))|~ca_vx3(A))&(rs(A,y_nn_1(A))|~ca_vx3(A))&(ca_vx3(A)|~rs(A,C)|~cp(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163775640,plain,(rs(A,y_nn_1(A))|~ca_vx3(A)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% fof(axiom_5,plain,(((~rinvf(A,C)|ca_vx3(C)|~ca_ax2(A))&(~rinvs(A,B)|cp(B)|~ca_ax2(A))&(~ca_vx3(y(A,B,C))|~cp(y_nn_1(A,B,C))|ca_ax2(A))&(rinvf(A,y(A,B,C))|~cp(y_nn_1(A,B,C))|ca_ax2(A))&(~ca_vx3(y(A,B,C))|rinvs(A,y_nn_1(A,B,C))|ca_ax2(A))&(rinvf(A,y(A,B,C))|rinvs(A,y_nn_1(A,B,C))|ca_ax2(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163755584,plain,(~rinvf(A,C)|ca_vx3(C)|~ca_ax2(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(163651200,plain,(ca_ax2(y_nn_1(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(169147248,plain,(ca_ax2(y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[163651200,163865040]),[]).
%
% cnf(169259392,plain,(~rinvf(y_nn_1(i2003_11_14_17_21_08508),B)|ca_vx3(B)),inference(resolution,[status(thm)],[163755584,169147248]),[]).
%
% fof(axiom_9,plain,(((~rinvf(A,B)|rf(B,A))&(rinvf(A,B)|~rf(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163809416,plain,(rinvf(A,B)|~rf(B,A)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(169269648,plain,(rinvf(y_nn_1(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)),inference(resolution,[status(thm)],[163809416,169162392]),[]).
%
% cnf(169429704,plain,(ca_vx3(i2003_11_14_17_21_08508)),inference(resolution,[status(thm)],[169259392,169269648]),[]).
%
% cnf(169471736,plain,(rs(i2003_11_14_17_21_08508,y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[163775640,169429704]),[]).
%
% cnf(169563224,plain,(rf(i2003_11_14_17_21_08508,y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[163870576,169471736]),[]).
%
% cnf(169659048,plain,($equal(y_nn_1(i2003_11_14_17_21_08508),y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[169304592,169563224]),[]).
%
% fof(ca_Ax2_substitution_1,plain,(~$equal(B,A)|~ca_ax2(A)|ca_ax2(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163420632,plain,(~$equal(B,A)|~ca_ax2(A)|ca_ax2(B)),inference(rewrite,[status(thm)],[ca_Ax2_substitution_1]),[]).
%
% cnf(163742792,plain,(~rinvs(A,B)|cp(B)|~ca_ax2(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% fof(axiom_3,plain,(((~cp(A)|~ra_px1(A,B))&(cp(A)|ra_px1(A,y(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163676960,plain,(~cp(A)|~ra_px1(A,B)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% fof(axiom_4,plain,(((~cpxcomp(A)|ra_px1(A,y0_nn_1(A)))&(cpxcomp(A)|~ra_px1(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163693344,plain,(~cpxcomp(A)|ra_px1(A,y0_nn_1(A))),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% cnf(163639776,plain,(cpxcomp(A)|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(167930096,plain,(cpxcomp(i2003_11_14_17_21_08508)),inference(resolution,[status(thm)],[163639776,163865040]),[]).
%
% cnf(169197088,plain,(ra_px1(i2003_11_14_17_21_08508,y0_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[163693344,167930096]),[]).
%
% cnf(169325560,plain,(~cp(i2003_11_14_17_21_08508)),inference(resolution,[status(thm)],[163676960,169197088]),[]).
%
% cnf(169403440,plain,(~rinvs(A,i2003_11_14_17_21_08508)|~ca_ax2(A)),inference(resolution,[status(thm)],[163742792,169325560]),[]).
%
% fof(axiom_11,plain,(((~rinvs(A,B)|rs(B,A))&(rinvs(A,B)|~rs(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS109+1.tptp',unknown),[]).
%
% cnf(163843184,plain,(rinvs(A,B)|~rs(B,A)),inference(rewrite,[status(thm)],[axiom_11]),[]).
%
% cnf(169555248,plain,(rinvs(y_nn_1(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)),inference(resolution,[status(thm)],[163843184,169471736]),[]).
%
% cnf(169631632,plain,(~ca_ax2(y_nn_1(i2003_11_14_17_21_08508))),inference(resolution,[status(thm)],[169403440,169555248]),[]).
%
% cnf(169739120,plain,(~$equal(y_nn_1(i2003_11_14_17_21_08508),A)|~ca_ax2(A)),inference(resolution,[status(thm)],[163420632,169631632]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[169659048,169739120,169147248]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------