TSTP Solution File: SYN191-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN191-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 17:11:12 EDT 2009
% Result : Unsatisfiable 17.8s
% Output : Refutation 17.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 55 ( 28 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 47 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 65 ( 12 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_26,plain,
n0(d,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177598248,plain,
n0(d,c),
inference(rewrite,[status(thm)],[axiom_26]),
[] ).
fof(rule_001,plain,
! [A,B] :
( k1(A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177665256,plain,
( k1(A)
| ~ n0(B,A) ),
inference(rewrite,[status(thm)],[rule_001]),
[] ).
cnf(193952888,plain,
k1(c),
inference(resolution,[status(thm)],[177598248,177665256]),
[] ).
fof(rule_127,plain,
! [A,B,C,D] :
( k2(A,B)
| ~ m1(C,B,A)
| ~ k1(D)
| ~ k2(D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(178999864,plain,
( k2(A,B)
| ~ m1(C,B,A)
| ~ k1(D)
| ~ k2(D,B) ),
inference(rewrite,[status(thm)],[rule_127]),
[] ).
fof(rule_007,plain,
! [A,B,C] :
( m1(A,B,A)
| ~ p0(C,B)
| ~ r0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177748704,plain,
( m1(A,B,A)
| ~ p0(C,B)
| ~ r0(A) ),
inference(rewrite,[status(thm)],[rule_007]),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177544992,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
cnf(191791280,plain,
( m1(A,B,A)
| ~ r0(A) ),
inference(resolution,[status(thm)],[177748704,177544992]),
[] ).
fof(axiom_9,plain,
r0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177517048,plain,
r0(b),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(191795688,plain,
m1(b,A,b),
inference(resolution,[status(thm)],[191791280,177517048]),
[] ).
cnf(203430616,plain,
( k2(b,A)
| ~ k1(B)
| ~ k2(B,A) ),
inference(resolution,[status(thm)],[178999864,191795688]),
[] ).
fof(rule_129,plain,
! [A,B] :
( k2(A,A)
| ~ q1(B,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(179036192,plain,
( k2(A,A)
| ~ q1(B,A,A) ),
inference(rewrite,[status(thm)],[rule_129]),
[] ).
fof(rule_107,plain,
! [A] :
( q1(e,A,A)
| ~ m0(A,d,A)
| ~ m0(e,d,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177567760,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).
cnf(178825528,plain,
q1(e,A,A),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,177567760]),
[] ).
cnf(193862504,plain,
k2(A,A),
inference(resolution,[status(thm)],[179036192,178825528]),
[] ).
cnf(461246576,plain,
( k2(b,A)
| ~ k1(A) ),
inference(resolution,[status(thm)],[203430616,193862504]),
[] ).
fof(prove_this,plain,
~ r3(c,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(179876656,plain,
~ r3(c,b,c),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
fof(rule_097,plain,
! [A] :
( q1(A,A,A)
| ~ s0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(178729136,plain,
( q1(A,A,A)
| ~ s0(A) ),
inference(rewrite,[status(thm)],[rule_097]),
[] ).
fof(axiom_1,plain,
s0(d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177456944,plain,
s0(d),
inference(rewrite,[status(thm)],[axiom_1]),
[] ).
cnf(190139200,plain,
q1(d,d,d),
inference(resolution,[status(thm)],[178729136,177456944]),
[] ).
fof(rule_124,plain,
! [A,B] :
( r1(A)
| ~ q0(A,B)
| ~ s0(d)
| ~ q1(d,B,d) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(178960048,plain,
( r1(A)
| ~ q0(A,B)
| ~ q1(d,B,d) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,177456944]),
[] ).
fof(axiom_17,plain,
! [A] : q0(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177560280,plain,
q0(A,d),
inference(rewrite,[status(thm)],[axiom_17]),
[] ).
cnf(199677688,plain,
r1(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[190139200,178960048,177560280]),
[] ).
fof(rule_188,plain,
! [A] :
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(179856720,plain,
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
inference(rewrite,[status(thm)],[rule_188]),
[] ).
fof(axiom_24,plain,
l0(c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177594416,plain,
l0(c),
inference(rewrite,[status(thm)],[axiom_24]),
[] ).
cnf(190644648,plain,
( r2(c)
| ~ r1(c) ),
inference(resolution,[status(thm)],[179856720,177594416]),
[] ).
cnf(199878256,plain,
r2(c),
inference(resolution,[status(thm)],[199677688,190644648]),
[] ).
fof(rule_272,plain,
! [A,B,C] :
( r3(A,B,C)
| ~ k2(B,C)
| ~ r2(C)
| ~ r3(C,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(181022920,plain,
( r3(A,B,C)
| ~ k2(B,C)
| ~ r2(C)
| ~ r3(C,A,A) ),
inference(rewrite,[status(thm)],[rule_272]),
[] ).
fof(rule_267,plain,
! [A,B,C] :
( r3(A,B,A)
| ~ p2(A,C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(180923304,plain,
( r3(A,B,A)
| ~ p2(A,C,B) ),
inference(rewrite,[status(thm)],[rule_267]),
[] ).
fof(rule_150,plain,
! [A,B] :
( p2(A,A,A)
| ~ m1(B,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(179344808,plain,
( p2(A,A,A)
| ~ m1(B,B,A) ),
inference(rewrite,[status(thm)],[rule_150]),
[] ).
fof(rule_020,plain,
( m1(c,c,c)
| ~ l0(c) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),
[] ).
