TSTP Solution File: KRS118+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS118+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 13:28:05 EDT 2009
% Result : Unsatisfiable 18.9s
% Output : Refutation 18.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 13 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 151 ( 71 ~; 66 |; 14 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 6 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_6,plain,
! [A,C] :
( ( cd(y_nn_1(A))
| ~ ca_vx3(A) )
& ( rinvf(A,y_nn_1(A))
| ~ ca_vx3(A) )
& ( ca_vx3(A)
| ~ rinvf(A,C)
| ~ cd(C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151808800,plain,
( ca_vx3(A)
| ~ rinvf(A,C)
| ~ cd(C) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
fof(axiom_2,plain,
! [A,B,E] :
( ( rinvf(A,y_nn_2(A,B))
| ~ cunsatisfiable(A) )
& ( cd(y_nn_2(A,B))
| ~ cunsatisfiable(A) )
& ( ccxcomp(A)
| ~ cunsatisfiable(A) )
& ( ~ rinvr(A,B)
| ca_vx3(B)
| ~ cunsatisfiable(A) )
& ( ~ ca_vx3(y_nn_1(A,B))
| ~ rinvf(A,E)
| ~ cd(E)
| ~ ccxcomp(A)
| cunsatisfiable(A) )
& ( rinvr(A,y_nn_1(A,B))
| ~ rinvf(A,E)
| ~ cd(E)
| ~ ccxcomp(A)
| cunsatisfiable(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151721360,plain,
( cd(y_nn_2(A,B))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
fof(axiom_11,plain,
cunsatisfiable(i2003_11_14_17_21_4056),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151879488,plain,
cunsatisfiable(i2003_11_14_17_21_4056),
inference(rewrite,[status(thm)],[axiom_11]),
[] ).
cnf(157145144,plain,
cd(y_nn_2(i2003_11_14_17_21_4056,A)),
inference(resolution,[status(thm)],[151721360,151879488]),
[] ).
cnf(157307296,plain,
( ca_vx3(A)
| ~ rinvf(A,y_nn_2(i2003_11_14_17_21_4056,C)) ),
inference(resolution,[status(thm)],[151808800,157145144]),
[] ).
cnf(151732640,plain,
( rinvf(A,y_nn_2(A,B))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(157155376,plain,
rinvf(i2003_11_14_17_21_4056,y_nn_2(i2003_11_14_17_21_4056,A)),
inference(resolution,[status(thm)],[151732640,151879488]),
[] ).
cnf(157442584,plain,
ca_vx3(i2003_11_14_17_21_4056),
inference(resolution,[status(thm)],[157307296,157155376]),
[] ).
cnf(151703096,plain,
( ~ rinvr(A,B)
| ca_vx3(B)
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(157190008,plain,
( ~ rinvr(i2003_11_14_17_21_4056,A)
| ca_vx3(A) ),
inference(resolution,[status(thm)],[151703096,151879488]),
[] ).
fof(axiom_12,plain,
! [A,B] :
( ~ rf(A,B)
| rr(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151884880,plain,
( ~ rf(A,B)
| rr(A,B) ),
inference(rewrite,[status(thm)],[axiom_12]),
[] ).
fof(axiom_9,plain,
! [A,B] :
( ( ~ rinvr(A,B)
| rr(B,A) )
& ( rinvr(A,B)
| ~ rr(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151856888,plain,
( rinvr(A,B)
| ~ rr(B,A) ),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(158756392,plain,
( ~ rf(A,B)
| rinvr(B,A) ),
inference(resolution,[status(thm)],[151884880,151856888]),
[] ).
fof(axiom_8,plain,
! [A,B] :
( ( ~ rinvf(A,B)
| rf(B,A) )
& ( rinvf(A,B)
| ~ rf(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151851200,plain,
( ~ rinvf(A,B)
| rf(B,A) ),
inference(rewrite,[status(thm)],[axiom_8]),
[] ).
