TSTP Solution File: SYN162-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN162-1 : TPTP v3.4.2. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 17:02:20 EDT 2009
% Result : Unsatisfiable 0.8s
% Output : Refutation 0.8s
% 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 91 ( 26 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_188,plain,
! [A] :
( r2(A)
| ~ r1(A)
| ~ l0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(177172176,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/SYN162-1.tptp',unknown),
[] ).
cnf(174887576,plain,
l0(a),
inference(rewrite,[status(thm)],[axiom_20]),
[] ).
cnf(187995000,plain,
( r2(a)
| ~ r1(a) ),
inference(resolution,[status(thm)],[177172176,174887576]),
[] ).
fof(rule_314,plain,
! [A] :
( n5(A,A)
| ~ r4(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(178913416,plain,
( n5(A,A)
| ~ r4(A) ),
inference(rewrite,[status(thm)],[rule_314]),
[] ).
fof(prove_this,plain,
~ n5(c,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(179156656,plain,
~ n5(c,c),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(190577744,plain,
~ r4(c),
inference(resolution,[status(thm)],[178913416,179156656]),
[] ).
fof(rule_240,plain,
! [A,B,C] :
( n3(A)
| ~ p2(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(177879968,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/SYN162-1.tptp',unknown),
[] ).
cnf(176772504,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/SYN162-1.tptp',unknown),
[] ).
cnf(174980712,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/SYN162-1.tptp',unknown),
[] ).
cnf(174790872,plain,
n0(d,e),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(188363264,plain,
k1(e),
inference(resolution,[status(thm)],[174980712,174790872]),
[] ).
cnf(188478432,plain,
p2(e,e,e),
inference(resolution,[status(thm)],[176772504,188363264]),
[] ).
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/SYN162-1.tptp',unknown),
[] ).
cnf(176878464,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/SYN162-1.tptp',unknown),
[] ).
fof(axiom_19,plain,
! [A,B] : m0(A,d,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(174883216,plain,
m0(A,d,B),
inference(rewrite,[status(thm)],[axiom_19]),
[] ).
cnf(176140984,plain,
q1(e,A,A),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,174883216]),
[] ).
cnf(190433024,plain,
p2(A,A,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[188478432,176878464,176140984]),
[] ).
cnf(191911600,plain,
n3(A),
inference(resolution,[status(thm)],[177879968,190433024]),
[] ).
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/SYN162-1.tptp',unknown),
[] ).
cnf(178693368,plain,
( r4(A)
| ~ n3(A)
| ~ q3(B,C)
| ~ p0(D,A) ),
inference(rewrite,[status(thm)],[rule_298]),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(174860448,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
cnf(188955152,plain,
( r4(A)
| ~ n3(A)
| ~ q3(B,C) ),
inference(resolution,[status(thm)],[178693368,174860448]),
[] ).
cnf(193645912,plain,
( r4(A)
| ~ q3(B,C) ),
inference(resolution,[status(thm)],[191911600,188955152]),
[] ).
cnf(193620048,plain,
~ q3(A,B),
inference(resolution,[status(thm)],[190577744,193645912]),
[] ).
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/SYN162-1.tptp',unknown),
[] ).
cnf(178124296,plain,
( q3(A,A)
| ~ r2(A)
| ~ s1(B)
| ~ l2(C,C) ),
inference(rewrite,[status(thm)],[rule_258]),
[] ).
fof(rule_125,plain,
! [A] :
( s1(A)
| ~ p0(A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(176287680,plain,
( s1(A)
| ~ p0(A,A) ),
inference(rewrite,[status(thm)],[rule_125]),
[] ).
cnf(188875256,plain,
s1(b),
inference(resolution,[status(thm)],[176287680,174860448]),
[] ).
cnf(189140392,plain,
( q3(A,A)
| ~ r2(A)
| ~ l2(B,B) ),
inference(resolution,[status(thm)],[178124296,188875256]),
[] ).
cnf(194415200,plain,
( ~ r2(A)
| ~ l2(B,B) ),
inference(resolution,[status(thm)],[193620048,189140392]),
[] ).
cnf(194426520,plain,
( ~ r1(a)
| ~ l2(A,A) ),
inference(resolution,[status(thm)],[187995000,194415200]),
[] ).
fof(rule_097,plain,
! [A] :
( q1(A,A,A)
| ~ s0(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(176044592,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/SYN162-1.tptp',unknown),
[] ).
cnf(174772400,plain,
s0(d),
inference(rewrite,[status(thm)],[axiom_1]),
[] ).
cnf(177192072,plain,
q1(d,d,d),
inference(resolution,[status(thm)],[176044592,174772400]),
[] ).
fof(axiom_17,plain,
! [A] : q0(A,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(174875736,plain,
q0(A,d),
inference(rewrite,[status(thm)],[axiom_17]),
[] ).
