TSTP Solution File: KRS108+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS108+1 : TPTP v3.4.2. Released v3.1.0.
% 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 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:27:40 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 130 ( 59 ~; 56 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 37 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cp1_substitution_1,plain,
! [B,A] :
( ~ $equal(B,A)
| ~ cp1(A)
| cp1(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(143568904,plain,
( ~ $equal(B,A)
| ~ cp1(A)
| cp1(B) ),
inference(rewrite,[status(thm)],[cp1_substitution_1]),
[] ).
fof(axiom_15,plain,
! [A,C,D,E] :
( ( ~ rr(A,C)
| ~ rr(A,D)
| $equal(D,C)
| ~ ca_ax14(A) )
& ( rr(A,y_nn_3(A))
| ~ ca_ax14(A) )
& ( cp1(y_nn_3(A))
| ~ ca_ax14(A) )
& ( rr(A,y0(A,C,D,E))
| ~ rr(A,E)
| ~ cp1(E)
| ca_ax14(A) )
& ( rr(A,y1(A,C,D,E))
| ~ rr(A,E)
| ~ cp1(E)
| ca_ax14(A) )
& ( ~ $equal(y1(A,C,D,E),y0(A,C,D,E))
| ~ rr(A,E)
| ~ cp1(E)
| ca_ax14(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(144209648,plain,
( cp1(y_nn_3(A))
| ~ ca_ax14(A) ),
inference(rewrite,[status(thm)],[axiom_15]),
[] ).
fof(axiom_2,plain,
! [A,C] :
( ( cp2(A)
| ~ cunsatisfiable(A) )
& ( rinvr(A,y_nn_1(A))
| ~ cunsatisfiable(A) )
& ( ca_ax14(y_nn_1(A))
| ~ cunsatisfiable(A) )
& ( cunsatisfiable(A)
| ~ rinvr(A,C)
| ~ ca_ax14(C)
| ~ cp2(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(143899264,plain,
( ca_ax14(y_nn_1(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
fof(axiom_26,plain,
cunsatisfiable(i2003_11_14_17_21_04740),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(144517224,plain,
cunsatisfiable(i2003_11_14_17_21_04740),
inference(rewrite,[status(thm)],[axiom_26]),
[] ).
cnf(149924352,plain,
ca_ax14(y_nn_1(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[143899264,144517224]),
[] ).
cnf(150235664,plain,
cp1(y_nn_3(y_nn_1(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[144209648,149924352]),
[] ).
cnf(150765256,plain,
( ~ $equal(A,y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))
| cp1(A) ),
inference(resolution,[status(thm)],[143568904,150235664]),
[] ).
fof(axiom_3,plain,
! [A] :
( ~ cp1(A)
| ca_cx1(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(143936736,plain,
( ~ cp1(A)
| ca_cx1(A) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
fof(axiom_16,plain,
! [A] :
( ( cp5xcomp(A)
| ~ ca_cx1(A) )
& ( cp3xcomp(A)
| ~ ca_cx1(A) )
& ( cp4xcomp(A)
| ~ ca_cx1(A) )
& ( cp2xcomp(A)
| ~ ca_cx1(A) )
& ( ca_cx1(A)
| ~ cp2xcomp(A)
| ~ cp5xcomp(A)
| ~ cp3xcomp(A)
| ~ cp4xcomp(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(144260696,plain,
( cp2xcomp(A)
| ~ ca_cx1(A) ),
inference(rewrite,[status(thm)],[axiom_16]),
[] ).
fof(axiom_6,plain,
! [A,B] :
( ( ~ cp2xcomp(A)
| ~ ra_px5(A,B) )
& ( cp2xcomp(A)
| ra_px5(A,y(A,B)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(143990824,plain,
( ~ cp2xcomp(A)
| ~ ra_px5(A,B) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
fof(axiom_4,plain,
! [A,C] :
( ( ~ cp2(A)
| ra_px5(A,y0_nn_1(A)) )
& ( cp2(A)
| ~ ra_px5(A,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(143960136,plain,
( ~ cp2(A)
| ra_px5(A,y0_nn_1(A)) ),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
cnf(143924384,plain,
( cp2(A)
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(149906800,plain,
cp2(i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[143924384,144517224]),
[] ).
cnf(149990680,plain,
ra_px5(i2003_11_14_17_21_04740,y0_nn_1(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[143960136,149906800]),
[] ).
cnf(150328824,plain,
~ cp2xcomp(i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[143990824,149990680]),
[] ).