cnf(151815056,plain,
( rinvf(A,y_nn_1(A))
| ~ ca_vx3(A) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
cnf(158638216,plain,
( rf(y_nn_1(A),A)
| ~ ca_vx3(A) ),
inference(resolution,[status(thm)],[151851200,151815056]),
[] ).
cnf(159094384,plain,
( rinvr(A,y_nn_1(A))
| ~ ca_vx3(A) ),
inference(resolution,[status(thm)],[158756392,158638216]),
[] ).
cnf(160494632,plain,
ca_vx3(y_nn_1(i2003_11_14_17_21_4056)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[157442584,157190008,159094384]),
[] ).
cnf(151825504,plain,
( cd(y_nn_1(A))
| ~ ca_vx3(A) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
cnf(160519304,plain,
cd(y_nn_1(y_nn_1(i2003_11_14_17_21_4056))),
inference(resolution,[status(thm)],[160494632,151825504]),
[] ).
fof(axiom_5,plain,
! [A,C] :
( ( cc(A)
| ~ cd(A) )
& ( rf(A,y_nn_1(A))
| ~ cd(A) )
& ( ccxcomp(y_nn_1(A))
| ~ cd(A) )
& ( cd(A)
| ~ rf(A,C)
| ~ ccxcomp(C)
| ~ cc(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151790248,plain,
( rf(A,y_nn_1(A))
| ~ cd(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(160627640,plain,
rf(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)),y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)))),
inference(resolution,[status(thm)],[160519304,151790248]),
[] ).
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/KRS118+1.tptp',unknown),
[] ).
cnf(151834216,plain,
( ~ rf(A,B)
| ~ rf(A,C)
| $equal(C,B) ),
inference(rewrite,[status(thm)],[axiom_7]),
[] ).
cnf(160574264,plain,
rf(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)),y_nn_1(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[160494632,158638216]),
[] ).
cnf(175017224,plain,
( ~ rf(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)),A)
| $equal(A,y_nn_1(i2003_11_14_17_21_4056)) ),
inference(resolution,[status(thm)],[151834216,160574264]),
[] ).
fof(cd_substitution_1,plain,
! [B,A] :
( ~ $equal(B,A)
| ~ cd(A)
| cd(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151525984,plain,
( ~ $equal(B,A)
| ~ cd(A)
| cd(B) ),
inference(rewrite,[status(thm)],[cd_substitution_1]),
[] ).
cnf(157471264,plain,
cd(y_nn_1(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[151825504,157442584]),
[] ).
cnf(157542208,plain,
( ~ $equal(A,y_nn_1(i2003_11_14_17_21_4056))
| cd(A) ),
inference(resolution,[status(thm)],[151525984,157471264]),
[] ).
fof(axiom_4,plain,
! [A,C] :
( ( ~ ccxcomp(A)
| ra_px1(A,y0_nn_1(A)) )
& ( ccxcomp(A)
| ~ ra_px1(A,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151763248,plain,
( ~ ccxcomp(A)
| ra_px1(A,y0_nn_1(A)) ),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
fof(axiom_3,plain,
! [A,B] :
( ( ~ cc(A)
| ~ ra_px1(A,B) )
& ( cc(A)
| ra_px1(A,y(A,B)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),
[] ).
cnf(151746992,plain,
( ~ cc(A)
| ~ ra_px1(A,B) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(158445128,plain,
( ~ ccxcomp(A)
| ~ cc(A) ),
inference(resolution,[status(thm)],[151763248,151746992]),
[] ).
cnf(151799792,plain,
( cc(A)
| ~ cd(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(158563064,plain,
( ~ ccxcomp(A)
| ~ cd(A) ),
inference(resolution,[status(thm)],[158445128,151799792]),
[] ).
cnf(151783088,plain,
( ccxcomp(y_nn_1(A))
| ~ cd(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(158709384,plain,
( ~ cd(y_nn_1(A))
| ~ cd(A) ),
inference(resolution,[status(thm)],[158563064,151783088]),
[] ).
