TSTP Solution File: KRS112+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS112+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 13:27:51 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 18 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 135 ( 64 ~; 59 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 58 ( 2 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_2,plain,
! [A,D,E] :
( ( rf(A,y_nn_2(A))
| ~ cunsatisfiable(A) )
& ( cp(y_nn_2(A))
| ~ cunsatisfiable(A) )
& ( rf1(A,y_nn_3(A))
| ~ cunsatisfiable(A) )
& ( ca_ax2(y_nn_3(A))
| ~ cunsatisfiable(A) )
& ( cunsatisfiable(A)
| ~ rf1(A,D)
| ~ ca_ax2(D)
| ~ rf(A,E)
| ~ cp(E) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171549352,plain,
( ca_ax2(y_nn_3(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
fof(axiom_13,plain,
cunsatisfiable(i2003_11_14_17_21_19256),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171754056,plain,
cunsatisfiable(i2003_11_14_17_21_19256),
inference(rewrite,[status(thm)],[axiom_13]),
[] ).
cnf(177027296,plain,
ca_ax2(y_nn_3(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171549352,171754056]),
[] ).
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/KRS112+1.tptp',unknown),
[] ).
cnf(171333384,plain,
( ~ $equal(B,A)
| ~ ca_ax2(A)
| ca_ax2(B) ),
inference(rewrite,[status(thm)],[ca_Ax2_substitution_1]),
[] ).
fof(axiom_5,plain,
! [A,B] :
( ( ~ rinvf1(A,B)
| ca_vx3(B)
| ~ ca_ax2(A) )
& ( cpxcomp(A)
| ~ ca_ax2(A) )
& ( rinvf1(A,y(A,B))
| ~ cpxcomp(A)
| ca_ax2(A) )
& ( ~ ca_vx3(y(A,B))
| ~ cpxcomp(A)
| ca_ax2(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171642312,plain,
( cpxcomp(A)
| ~ ca_ax2(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
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/KRS112+1.tptp',unknown),
[] ).
cnf(171611008,plain,
( ~ cpxcomp(A)
| ra_px1(A,y0_nn_1(A)) ),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
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/KRS112+1.tptp',unknown),
[] ).
cnf(171307712,plain,
( ~ cp(A)
| ~ ra_px1(A,B) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(171568048,plain,
( cp(y_nn_2(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(177040144,plain,
cp(y_nn_2(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171568048,171754056]),
[] ).
cnf(177167296,plain,
~ ra_px1(y_nn_2(i2003_11_14_17_21_19256),A),
inference(resolution,[status(thm)],[171307712,177040144]),
[] ).
cnf(177609392,plain,
~ cpxcomp(y_nn_2(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171611008,177167296]),
[] ).
fof(cpxcomp_substitution_1,plain,
! [B,A] :
( ~ $equal(B,A)
| ~ cpxcomp(A)
| cpxcomp(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171382672,plain,
( ~ $equal(B,A)
| ~ cpxcomp(A)
| cpxcomp(B) ),
inference(rewrite,[status(thm)],[cpxcomp_substitution_1]),
[] ).
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/KRS112+1.tptp',unknown),
[] ).
cnf(171678184,plain,
( ~ rf(A,B)
| ~ rf(A,C)
| $equal(C,B) ),
inference(rewrite,[status(thm)],[axiom_7]),
[] ).
fof(axiom_14,plain,
! [A,B] :
( ~ rs(A,B)
| rf(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171759560,plain,
( ~ rs(A,B)
| rf(A,B) ),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
fof(axiom_6,plain,
! [A,C] :
( ( cowlthing(y_nn_1(A))
| ~ ca_vx3(A) )
& ( rs(A,y_nn_1(A))
| ~ ca_vx3(A) )
& ( ca_vx3(A)
| ~ rs(A,C)
| ~ cowlthing(C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171669576,plain,
( rs(A,y_nn_1(A))
| ~ ca_vx3(A) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
cnf(171651048,plain,
( ~ rinvf1(A,B)
| ca_vx3(B)
| ~ ca_ax2(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
fof(axiom_10,plain,
! [A,B] :
( ( ~ rinvf1(A,B)
| rf1(B,A) )
& ( rinvf1(A,B)
| ~ rf1(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171710440,plain,
( rinvf1(A,B)
| ~ rf1(B,A) ),
inference(rewrite,[status(thm)],[axiom_10]),
[] ).
cnf(171560696,plain,
( rf1(A,y_nn_3(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(177055384,plain,
rf1(i2003_11_14_17_21_19256,y_nn_3(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171560696,171754056]),
[] ).
cnf(177241504,plain,
rinvf1(y_nn_3(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256),
inference(resolution,[status(thm)],[171710440,177055384]),
[] ).
