TSTP Solution File: SYN157-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN157-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 17:01:11 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 65 ( 30 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 127 ( 67 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 93 ( 29 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_126,plain,
! [A,B,C] :
( s1(A)
| ~ q0(A,B)
| ~ s1(C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(152096600,plain,
( s1(A)
| ~ q0(A,B)
| ~ s1(C) ),
inference(rewrite,[status(thm)],[rule_126]),
[] ).
fof(axiom_17,plain,
! [A] : q0(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150672512,plain,
q0(A,d),
inference(rewrite,[status(thm)],[axiom_17]),
[] ).
cnf(169059608,plain,
( s1(A)
| ~ s1(B) ),
inference(resolution,[status(thm)],[152096600,150672512]),
[] ).
fof(rule_125,plain,
! [A] :
( s1(A)
| ~ p0(A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(152084456,plain,
( s1(A)
| ~ p0(A,A) ),
inference(rewrite,[status(thm)],[rule_125]),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150657224,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
cnf(165038784,plain,
s1(b),
inference(resolution,[status(thm)],[152084456,150657224]),
[] ).
cnf(169067224,plain,
s1(A),
inference(resolution,[status(thm)],[169059608,165038784]),
[] ).
fof(rule_133,plain,
! [A,B,C,D] :
( l2(A,A)
| ~ p0(B,B)
| ~ s1(C)
| ~ m0(D,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(152205544,plain,
( l2(A,A)
| ~ p0(B,B)
| ~ s1(C)
| ~ m0(D,C,A) ),
inference(rewrite,[status(thm)],[rule_133]),
[] ).
cnf(165233808,plain,
( l2(A,A)
| ~ s1(B)
| ~ m0(C,B,A) ),
inference(resolution,[status(thm)],[152205544,150657224]),
[] ).
fof(axiom_4,plain,
m0(e,d,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150598808,plain,
m0(e,d,a),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
cnf(173576912,plain,
l2(a,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169067224,165233808,150598808]),
[] ).
fof(rule_097,plain,
! [A] :
( q1(A,A,A)
| ~ s0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(151841368,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/SYN157-1.tptp',unknown),
[] ).
cnf(150569176,plain,
s0(d),
inference(rewrite,[status(thm)],[axiom_1]),
[] ).
cnf(163251528,plain,
q1(d,d,d),
inference(resolution,[status(thm)],[151841368,150569176]),
[] ).
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/SYN157-1.tptp',unknown),
[] ).
cnf(152072280,plain,
( r1(A)
| ~ q0(A,B)
| ~ q1(d,B,d) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,150569176]),
[] ).
cnf(170955360,plain,
r1(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[163251528,152072280,150672512]),
[] ).
fof(rule_258,plain,
! [A,B,C] :
( q3(A,A)
| ~ r2(A)
| ~ s1(B)
| ~ l2(C,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(153921072,plain,
( q3(A,A)
| ~ r2(A)
| ~ s1(B)
| ~ l2(C,C) ),
inference(rewrite,[status(thm)],[rule_258]),
[] ).
cnf(165376112,plain,
( q3(A,A)
| ~ r2(A)
| ~ l2(B,B) ),
inference(resolution,[status(thm)],[153921072,165038784]),
[] ).
fof(rule_298,plain,
! [A,B,C,D] :
( r4(A)
| ~ n3(A)
| ~ q3(B,C)
| ~ p0(D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(154490144,plain,
( r4(A)
| ~ n3(A)
| ~ q3(B,C)
| ~ p0(D,A) ),
inference(rewrite,[status(thm)],[rule_298]),
[] ).
cnf(165153696,plain,
( r4(A)
| ~ n3(A)
| ~ q3(B,C) ),
inference(resolution,[status(thm)],[154490144,150657224]),
[] ).
fof(rule_240,plain,
! [A,B,C] :
( n3(A)
| ~ p2(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(153676744,plain,
( n3(A)
| ~ p2(B,C,A) ),
inference(rewrite,[status(thm)],[rule_240]),
[] ).
fof(rule_159,plain,
! [A] :
( p2(A,A,A)
| ~ k1(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(152569280,plain,
( p2(A,A,A)
| ~ k1(A) ),
inference(rewrite,[status(thm)],[rule_159]),
[] ).
