TSTP Solution File: KRS106+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS106+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 13:27:35 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 106 ( 51 ~; 47 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 4 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_6,plain,
! [A,B,C] :
( ~ rf2(A,B)
| ~ rf2(A,C)
| $equal(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169195016,plain,
( ~ rf2(A,B)
| ~ rf2(A,C)
| $equal(C,B) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
fof(axiom_2,plain,
! [A,E,F,G] :
( ( rf1(A,y_nn_4(A))
| ~ cunsatisfiable(A) )
& ( cp1(y_nn_4(A))
| ~ cunsatisfiable(A) )
& ( rf2(A,y_nn_3(A))
| ~ cunsatisfiable(A) )
& ( cp1xcomp(y_nn_3(A))
| ~ cunsatisfiable(A) )
& ( rf3(A,y_nn_5(A))
| ~ cunsatisfiable(A) )
& ( cp2(y_nn_5(A))
| ~ cunsatisfiable(A) )
& ( cunsatisfiable(A)
| ~ rf3(A,E)
| ~ cp2(E)
| ~ rf1(A,F)
| ~ cp1(F)
| ~ rf2(A,G)
| ~ cp1xcomp(G) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169126424,plain,
( rf2(A,y_nn_3(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
fof(axiom_8,plain,
cunsatisfiable(i2003_11_14_17_20_57644),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169207624,plain,
cunsatisfiable(i2003_11_14_17_20_57644),
inference(rewrite,[status(thm)],[axiom_8]),
[] ).
cnf(174500800,plain,
rf2(i2003_11_14_17_20_57644,y_nn_3(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169126424,169207624]),
[] ).
cnf(174789016,plain,
( ~ rf2(i2003_11_14_17_20_57644,A)
| $equal(y_nn_3(i2003_11_14_17_20_57644),A) ),
inference(resolution,[status(thm)],[169195016,174500800]),
[] ).
fof(axiom_10,plain,
! [A,B] :
( ~ rf3(A,B)
| rf2(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169222432,plain,
( ~ rf3(A,B)
| rf2(A,B) ),
inference(rewrite,[status(thm)],[axiom_10]),
[] ).
cnf(169112488,plain,
( rf3(A,y_nn_5(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(174490832,plain,
rf3(i2003_11_14_17_20_57644,y_nn_5(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169112488,169207624]),
[] ).
cnf(174709960,plain,
rf2(i2003_11_14_17_20_57644,y_nn_5(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169222432,174490832]),
[] ).
cnf(174868960,plain,
$equal(y_nn_3(i2003_11_14_17_20_57644),y_nn_5(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[174789016,174709960]),
[] ).
fof(axiom_3,plain,
! [A,B] :
( ( ~ cp1(A)
| ~ ra_px1(A,B) )
& ( cp1(A)
| ra_px1(A,y(A,B)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169150424,plain,
( cp1(A)
| ra_px1(A,y(A,B)) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(169161544,plain,
( ~ cp1(A)
| ~ ra_px1(A,B) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(169137352,plain,
( cp1(y_nn_4(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(174479936,plain,
cp1(y_nn_4(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169137352,169207624]),
[] ).
cnf(174640576,plain,
~ ra_px1(y_nn_4(i2003_11_14_17_20_57644),A),
inference(resolution,[status(thm)],[169161544,174479936]),
[] ).
fof(ra_Px1_substitution_1,plain,
! [B,A,C] :
( ~ $equal(B,A)
| ~ ra_px1(A,C)
| ra_px1(B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(168980704,plain,
( ~ $equal(B,A)
| ~ ra_px1(A,C)
| ra_px1(B,C) ),
inference(rewrite,[status(thm)],[ra_Px1_substitution_1]),
[] ).
fof(axiom_5,plain,
! [A,B,C] :
( ~ rf1(A,B)
| ~ rf1(A,C)
| $equal(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169182560,plain,
( ~ rf1(A,B)
| ~ rf1(A,C)
| $equal(C,B) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(169144352,plain,
( rf1(A,y_nn_4(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(174514856,plain,
rf1(i2003_11_14_17_20_57644,y_nn_4(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169144352,169207624]),
[] ).