cnf(150370992,plain,
~ ca_cx1(i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[144260696,150328824]),
[] ).
cnf(150425696,plain,
~ cp1(i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[143936736,150370992]),
[] ).
cnf(150779920,plain,
~ $equal(i2003_11_14_17_21_04740,y_nn_3(y_nn_1(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[150765256,150425696]),
[] ).
cnf(144236656,plain,
( ~ rr(A,C)
| ~ rr(A,D)
| $equal(D,C)
| ~ ca_ax14(A) ),
inference(rewrite,[status(thm)],[axiom_15]),
[] ).
cnf(150891872,plain,
( ~ rr(y_nn_1(i2003_11_14_17_21_04740),B)
| ~ rr(y_nn_1(i2003_11_14_17_21_04740),C)
| $equal(C,B) ),
inference(resolution,[status(thm)],[144236656,149924352]),
[] ).
cnf(144220768,plain,
( rr(A,y_nn_3(A))
| ~ ca_ax14(A) ),
inference(rewrite,[status(thm)],[axiom_15]),
[] ).
cnf(150248024,plain,
rr(y_nn_1(i2003_11_14_17_21_04740),y_nn_3(y_nn_1(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[144220768,149924352]),
[] ).
cnf(151170800,plain,
( ~ rr(y_nn_1(i2003_11_14_17_21_04740),B)
| $equal(B,y_nn_3(y_nn_1(i2003_11_14_17_21_04740))) ),
inference(resolution,[status(thm)],[150891872,150248024]),
[] ).
fof(axiom_25,plain,
! [A,B] :
( ( ~ rinvr(A,B)
| rr(B,A) )
& ( rinvr(A,B)
| ~ rr(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),
[] ).
cnf(144512936,plain,
( ~ rinvr(A,B)
| rr(B,A) ),
inference(rewrite,[status(thm)],[axiom_25]),
[] ).
cnf(143911696,plain,
( rinvr(A,y_nn_1(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(149940232,plain,
rinvr(i2003_11_14_17_21_04740,y_nn_1(i2003_11_14_17_21_04740)),
inference(resolution,[status(thm)],[143911696,144517224]),
[] ).
cnf(150303416,plain,
rr(y_nn_1(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740),
inference(resolution,[status(thm)],[144512936,149940232]),
[] ).
cnf(151198496,plain,
$equal(i2003_11_14_17_21_04740,y_nn_3(y_nn_1(i2003_11_14_17_21_04740))),
inference(resolution,[status(thm)],[151170800,150303416]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[150779920,151198496]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cp1_substitution_1,plain,(~$equal(B,A)|~cp1(A)|cp1(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(143568904,plain,(~$equal(B,A)|~cp1(A)|cp1(B)),inference(rewrite,[status(thm)],[cp1_substitution_1]),[]).
%
% fof(axiom_15,plain,(((~rr(A,C)|~rr(A,D)|$equal(D,C)|~ca_ax14(A))&(rr(A,y_nn_3(A))|~ca_ax14(A))&(cp1(y_nn_3(A))|~ca_ax14(A))&(rr(A,y0(A,C,D,E))|~rr(A,E)|~cp1(E)|ca_ax14(A))&(rr(A,y1(A,C,D,E))|~rr(A,E)|~cp1(E)|ca_ax14(A))&(~$equal(y1(A,C,D,E),y0(A,C,D,E))|~rr(A,E)|~cp1(E)|ca_ax14(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(144209648,plain,(cp1(y_nn_3(A))|~ca_ax14(A)),inference(rewrite,[status(thm)],[axiom_15]),[]).
%
% fof(axiom_2,plain,(((cp2(A)|~cunsatisfiable(A))&(rinvr(A,y_nn_1(A))|~cunsatisfiable(A))&(ca_ax14(y_nn_1(A))|~cunsatisfiable(A))&(cunsatisfiable(A)|~rinvr(A,C)|~ca_ax14(C)|~cp2(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(143899264,plain,(ca_ax14(y_nn_1(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% fof(axiom_26,plain,(cunsatisfiable(i2003_11_14_17_21_04740)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(144517224,plain,(cunsatisfiable(i2003_11_14_17_21_04740)),inference(rewrite,[status(thm)],[axiom_26]),[]).
%
% cnf(149924352,plain,(ca_ax14(y_nn_1(i2003_11_14_17_21_04740))),inference(resolution,[status(thm)],[143899264,144517224]),[]).
%
% cnf(150235664,plain,(cp1(y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))),inference(resolution,[status(thm)],[144209648,149924352]),[]).