fof(rule_001,plain,
! [A,B] :
( k1(A)
| ~ n0(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150777488,plain,
( k1(A)
| ~ n0(B,A) ),
inference(rewrite,[status(thm)],[rule_001]),
[] ).
fof(axiom_3,plain,
n0(d,e),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150587648,plain,
n0(d,e),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(164119448,plain,
k1(e),
inference(resolution,[status(thm)],[150777488,150587648]),
[] ).
cnf(164244696,plain,
p2(e,e,e),
inference(resolution,[status(thm)],[152569280,164119448]),
[] ).
fof(rule_165,plain,
! [A,B,C] :
( p2(A,A,A)
| ~ q1(B,C,B)
| ~ p2(B,B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(152675240,plain,
( p2(A,A,A)
| ~ q1(B,C,B)
| ~ p2(B,B,C) ),
inference(rewrite,[status(thm)],[rule_165]),
[] ).
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/SYN157-1.tptp',unknown),
[] ).
fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150679992,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).
cnf(151937760,plain,
q1(e,A,A),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,150679992]),
[] ).
cnf(167030312,plain,
p2(A,A,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164244696,152675240,151937760]),
[] ).
cnf(168009792,plain,
n3(A),
inference(resolution,[status(thm)],[153676744,167030312]),
[] ).
cnf(169884024,plain,
( r4(A)
| ~ q3(B,C) ),
inference(resolution,[status(thm)],[165153696,168009792]),
[] ).
fof(rule_314,plain,
! [A] :
( n5(A,A)
| ~ r4(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(154710192,plain,
( n5(A,A)
| ~ r4(A) ),
inference(rewrite,[status(thm)],[rule_314]),
[] ).
fof(prove_this,plain,
! [A] : ~ n5(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(154953448,plain,
~ n5(A,d),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(167051000,plain,
~ r4(d),
inference(resolution,[status(thm)],[154710192,154953448]),
[] ).
cnf(169942896,plain,
~ q3(A,B),
inference(resolution,[status(thm)],[169884024,167051000]),
[] ).
cnf(170498896,plain,
( ~ r2(A)
| ~ l2(B,B) ),
inference(resolution,[status(thm)],[165376112,169942896]),
[] ).
fof(rule_188,plain,
! [A] :
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(152968952,plain,
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
inference(rewrite,[status(thm)],[rule_188]),
[] ).
fof(axiom_20,plain,
l0(a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),
[] ).
cnf(150684352,plain,
l0(a),
inference(rewrite,[status(thm)],[axiom_20]),
[] ).
cnf(163581592,plain,
( r2(a)
| ~ r1(a) ),
inference(resolution,[status(thm)],[152968952,150684352]),
[] ).
cnf(170507760,plain,
( ~ l2(A,A)
| ~ r1(a) ),
inference(resolution,[status(thm)],[170498896,163581592]),
[] ).
cnf(171122312,plain,
~ l2(A,A),
inference(resolution,[status(thm)],[170955360,170507760]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[173576912,171122312]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(rule_126,plain,(s1(A)|~q0(A,B)|~s1(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152096600,plain,(s1(A)|~q0(A,B)|~s1(C)),inference(rewrite,[status(thm)],[rule_126]),[]).
%
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150672512,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
%
% cnf(169059608,plain,(s1(A)|~s1(B)),inference(resolution,[status(thm)],[152096600,150672512]),[]).
%
% fof(rule_125,plain,(s1(A)|~p0(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152084456,plain,(s1(A)|~p0(A,A)),inference(rewrite,[status(thm)],[rule_125]),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150657224,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(165038784,plain,(s1(b)),inference(resolution,[status(thm)],[152084456,150657224]),[]).
%
% cnf(169067224,plain,(s1(A)),inference(resolution,[status(thm)],[169059608,165038784]),[]).
%
% fof(rule_133,plain,(l2(A,A)|~p0(B,B)|~s1(C)|~m0(D,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152205544,plain,(l2(A,A)|~p0(B,B)|~s1(C)|~m0(D,C,A)),inference(rewrite,[status(thm)],[rule_133]),[]).
%
% cnf(165233808,plain,(l2(A,A)|~s1(B)|~m0(C,B,A)),inference(resolution,[status(thm)],[152205544,150657224]),[]).
%
% fof(axiom_4,plain,(m0(e,d,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150598808,plain,(m0(e,d,a)),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% cnf(173576912,plain,(l2(a,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169067224,165233808,150598808]),[]).