cnf(177341032,plain,
ca_vx3(i2003_11_14_17_21_19256),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177027296,171651048,177241504]),
[] ).
cnf(177373904,plain,
rs(i2003_11_14_17_21_19256,y_nn_1(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171669576,177341032]),
[] ).
cnf(177428472,plain,
rf(i2003_11_14_17_21_19256,y_nn_1(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171759560,177373904]),
[] ).
cnf(177541856,plain,
( ~ rf(i2003_11_14_17_21_19256,A)
| $equal(A,y_nn_1(i2003_11_14_17_21_19256)) ),
inference(resolution,[status(thm)],[171678184,177428472]),
[] ).
cnf(171579392,plain,
( rf(A,y_nn_2(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(177065512,plain,
rf(i2003_11_14_17_21_19256,y_nn_2(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171579392,171754056]),
[] ).
cnf(177555512,plain,
$equal(y_nn_2(i2003_11_14_17_21_19256),y_nn_1(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[177541856,177065512]),
[] ).
cnf(177686584,plain,
~ cpxcomp(y_nn_1(i2003_11_14_17_21_19256)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177609392,171382672,177555512]),
[] ).
cnf(177840640,plain,
~ ca_ax2(y_nn_1(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171642312,177686584]),
[] ).
cnf(177892848,plain,
( ~ $equal(y_nn_1(i2003_11_14_17_21_19256),A)
| ~ ca_ax2(A) ),
inference(resolution,[status(thm)],[171333384,177840640]),
[] ).
fof(axiom_8,plain,
! [A,B,C] :
( ~ rf1(A,B)
| ~ rf1(A,C)
| $equal(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171686712,plain,
( ~ rf1(A,B)
| ~ rf1(A,C)
| $equal(C,B) ),
inference(rewrite,[status(thm)],[axiom_8]),
[] ).
cnf(177273088,plain,
( ~ rf1(i2003_11_14_17_21_19256,A)
| $equal(A,y_nn_3(i2003_11_14_17_21_19256)) ),
inference(resolution,[status(thm)],[171686712,177055384]),
[] ).
fof(axiom_15,plain,
! [A,B] :
( ~ rs(A,B)
| rf1(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),
[] ).
cnf(171764952,plain,
( ~ rs(A,B)
| rf1(A,B) ),
inference(rewrite,[status(thm)],[axiom_15]),
[] ).
cnf(177436256,plain,
rf1(i2003_11_14_17_21_19256,y_nn_1(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[171764952,177373904]),
[] ).
cnf(177591096,plain,
$equal(y_nn_1(i2003_11_14_17_21_19256),y_nn_3(i2003_11_14_17_21_19256)),
inference(resolution,[status(thm)],[177273088,177436256]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[177027296,177892848,177591096]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(axiom_2,plain,(((rf(A,y_nn_2(A))|~cunsatisfiable(A))&(cp(y_nn_2(A))|~cunsatisfiable(A))&(rf1(A,y_nn_3(A))|~cunsatisfiable(A))&(ca_ax2(y_nn_3(A))|~cunsatisfiable(A))&(cunsatisfiable(A)|~rf1(A,D)|~ca_ax2(D)|~rf(A,E)|~cp(E)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171549352,plain,(ca_ax2(y_nn_3(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% fof(axiom_13,plain,(cunsatisfiable(i2003_11_14_17_21_19256)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171754056,plain,(cunsatisfiable(i2003_11_14_17_21_19256)),inference(rewrite,[status(thm)],[axiom_13]),[]).
%
% cnf(177027296,plain,(ca_ax2(y_nn_3(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171549352,171754056]),[]).
%
% fof(ca_Ax2_substitution_1,plain,(~$equal(B,A)|~ca_ax2(A)|ca_ax2(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171333384,plain,(~$equal(B,A)|~ca_ax2(A)|ca_ax2(B)),inference(rewrite,[status(thm)],[ca_Ax2_substitution_1]),[]).
%
% fof(axiom_5,plain,(((~rinvf1(A,B)|ca_vx3(B)|~ca_ax2(A))&(cpxcomp(A)|~ca_ax2(A))&(rinvf1(A,y(A,B))|~cpxcomp(A)|ca_ax2(A))&(~ca_vx3(y(A,B))|~cpxcomp(A)|ca_ax2(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171642312,plain,(cpxcomp(A)|~ca_ax2(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% fof(axiom_4,plain,(((~cpxcomp(A)|ra_px1(A,y0_nn_1(A)))&(cpxcomp(A)|~ra_px1(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171611008,plain,(~cpxcomp(A)|ra_px1(A,y0_nn_1(A))),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% fof(axiom_3,plain,(((~cp(A)|~ra_px1(A,B))&(cp(A)|ra_px1(A,y(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171307712,plain,(~cp(A)|~ra_px1(A,B)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(171568048,plain,(cp(y_nn_2(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(177040144,plain,(cp(y_nn_2(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171568048,171754056]),[]).