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/SYN162-1.tptp',unknown),
[] ).
cnf(176275504,plain,
( r1(A)
| ~ q0(A,B)
| ~ q1(d,B,d) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,174772400]),
[] ).
cnf(194638080,plain,
r1(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177192072,174875736,176275504]),
[] ).
cnf(194847848,plain,
~ l2(A,A),
inference(resolution,[status(thm)],[194426520,194638080]),
[] ).
fof(rule_126,plain,
! [A,B,C] :
( s1(A)
| ~ q0(A,B)
| ~ s1(C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(176299824,plain,
( s1(A)
| ~ q0(A,B)
| ~ s1(C) ),
inference(rewrite,[status(thm)],[rule_126]),
[] ).
cnf(189088352,plain,
( s1(A)
| ~ q0(A,B) ),
inference(resolution,[status(thm)],[176299824,188875256]),
[] ).
fof(axiom_29,plain,
q0(d,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),
[] ).
cnf(174937024,plain,
q0(d,b),
inference(rewrite,[status(thm)],[axiom_29]),
[] ).
cnf(189373640,plain,
s1(d),
inference(resolution,[status(thm)],[189088352,174937024]),
[] ).
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/SYN162-1.tptp',unknown),
[] ).
cnf(176408768,plain,
( l2(A,A)
| ~ p0(B,B)
| ~ s1(C)
| ~ m0(D,C,A) ),
inference(rewrite,[status(thm)],[rule_133]),
[] ).
cnf(189010992,plain,
( l2(A,A)
| ~ s1(B)
| ~ m0(C,B,A) ),
inference(resolution,[status(thm)],[176408768,174860448]),
[] ).
cnf(198284160,plain,
l2(A,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174883216,189373640,189010992]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[194847848,198284160]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(rule_188,plain,(r2(A)|~r1(A)|~l0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(177172176,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/SYN162-1.tptp',unknown),[]).
%
% cnf(174887576,plain,(l0(a)),inference(rewrite,[status(thm)],[axiom_20]),[]).
%
% cnf(187995000,plain,(r2(a)|~r1(a)),inference(resolution,[status(thm)],[177172176,174887576]),[]).
%
% fof(rule_314,plain,(n5(A,A)|~r4(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(178913416,plain,(n5(A,A)|~r4(A)),inference(rewrite,[status(thm)],[rule_314]),[]).
%
% fof(prove_this,plain,(~n5(c,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(179156656,plain,(~n5(c,c)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(190577744,plain,(~r4(c)),inference(resolution,[status(thm)],[178913416,179156656]),[]).
%
% fof(rule_240,plain,(n3(A)|~p2(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(177879968,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/SYN162-1.tptp',unknown),[]).
%
% cnf(176772504,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/SYN162-1.tptp',unknown),[]).
%
% cnf(174980712,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/SYN162-1.tptp',unknown),[]).
%
% cnf(174790872,plain,(n0(d,e)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(188363264,plain,(k1(e)),inference(resolution,[status(thm)],[174980712,174790872]),[]).
%
% cnf(188478432,plain,(p2(e,e,e)),inference(resolution,[status(thm)],[176772504,188363264]),[]).
%
% 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/SYN162-1.tptp',unknown),[]).
%
% cnf(176878464,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/SYN162-1.tptp',unknown),[]).
%
% fof(axiom_19,plain,(m0(A,d,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(174883216,plain,(m0(A,d,B)),inference(rewrite,[status(thm)],[axiom_19]),[]).
%
% cnf(176140984,plain,(q1(e,A,A)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_107,174883216]),[]).