cnf(160681456,plain,
~ cd(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)))),
inference(resolution,[status(thm)],[160519304,158709384]),
[] ).
cnf(162301416,plain,
~ $equal(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_4056))),y_nn_1(i2003_11_14_17_21_4056)),
inference(resolution,[status(thm)],[157542208,160681456]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[160627640,175017224,162301416]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 19 seconds
% START OF PROOF SEQUENCE
% fof(axiom_6,plain,(((cd(y_nn_1(A))|~ca_vx3(A))&(rinvf(A,y_nn_1(A))|~ca_vx3(A))&(ca_vx3(A)|~rinvf(A,C)|~cd(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151808800,plain,(ca_vx3(A)|~rinvf(A,C)|~cd(C)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% fof(axiom_2,plain,(((rinvf(A,y_nn_2(A,B))|~cunsatisfiable(A))&(cd(y_nn_2(A,B))|~cunsatisfiable(A))&(ccxcomp(A)|~cunsatisfiable(A))&(~rinvr(A,B)|ca_vx3(B)|~cunsatisfiable(A))&(~ca_vx3(y_nn_1(A,B))|~rinvf(A,E)|~cd(E)|~ccxcomp(A)|cunsatisfiable(A))&(rinvr(A,y_nn_1(A,B))|~rinvf(A,E)|~cd(E)|~ccxcomp(A)|cunsatisfiable(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151721360,plain,(cd(y_nn_2(A,B))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% fof(axiom_11,plain,(cunsatisfiable(i2003_11_14_17_21_4056)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151879488,plain,(cunsatisfiable(i2003_11_14_17_21_4056)),inference(rewrite,[status(thm)],[axiom_11]),[]).
%
% cnf(157145144,plain,(cd(y_nn_2(i2003_11_14_17_21_4056,A))),inference(resolution,[status(thm)],[151721360,151879488]),[]).
%
% cnf(157307296,plain,(ca_vx3(A)|~rinvf(A,y_nn_2(i2003_11_14_17_21_4056,C))),inference(resolution,[status(thm)],[151808800,157145144]),[]).
%
% cnf(151732640,plain,(rinvf(A,y_nn_2(A,B))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(157155376,plain,(rinvf(i2003_11_14_17_21_4056,y_nn_2(i2003_11_14_17_21_4056,A))),inference(resolution,[status(thm)],[151732640,151879488]),[]).
%
% cnf(157442584,plain,(ca_vx3(i2003_11_14_17_21_4056)),inference(resolution,[status(thm)],[157307296,157155376]),[]).
%
% cnf(151703096,plain,(~rinvr(A,B)|ca_vx3(B)|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(157190008,plain,(~rinvr(i2003_11_14_17_21_4056,A)|ca_vx3(A)),inference(resolution,[status(thm)],[151703096,151879488]),[]).
%
% fof(axiom_12,plain,(~rf(A,B)|rr(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151884880,plain,(~rf(A,B)|rr(A,B)),inference(rewrite,[status(thm)],[axiom_12]),[]).
%
% fof(axiom_9,plain,(((~rinvr(A,B)|rr(B,A))&(rinvr(A,B)|~rr(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151856888,plain,(rinvr(A,B)|~rr(B,A)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(158756392,plain,(~rf(A,B)|rinvr(B,A)),inference(resolution,[status(thm)],[151884880,151856888]),[]).
%
% fof(axiom_8,plain,(((~rinvf(A,B)|rf(B,A))&(rinvf(A,B)|~rf(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151851200,plain,(~rinvf(A,B)|rf(B,A)),inference(rewrite,[status(thm)],[axiom_8]),[]).
%
% cnf(151815056,plain,(rinvf(A,y_nn_1(A))|~ca_vx3(A)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% cnf(158638216,plain,(rf(y_nn_1(A),A)|~ca_vx3(A)),inference(resolution,[status(thm)],[151851200,151815056]),[]).