cnf(174821952,plain,
( ~ rf1(i2003_11_14_17_20_57644,A)
| $equal(y_nn_4(i2003_11_14_17_20_57644),A) ),
inference(resolution,[status(thm)],[169182560,174514856]),
[] ).
fof(axiom_9,plain,
! [A,B] :
( ~ rf3(A,B)
| rf1(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169217232,plain,
( ~ rf3(A,B)
| rf1(A,B) ),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(174702176,plain,
rf1(i2003_11_14_17_20_57644,y_nn_5(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169217232,174490832]),
[] ).
cnf(174838568,plain,
$equal(y_nn_4(i2003_11_14_17_20_57644),y_nn_5(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[174821952,174702176]),
[] ).
cnf(175021312,plain,
~ ra_px1(y_nn_5(i2003_11_14_17_20_57644),A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174640576,168980704,174838568]),
[] ).
cnf(175105240,plain,
cp1(y_nn_5(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169150424,175021312]),
[] ).
fof(cp1_substitution_1,plain,
! [B,A] :
( ~ $equal(B,A)
| ~ cp1(A)
| cp1(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(168955328,plain,
( ~ $equal(B,A)
| ~ cp1(A)
| cp1(B) ),
inference(rewrite,[status(thm)],[cp1_substitution_1]),
[] ).
fof(axiom_4,plain,
! [A,C] :
( ( ~ cp1xcomp(A)
| ra_px1(A,y0_nn_1(A)) )
& ( cp1xcomp(A)
| ~ ra_px1(A,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),
[] ).
cnf(169174232,plain,
( ~ cp1xcomp(A)
| ra_px1(A,y0_nn_1(A)) ),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
cnf(169119424,plain,
( cp1xcomp(y_nn_3(A))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(174459200,plain,
cp1xcomp(y_nn_3(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[169119424,169207624]),
[] ).
cnf(174588520,plain,
ra_px1(y_nn_3(i2003_11_14_17_20_57644),y0_nn_1(y_nn_3(i2003_11_14_17_20_57644))),
inference(resolution,[status(thm)],[169174232,174459200]),
[] ).
cnf(175326560,plain,
~ cp1(y_nn_3(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[174588520,169161544]),
[] ).
cnf(175641256,plain,
( ~ $equal(y_nn_3(i2003_11_14_17_20_57644),A)
| ~ cp1(A) ),
inference(resolution,[status(thm)],[168955328,175326560]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[174868960,175105240,175641256]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(axiom_6,plain,(~rf2(A,B)|~rf2(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169195016,plain,(~rf2(A,B)|~rf2(A,C)|$equal(C,B)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% fof(axiom_2,plain,(((rf1(A,y_nn_4(A))|~cunsatisfiable(A))&(cp1(y_nn_4(A))|~cunsatisfiable(A))&(rf2(A,y_nn_3(A))|~cunsatisfiable(A))&(cp1xcomp(y_nn_3(A))|~cunsatisfiable(A))&(rf3(A,y_nn_5(A))|~cunsatisfiable(A))&(cp2(y_nn_5(A))|~cunsatisfiable(A))&(cunsatisfiable(A)|~rf3(A,E)|~cp2(E)|~rf1(A,F)|~cp1(F)|~rf2(A,G)|~cp1xcomp(G)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169126424,plain,(rf2(A,y_nn_3(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% fof(axiom_8,plain,(cunsatisfiable(i2003_11_14_17_20_57644)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169207624,plain,(cunsatisfiable(i2003_11_14_17_20_57644)),inference(rewrite,[status(thm)],[axiom_8]),[]).
%
% cnf(174500800,plain,(rf2(i2003_11_14_17_20_57644,y_nn_3(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169126424,169207624]),[]).
%
% cnf(174789016,plain,(~rf2(i2003_11_14_17_20_57644,A)|$equal(y_nn_3(i2003_11_14_17_20_57644),A)),inference(resolution,[status(thm)],[169195016,174500800]),[]).
%
% fof(axiom_10,plain,(~rf3(A,B)|rf2(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169222432,plain,(~rf3(A,B)|rf2(A,B)),inference(rewrite,[status(thm)],[axiom_10]),[]).