%
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(151841368,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/SYN157-1.tptp',unknown),[]).
%
% cnf(150569176,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
%
% cnf(163251528,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[151841368,150569176]),[]).
%
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152072280,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,150569176]),[]).
%
% cnf(170955360,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163251528,152072280,150672512]),[]).
%
% fof(rule_258,plain,(q3(A,A)|~r2(A)|~s1(B)|~l2(C,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(153921072,plain,(q3(A,A)|~r2(A)|~s1(B)|~l2(C,C)),inference(rewrite,[status(thm)],[rule_258]),[]).
%
% cnf(165376112,plain,(q3(A,A)|~r2(A)|~l2(B,B)),inference(resolution,[status(thm)],[153921072,165038784]),[]).
%
% fof(rule_298,plain,(r4(A)|~n3(A)|~q3(B,C)|~p0(D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(154490144,plain,(r4(A)|~n3(A)|~q3(B,C)|~p0(D,A)),inference(rewrite,[status(thm)],[rule_298]),[]).
%
% cnf(165153696,plain,(r4(A)|~n3(A)|~q3(B,C)),inference(resolution,[status(thm)],[154490144,150657224]),[]).
%
% fof(rule_240,plain,(n3(A)|~p2(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(153676744,plain,(n3(A)|~p2(B,C,A)),inference(rewrite,[status(thm)],[rule_240]),[]).
%
% fof(rule_159,plain,(p2(A,A,A)|~k1(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152569280,plain,(p2(A,A,A)|~k1(A)),inference(rewrite,[status(thm)],[rule_159]),[]).
%
% fof(rule_001,plain,(k1(A)|~n0(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150777488,plain,(k1(A)|~n0(B,A)),inference(rewrite,[status(thm)],[rule_001]),[]).
%
% fof(axiom_3,plain,(n0(d,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150587648,plain,(n0(d,e)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(164119448,plain,(k1(e)),inference(resolution,[status(thm)],[150777488,150587648]),[]).
%
% cnf(164244696,plain,(p2(e,e,e)),inference(resolution,[status(thm)],[152569280,164119448]),[]).
%
% fof(rule_165,plain,(p2(A,A,A)|~q1(B,C,B)|~p2(B,B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152675240,plain,(p2(A,A,A)|~q1(B,C,B)|~p2(B,B,C)),inference(rewrite,[status(thm)],[rule_165]),[]).
%
% 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/SYN157-1.tptp',unknown),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150679992,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(151937760,plain,(q1(e,A,A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,150679992]),[]).
%
% cnf(167030312,plain,(p2(A,A,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164244696,152675240,151937760]),[]).
%
% cnf(168009792,plain,(n3(A)),inference(resolution,[status(thm)],[153676744,167030312]),[]).
%
% cnf(169884024,plain,(r4(A)|~q3(B,C)),inference(resolution,[status(thm)],[165153696,168009792]),[]).
%
% fof(rule_314,plain,(n5(A,A)|~r4(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(154710192,plain,(n5(A,A)|~r4(A)),inference(rewrite,[status(thm)],[rule_314]),[]).
%
% fof(prove_this,plain,(~n5(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(154953448,plain,(~n5(A,d)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(167051000,plain,(~r4(d)),inference(resolution,[status(thm)],[154710192,154953448]),[]).
%
% cnf(169942896,plain,(~q3(A,B)),inference(resolution,[status(thm)],[169884024,167051000]),[]).
%
% cnf(170498896,plain,(~r2(A)|~l2(B,B)),inference(resolution,[status(thm)],[165376112,169942896]),[]).
%
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(152968952,plain,(r2(A)|~r1(A)|~l0(A)),inference(rewrite,[status(thm)],[rule_188]),[]).
%
% fof(axiom_20,plain,(l0(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN157-1.tptp',unknown),[]).
%
% cnf(150684352,plain,(l0(a)),inference(rewrite,[status(thm)],[axiom_20]),[]).
%
% cnf(163581592,plain,(r2(a)|~r1(a)),inference(resolution,[status(thm)],[152968952,150684352]),[]).
%
% cnf(170507760,plain,(~l2(A,A)|~r1(a)),inference(resolution,[status(thm)],[170498896,163581592]),[]).
%
% cnf(171122312,plain,(~l2(A,A)),inference(resolution,[status(thm)],[170955360,170507760]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[173576912,171122312]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------