cnf(177891608,plain,
m1(c,c,c),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_020,177594416]),
[] ).
cnf(193510536,plain,
p2(c,c,c),
inference(resolution,[status(thm)],[179344808,177891608]),
[] ).
cnf(197582800,plain,
r3(c,c,c),
inference(resolution,[status(thm)],[180923304,193510536]),
[] ).
cnf(203821384,plain,
( r3(c,A,c)
| ~ k2(A,c) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[199878256,181022920,197582800]),
[] ).
cnf(204549480,plain,
~ k2(b,c),
inference(resolution,[status(thm)],[179876656,203821384]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[193952888,461246576,204549480]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 16 seconds
% START OF PROOF SEQUENCE
% fof(axiom_26,plain,(n0(d,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177598248,plain,(n0(d,c)),inference(rewrite,[status(thm)],[axiom_26]),[]).
%
% fof(rule_001,plain,(k1(A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177665256,plain,(k1(A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_001]),[]).
%
% cnf(193952888,plain,(k1(c)),inference(resolution,[status(thm)],[177598248,177665256]),[]).
%
% fof(rule_127,plain,(k2(A,B)|~m1(C,B,A)|~k1(D)|~k2(D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(178999864,plain,(k2(A,B)|~m1(C,B,A)|~k1(D)|~k2(D,B)),inference(rewrite,[status(thm)],[rule_127]),[]).
%
% fof(rule_007,plain,(m1(A,B,A)|~p0(C,B)|~r0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177748704,plain,(m1(A,B,A)|~p0(C,B)|~r0(A)),inference(rewrite,[status(thm)],[rule_007]),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177544992,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(191791280,plain,(m1(A,B,A)|~r0(A)),inference(resolution,[status(thm)],[177748704,177544992]),[]).
%
% fof(axiom_9,plain,(r0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177517048,plain,(r0(b)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(191795688,plain,(m1(b,A,b)),inference(resolution,[status(thm)],[191791280,177517048]),[]).
%
% cnf(203430616,plain,(k2(b,A)|~k1(B)|~k2(B,A)),inference(resolution,[status(thm)],[178999864,191795688]),[]).
%
% fof(rule_129,plain,(k2(A,A)|~q1(B,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(179036192,plain,(k2(A,A)|~q1(B,A,A)),inference(rewrite,[status(thm)],[rule_129]),[]).
%
% fof(rule_107,plain,(q1(e,A,A)|~m0(A,d,A)|~m0(e,d,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177567760,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(178825528,plain,(q1(e,A,A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,177567760]),[]).
%
% cnf(193862504,plain,(k2(A,A)),inference(resolution,[status(thm)],[179036192,178825528]),[]).
%
% cnf(461246576,plain,(k2(b,A)|~k1(A)),inference(resolution,[status(thm)],[203430616,193862504]),[]).
%
% fof(prove_this,plain,(~r3(c,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(179876656,plain,(~r3(c,b,c)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(178729136,plain,(q1(A,A,A)|~s0(A)),inference(rewrite,[status(thm)],[rule_097]),[]).
%
% fof(axiom_1,plain,(s0(d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177456944,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
%
% cnf(190139200,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[178729136,177456944]),[]).
%
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(178960048,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,177456944]),[]).
%
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177560280,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
%
% cnf(199677688,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[190139200,178960048,177560280]),[]).
%
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(179856720,plain,(r2(A)|~r1(A)|~l0(A)),inference(rewrite,[status(thm)],[rule_188]),[]).
%
% fof(axiom_24,plain,(l0(c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177594416,plain,(l0(c)),inference(rewrite,[status(thm)],[axiom_24]),[]).
%
% cnf(190644648,plain,(r2(c)|~r1(c)),inference(resolution,[status(thm)],[179856720,177594416]),[]).
%
% cnf(199878256,plain,(r2(c)),inference(resolution,[status(thm)],[199677688,190644648]),[]).
%
% fof(rule_272,plain,(r3(A,B,C)|~k2(B,C)|~r2(C)|~r3(C,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(181022920,plain,(r3(A,B,C)|~k2(B,C)|~r2(C)|~r3(C,A,A)),inference(rewrite,[status(thm)],[rule_272]),[]).
%
% fof(rule_267,plain,(r3(A,B,A)|~p2(A,C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(180923304,plain,(r3(A,B,A)|~p2(A,C,B)),inference(rewrite,[status(thm)],[rule_267]),[]).
%
% fof(rule_150,plain,(p2(A,A,A)|~m1(B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(179344808,plain,(p2(A,A,A)|~m1(B,B,A)),inference(rewrite,[status(thm)],[rule_150]),[]).
%
% fof(rule_020,plain,(m1(c,c,c)|~l0(c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN191-1.tptp',unknown),[]).
%
% cnf(177891608,plain,(m1(c,c,c)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_020,177594416]),[]).
%
% cnf(193510536,plain,(p2(c,c,c)),inference(resolution,[status(thm)],[179344808,177891608]),[]).
%
% cnf(197582800,plain,(r3(c,c,c)),inference(resolution,[status(thm)],[180923304,193510536]),[]).
%
% cnf(203821384,plain,(r3(c,A,c)|~k2(A,c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[199878256,181022920,197582800]),[]).
%
% cnf(204549480,plain,(~k2(b,c)),inference(resolution,[status(thm)],[179876656,203821384]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[193952888,461246576,204549480]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------