%
% cnf(150765256,plain,(~$equal(A,y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))|cp1(A)),inference(resolution,[status(thm)],[143568904,150235664]),[]).
%
% fof(axiom_3,plain,(~cp1(A)|ca_cx1(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(143936736,plain,(~cp1(A)|ca_cx1(A)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% fof(axiom_16,plain,(((cp5xcomp(A)|~ca_cx1(A))&(cp3xcomp(A)|~ca_cx1(A))&(cp4xcomp(A)|~ca_cx1(A))&(cp2xcomp(A)|~ca_cx1(A))&(ca_cx1(A)|~cp2xcomp(A)|~cp5xcomp(A)|~cp3xcomp(A)|~cp4xcomp(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(144260696,plain,(cp2xcomp(A)|~ca_cx1(A)),inference(rewrite,[status(thm)],[axiom_16]),[]).
%
% fof(axiom_6,plain,(((~cp2xcomp(A)|~ra_px5(A,B))&(cp2xcomp(A)|ra_px5(A,y(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(143990824,plain,(~cp2xcomp(A)|~ra_px5(A,B)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% fof(axiom_4,plain,(((~cp2(A)|ra_px5(A,y0_nn_1(A)))&(cp2(A)|~ra_px5(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(143960136,plain,(~cp2(A)|ra_px5(A,y0_nn_1(A))),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% cnf(143924384,plain,(cp2(A)|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(149906800,plain,(cp2(i2003_11_14_17_21_04740)),inference(resolution,[status(thm)],[143924384,144517224]),[]).
%
% cnf(149990680,plain,(ra_px5(i2003_11_14_17_21_04740,y0_nn_1(i2003_11_14_17_21_04740))),inference(resolution,[status(thm)],[143960136,149906800]),[]).
%
% cnf(150328824,plain,(~cp2xcomp(i2003_11_14_17_21_04740)),inference(resolution,[status(thm)],[143990824,149990680]),[]).
%
% cnf(150370992,plain,(~ca_cx1(i2003_11_14_17_21_04740)),inference(resolution,[status(thm)],[144260696,150328824]),[]).
%
% cnf(150425696,plain,(~cp1(i2003_11_14_17_21_04740)),inference(resolution,[status(thm)],[143936736,150370992]),[]).
%
% cnf(150779920,plain,(~$equal(i2003_11_14_17_21_04740,y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))),inference(resolution,[status(thm)],[150765256,150425696]),[]).
%
% cnf(144236656,plain,(~rr(A,C)|~rr(A,D)|$equal(D,C)|~ca_ax14(A)),inference(rewrite,[status(thm)],[axiom_15]),[]).
%
% cnf(150891872,plain,(~rr(y_nn_1(i2003_11_14_17_21_04740),B)|~rr(y_nn_1(i2003_11_14_17_21_04740),C)|$equal(C,B)),inference(resolution,[status(thm)],[144236656,149924352]),[]).
%
% cnf(144220768,plain,(rr(A,y_nn_3(A))|~ca_ax14(A)),inference(rewrite,[status(thm)],[axiom_15]),[]).
%
% cnf(150248024,plain,(rr(y_nn_1(i2003_11_14_17_21_04740),y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))),inference(resolution,[status(thm)],[144220768,149924352]),[]).
%
% cnf(151170800,plain,(~rr(y_nn_1(i2003_11_14_17_21_04740),B)|$equal(B,y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))),inference(resolution,[status(thm)],[150891872,150248024]),[]).
%
% fof(axiom_25,plain,(((~rinvr(A,B)|rr(B,A))&(rinvr(A,B)|~rr(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS108+1.tptp',unknown),[]).
%
% cnf(144512936,plain,(~rinvr(A,B)|rr(B,A)),inference(rewrite,[status(thm)],[axiom_25]),[]).
%
% cnf(143911696,plain,(rinvr(A,y_nn_1(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(149940232,plain,(rinvr(i2003_11_14_17_21_04740,y_nn_1(i2003_11_14_17_21_04740))),inference(resolution,[status(thm)],[143911696,144517224]),[]).
%
% cnf(150303416,plain,(rr(y_nn_1(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)),inference(resolution,[status(thm)],[144512936,149940232]),[]).
%
% cnf(151198496,plain,($equal(i2003_11_14_17_21_04740,y_nn_3(y_nn_1(i2003_11_14_17_21_04740)))),inference(resolution,[status(thm)],[151170800,150303416]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[150779920,151198496]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------