%
% cnf(159094384,plain,(rinvr(A,y_nn_1(A))|~ca_vx3(A)),inference(resolution,[status(thm)],[158756392,158638216]),[]).
%
% cnf(160494632,plain,(ca_vx3(y_nn_1(i2003_11_14_17_21_4056))),inference(forward_subsumption_resolution__resolution,[status(thm)],[157442584,157190008,159094384]),[]).
%
% cnf(151825504,plain,(cd(y_nn_1(A))|~ca_vx3(A)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% cnf(160519304,plain,(cd(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)))),inference(resolution,[status(thm)],[160494632,151825504]),[]).
%
% fof(axiom_5,plain,(((cc(A)|~cd(A))&(rf(A,y_nn_1(A))|~cd(A))&(ccxcomp(y_nn_1(A))|~cd(A))&(cd(A)|~rf(A,C)|~ccxcomp(C)|~cc(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151790248,plain,(rf(A,y_nn_1(A))|~cd(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(160627640,plain,(rf(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)),y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_4056))))),inference(resolution,[status(thm)],[160519304,151790248]),[]).
%
% fof(axiom_7,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151834216,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),inference(rewrite,[status(thm)],[axiom_7]),[]).
%
% cnf(160574264,plain,(rf(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)),y_nn_1(i2003_11_14_17_21_4056))),inference(resolution,[status(thm)],[160494632,158638216]),[]).
%
% cnf(175017224,plain,(~rf(y_nn_1(y_nn_1(i2003_11_14_17_21_4056)),A)|$equal(A,y_nn_1(i2003_11_14_17_21_4056))),inference(resolution,[status(thm)],[151834216,160574264]),[]).
%
% fof(cd_substitution_1,plain,(~$equal(B,A)|~cd(A)|cd(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151525984,plain,(~$equal(B,A)|~cd(A)|cd(B)),inference(rewrite,[status(thm)],[cd_substitution_1]),[]).
%
% cnf(157471264,plain,(cd(y_nn_1(i2003_11_14_17_21_4056))),inference(resolution,[status(thm)],[151825504,157442584]),[]).
%
% cnf(157542208,plain,(~$equal(A,y_nn_1(i2003_11_14_17_21_4056))|cd(A)),inference(resolution,[status(thm)],[151525984,157471264]),[]).
%
% fof(axiom_4,plain,(((~ccxcomp(A)|ra_px1(A,y0_nn_1(A)))&(ccxcomp(A)|~ra_px1(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151763248,plain,(~ccxcomp(A)|ra_px1(A,y0_nn_1(A))),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% fof(axiom_3,plain,(((~cc(A)|~ra_px1(A,B))&(cc(A)|ra_px1(A,y(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS118+1.tptp',unknown),[]).
%
% cnf(151746992,plain,(~cc(A)|~ra_px1(A,B)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(158445128,plain,(~ccxcomp(A)|~cc(A)),inference(resolution,[status(thm)],[151763248,151746992]),[]).
%
% cnf(151799792,plain,(cc(A)|~cd(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(158563064,plain,(~ccxcomp(A)|~cd(A)),inference(resolution,[status(thm)],[158445128,151799792]),[]).
%
% cnf(151783088,plain,(ccxcomp(y_nn_1(A))|~cd(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(158709384,plain,(~cd(y_nn_1(A))|~cd(A)),inference(resolution,[status(thm)],[158563064,151783088]),[]).
%
% cnf(160681456,plain,(~cd(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_4056))))),inference(resolution,[status(thm)],[160519304,158709384]),[]).
%
% cnf(162301416,plain,(~$equal(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_4056))),y_nn_1(i2003_11_14_17_21_4056))),inference(resolution,[status(thm)],[157542208,160681456]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[160627640,175017224,162301416]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------