%
% cnf(190433024,plain,(p2(A,A,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[188478432,176878464,176140984]),[]).
%
% cnf(191911600,plain,(n3(A)),inference(resolution,[status(thm)],[177879968,190433024]),[]).
%
% fof(rule_298,plain,(r4(A)|~n3(A)|~q3(B,C)|~p0(D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(178693368,plain,(r4(A)|~n3(A)|~q3(B,C)|~p0(D,A)),inference(rewrite,[status(thm)],[rule_298]),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(174860448,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(188955152,plain,(r4(A)|~n3(A)|~q3(B,C)),inference(resolution,[status(thm)],[178693368,174860448]),[]).
%
% cnf(193645912,plain,(r4(A)|~q3(B,C)),inference(resolution,[status(thm)],[191911600,188955152]),[]).
%
% cnf(193620048,plain,(~q3(A,B)),inference(resolution,[status(thm)],[190577744,193645912]),[]).
%
% fof(rule_258,plain,(q3(A,A)|~r2(A)|~s1(B)|~l2(C,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(178124296,plain,(q3(A,A)|~r2(A)|~s1(B)|~l2(C,C)),inference(rewrite,[status(thm)],[rule_258]),[]).
%
% fof(rule_125,plain,(s1(A)|~p0(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(176287680,plain,(s1(A)|~p0(A,A)),inference(rewrite,[status(thm)],[rule_125]),[]).
%
% cnf(188875256,plain,(s1(b)),inference(resolution,[status(thm)],[176287680,174860448]),[]).
%
% cnf(189140392,plain,(q3(A,A)|~r2(A)|~l2(B,B)),inference(resolution,[status(thm)],[178124296,188875256]),[]).
%
% cnf(194415200,plain,(~r2(A)|~l2(B,B)),inference(resolution,[status(thm)],[193620048,189140392]),[]).
%
% cnf(194426520,plain,(~r1(a)|~l2(A,A)),inference(resolution,[status(thm)],[187995000,194415200]),[]).
%
% fof(rule_097,plain,(q1(A,A,A)|~s0(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(176044592,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/SYN162-1.tptp',unknown),[]).
%
% cnf(174772400,plain,(s0(d)),inference(rewrite,[status(thm)],[axiom_1]),[]).
%
% cnf(177192072,plain,(q1(d,d,d)),inference(resolution,[status(thm)],[176044592,174772400]),[]).
%
% fof(axiom_17,plain,(q0(A,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(174875736,plain,(q0(A,d)),inference(rewrite,[status(thm)],[axiom_17]),[]).
%
% fof(rule_124,plain,(r1(A)|~q0(A,B)|~s0(d)|~q1(d,B,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(176275504,plain,(r1(A)|~q0(A,B)|~q1(d,B,d)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_124,174772400]),[]).
%
% cnf(194638080,plain,(r1(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177192072,174875736,176275504]),[]).
%
% cnf(194847848,plain,(~l2(A,A)),inference(resolution,[status(thm)],[194426520,194638080]),[]).
%
% fof(rule_126,plain,(s1(A)|~q0(A,B)|~s1(C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(176299824,plain,(s1(A)|~q0(A,B)|~s1(C)),inference(rewrite,[status(thm)],[rule_126]),[]).
%
% cnf(189088352,plain,(s1(A)|~q0(A,B)),inference(resolution,[status(thm)],[176299824,188875256]),[]).
%
% fof(axiom_29,plain,(q0(d,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN162-1.tptp',unknown),[]).
%
% cnf(174937024,plain,(q0(d,b)),inference(rewrite,[status(thm)],[axiom_29]),[]).
%
% cnf(189373640,plain,(s1(d)),inference(resolution,[status(thm)],[189088352,174937024]),[]).
%
% 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/SYN162-1.tptp',unknown),[]).
%
% cnf(176408768,plain,(l2(A,A)|~p0(B,B)|~s1(C)|~m0(D,C,A)),inference(rewrite,[status(thm)],[rule_133]),[]).
%
% cnf(189010992,plain,(l2(A,A)|~s1(B)|~m0(C,B,A)),inference(resolution,[status(thm)],[176408768,174860448]),[]).
%
% cnf(198284160,plain,(l2(A,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174883216,189373640,189010992]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[194847848,198284160]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------