%
% cnf(169112488,plain,(rf3(A,y_nn_5(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(174490832,plain,(rf3(i2003_11_14_17_20_57644,y_nn_5(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169112488,169207624]),[]).
%
% cnf(174709960,plain,(rf2(i2003_11_14_17_20_57644,y_nn_5(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169222432,174490832]),[]).
%
% cnf(174868960,plain,($equal(y_nn_3(i2003_11_14_17_20_57644),y_nn_5(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[174789016,174709960]),[]).
%
% fof(axiom_3,plain,(((~cp1(A)|~ra_px1(A,B))&(cp1(A)|ra_px1(A,y(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169150424,plain,(cp1(A)|ra_px1(A,y(A,B))),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(169161544,plain,(~cp1(A)|~ra_px1(A,B)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(169137352,plain,(cp1(y_nn_4(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(174479936,plain,(cp1(y_nn_4(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169137352,169207624]),[]).
%
% cnf(174640576,plain,(~ra_px1(y_nn_4(i2003_11_14_17_20_57644),A)),inference(resolution,[status(thm)],[169161544,174479936]),[]).
%
% fof(ra_Px1_substitution_1,plain,(~$equal(B,A)|~ra_px1(A,C)|ra_px1(B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(168980704,plain,(~$equal(B,A)|~ra_px1(A,C)|ra_px1(B,C)),inference(rewrite,[status(thm)],[ra_Px1_substitution_1]),[]).
%
% fof(axiom_5,plain,(~rf1(A,B)|~rf1(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169182560,plain,(~rf1(A,B)|~rf1(A,C)|$equal(C,B)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(169144352,plain,(rf1(A,y_nn_4(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(174514856,plain,(rf1(i2003_11_14_17_20_57644,y_nn_4(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169144352,169207624]),[]).
%
% cnf(174821952,plain,(~rf1(i2003_11_14_17_20_57644,A)|$equal(y_nn_4(i2003_11_14_17_20_57644),A)),inference(resolution,[status(thm)],[169182560,174514856]),[]).
%
% fof(axiom_9,plain,(~rf3(A,B)|rf1(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169217232,plain,(~rf3(A,B)|rf1(A,B)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(174702176,plain,(rf1(i2003_11_14_17_20_57644,y_nn_5(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169217232,174490832]),[]).
%
% cnf(174838568,plain,($equal(y_nn_4(i2003_11_14_17_20_57644),y_nn_5(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[174821952,174702176]),[]).
%
% cnf(175021312,plain,(~ra_px1(y_nn_5(i2003_11_14_17_20_57644),A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174640576,168980704,174838568]),[]).
%
% cnf(175105240,plain,(cp1(y_nn_5(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169150424,175021312]),[]).
%
% fof(cp1_substitution_1,plain,(~$equal(B,A)|~cp1(A)|cp1(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(168955328,plain,(~$equal(B,A)|~cp1(A)|cp1(B)),inference(rewrite,[status(thm)],[cp1_substitution_1]),[]).
%
% fof(axiom_4,plain,(((~cp1xcomp(A)|ra_px1(A,y0_nn_1(A)))&(cp1xcomp(A)|~ra_px1(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS106+1.tptp',unknown),[]).
%
% cnf(169174232,plain,(~cp1xcomp(A)|ra_px1(A,y0_nn_1(A))),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% cnf(169119424,plain,(cp1xcomp(y_nn_3(A))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(174459200,plain,(cp1xcomp(y_nn_3(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[169119424,169207624]),[]).
%
% cnf(174588520,plain,(ra_px1(y_nn_3(i2003_11_14_17_20_57644),y0_nn_1(y_nn_3(i2003_11_14_17_20_57644)))),inference(resolution,[status(thm)],[169174232,174459200]),[]).
%
% cnf(175326560,plain,(~cp1(y_nn_3(i2003_11_14_17_20_57644))),inference(resolution,[status(thm)],[174588520,169161544]),[]).
%
% cnf(175641256,plain,(~$equal(y_nn_3(i2003_11_14_17_20_57644),A)|~cp1(A)),inference(resolution,[status(thm)],[168955328,175326560]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[174868960,175105240,175641256]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------