%
% cnf(177167296,plain,(~ra_px1(y_nn_2(i2003_11_14_17_21_19256),A)),inference(resolution,[status(thm)],[171307712,177040144]),[]).
%
% cnf(177609392,plain,(~cpxcomp(y_nn_2(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171611008,177167296]),[]).
%
% fof(cpxcomp_substitution_1,plain,(~$equal(B,A)|~cpxcomp(A)|cpxcomp(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171382672,plain,(~$equal(B,A)|~cpxcomp(A)|cpxcomp(B)),inference(rewrite,[status(thm)],[cpxcomp_substitution_1]),[]).
%
% fof(axiom_7,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171678184,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),inference(rewrite,[status(thm)],[axiom_7]),[]).
%
% fof(axiom_14,plain,(~rs(A,B)|rf(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171759560,plain,(~rs(A,B)|rf(A,B)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% fof(axiom_6,plain,(((cowlthing(y_nn_1(A))|~ca_vx3(A))&(rs(A,y_nn_1(A))|~ca_vx3(A))&(ca_vx3(A)|~rs(A,C)|~cowlthing(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171669576,plain,(rs(A,y_nn_1(A))|~ca_vx3(A)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% cnf(171651048,plain,(~rinvf1(A,B)|ca_vx3(B)|~ca_ax2(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% fof(axiom_10,plain,(((~rinvf1(A,B)|rf1(B,A))&(rinvf1(A,B)|~rf1(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171710440,plain,(rinvf1(A,B)|~rf1(B,A)),inference(rewrite,[status(thm)],[axiom_10]),[]).
%
% cnf(171560696,plain,(rf1(A,y_nn_3(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(177055384,plain,(rf1(i2003_11_14_17_21_19256,y_nn_3(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171560696,171754056]),[]).
%
% cnf(177241504,plain,(rinvf1(y_nn_3(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256)),inference(resolution,[status(thm)],[171710440,177055384]),[]).
%
% cnf(177341032,plain,(ca_vx3(i2003_11_14_17_21_19256)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177027296,171651048,177241504]),[]).
%
% cnf(177373904,plain,(rs(i2003_11_14_17_21_19256,y_nn_1(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171669576,177341032]),[]).
%
% cnf(177428472,plain,(rf(i2003_11_14_17_21_19256,y_nn_1(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171759560,177373904]),[]).
%
% cnf(177541856,plain,(~rf(i2003_11_14_17_21_19256,A)|$equal(A,y_nn_1(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171678184,177428472]),[]).
%
% cnf(171579392,plain,(rf(A,y_nn_2(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(177065512,plain,(rf(i2003_11_14_17_21_19256,y_nn_2(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171579392,171754056]),[]).
%
% cnf(177555512,plain,($equal(y_nn_2(i2003_11_14_17_21_19256),y_nn_1(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[177541856,177065512]),[]).
%
% cnf(177686584,plain,(~cpxcomp(y_nn_1(i2003_11_14_17_21_19256))),inference(forward_subsumption_resolution__resolution,[status(thm)],[177609392,171382672,177555512]),[]).
%
% cnf(177840640,plain,(~ca_ax2(y_nn_1(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171642312,177686584]),[]).
%
% cnf(177892848,plain,(~$equal(y_nn_1(i2003_11_14_17_21_19256),A)|~ca_ax2(A)),inference(resolution,[status(thm)],[171333384,177840640]),[]).
%
% fof(axiom_8,plain,(~rf1(A,B)|~rf1(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171686712,plain,(~rf1(A,B)|~rf1(A,C)|$equal(C,B)),inference(rewrite,[status(thm)],[axiom_8]),[]).
%
% cnf(177273088,plain,(~rf1(i2003_11_14_17_21_19256,A)|$equal(A,y_nn_3(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171686712,177055384]),[]).
%
% fof(axiom_15,plain,(~rs(A,B)|rf1(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS112+1.tptp',unknown),[]).
%
% cnf(171764952,plain,(~rs(A,B)|rf1(A,B)),inference(rewrite,[status(thm)],[axiom_15]),[]).
%
% cnf(177436256,plain,(rf1(i2003_11_14_17_21_19256,y_nn_1(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[171764952,177373904]),[]).
%
% cnf(177591096,plain,($equal(y_nn_1(i2003_11_14_17_21_19256),y_nn_3(i2003_11_14_17_21_19256))),inference(resolution,[status(thm)],[177273088,177436256]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[177027296,177892848,177591096]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------