TSTP Solution File: SYN155-1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN155-1 : 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 17:01:05 EDT 2009
% Result : Unsatisfiable 1.5s
% Output : Refutation 1.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 52 ( 28 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 79 ( 43 ~; 36 |; 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 51 ( 10 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_18,plain,
p0(c,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159555984,plain,
p0(c,b),
inference(rewrite,[status(thm)],[axiom_18]),
[] ).
fof(rule_003,plain,
! [A,B,C,D] :
( l1(A,B)
| ~ p0(C,A)
| ~ r0(D)
| ~ m0(B,A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159804888,plain,
( l1(A,B)
| ~ p0(C,A)
| ~ r0(D)
| ~ m0(B,A,C) ),
inference(rewrite,[status(thm)],[rule_003]),
[] ).
fof(axiom_9,plain,
r0(b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159620000,plain,
r0(b),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(172480080,plain,
( l1(A,B)
| ~ p0(C,A)
| ~ m0(B,A,C) ),
inference(resolution,[status(thm)],[159804888,159620000]),
[] ).
fof(axiom_27,plain,
m0(e,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159708984,plain,
m0(e,b,c),
inference(rewrite,[status(thm)],[axiom_27]),
[] ).
cnf(200585952,plain,
l1(b,e),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159555984,172480080,159708984]),
[] ).
fof(rule_255,plain,
! [A,B,C] :
( q3(A,B)
| ~ q2(C,A,B)
| ~ n0(C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(162866160,plain,
( q3(A,B)
| ~ q2(C,A,B)
| ~ n0(C,A) ),
inference(rewrite,[status(thm)],[rule_255]),
[] ).
fof(axiom_30,plain,
n0(e,e),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159728120,plain,
n0(e,e),
inference(rewrite,[status(thm)],[axiom_30]),
[] ).
cnf(195274592,plain,
( q3(e,A)
| ~ q2(e,e,A) ),
inference(resolution,[status(thm)],[162866160,159728120]),
[] ).
fof(rule_274,plain,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
fof(axiom_34,plain,
n0(c,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159742984,plain,
n0(c,d),
inference(rewrite,[status(thm)],[axiom_34]),
[] ).
cnf(163155912,plain,
( k4(c)
| ~ q3(e,b)
| ~ n3(e) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_274,159742984]),
[] ).
fof(rule_236,plain,
! [A] :
( m3(A,A,A)
| ~ n2(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(162619832,plain,
( m3(A,A,A)
| ~ n2(A) ),
inference(rewrite,[status(thm)],[rule_236]),
[] ).
fof(rule_137,plain,
! [A,B,C] :
( n2(A)
| ~ p1(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(161250896,plain,
( n2(A)
| ~ p1(B,C,A) ),
inference(rewrite,[status(thm)],[rule_137]),
[] ).
fof(rule_075,plain,
( p1(a,a,a)
| ~ p0(b,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
fof(axiom_14,plain,
! [A] : p0(b,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(159647944,plain,
p0(b,A),
inference(rewrite,[status(thm)],[axiom_14]),
[] ).
cnf(160580592,plain,
p1(a,a,a),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,159647944]),
[] ).
cnf(175840632,plain,
n2(a),
inference(resolution,[status(thm)],[161250896,160580592]),
[] ).
cnf(175892224,plain,
m3(a,a,a),
inference(resolution,[status(thm)],[162619832,175840632]),
[] ).
fof(rule_284,plain,
! [A,B] :
( n4(A,A)
| ~ k4(B)
| ~ m3(A,A,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(163280152,plain,
( n4(A,A)
| ~ k4(B)
| ~ m3(A,A,A) ),
inference(rewrite,[status(thm)],[rule_284]),
[] ).
fof(prove_this,plain,
! [A] : ~ n4(A,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(163944296,plain,
~ n4(A,a),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(176055488,plain,
~ k4(A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175892224,163280152,163944296]),
[] ).
cnf(176088200,plain,
( ~ q3(e,b)
| ~ n3(e) ),
inference(resolution,[status(thm)],[163155912,176055488]),
[] ).
fof(rule_240,plain,
! [A,B,C] :
( n3(A)
| ~ p2(B,C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(162667464,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/SYN155-1.tptp',unknown),
[] ).
cnf(161560000,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/SYN155-1.tptp',unknown),
[] ).
cnf(159768208,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/SYN155-1.tptp',unknown),
[] ).
cnf(159578368,plain,
n0(d,e),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(173110712,plain,
k1(e),
inference(resolution,[status(thm)],[159768208,159578368]),
[] ).
cnf(173235960,plain,
p2(e,e,e),
inference(resolution,[status(thm)],[161560000,173110712]),
[] ).
cnf(176280560,plain,
n3(e),
inference(resolution,[status(thm)],[162667464,173235960]),
[] ).
cnf(178753368,plain,
~ q3(e,b),
inference(resolution,[status(thm)],[176088200,176280560]),
[] ).
cnf(196232016,plain,
~ q2(e,e,b),
inference(resolution,[status(thm)],[195274592,178753368]),
[] ).
fof(rule_186,plain,
! [A,B] :
( q2(A,A,B)
| ~ l1(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),
[] ).
cnf(161925448,plain,
( q2(A,A,B)
| ~ l1(B,A) ),
inference(rewrite,[status(thm)],[rule_186]),
[] ).
cnf(196313664,plain,
~ l1(b,e),
inference(resolution,[status(thm)],[196232016,161925448]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[200585952,196313664]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(axiom_18,plain,(p0(c,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159555984,plain,(p0(c,b)),inference(rewrite,[status(thm)],[axiom_18]),[]).
%
% fof(rule_003,plain,(l1(A,B)|~p0(C,A)|~r0(D)|~m0(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159804888,plain,(l1(A,B)|~p0(C,A)|~r0(D)|~m0(B,A,C)),inference(rewrite,[status(thm)],[rule_003]),[]).
%
% fof(axiom_9,plain,(r0(b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159620000,plain,(r0(b)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(172480080,plain,(l1(A,B)|~p0(C,A)|~m0(B,A,C)),inference(resolution,[status(thm)],[159804888,159620000]),[]).
%
% fof(axiom_27,plain,(m0(e,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159708984,plain,(m0(e,b,c)),inference(rewrite,[status(thm)],[axiom_27]),[]).
%
% cnf(200585952,plain,(l1(b,e)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159555984,172480080,159708984]),[]).
%
% fof(rule_255,plain,(q3(A,B)|~q2(C,A,B)|~n0(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(162866160,plain,(q3(A,B)|~q2(C,A,B)|~n0(C,A)),inference(rewrite,[status(thm)],[rule_255]),[]).
%
% fof(axiom_30,plain,(n0(e,e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159728120,plain,(n0(e,e)),inference(rewrite,[status(thm)],[axiom_30]),[]).
%
% cnf(195274592,plain,(q3(e,A)|~q2(e,e,A)),inference(resolution,[status(thm)],[162866160,159728120]),[]).
%
% fof(rule_274,plain,(k4(c)|~n0(c,d)|~q3(e,b)|~n3(e)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% fof(axiom_34,plain,(n0(c,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159742984,plain,(n0(c,d)),inference(rewrite,[status(thm)],[axiom_34]),[]).
%
% cnf(163155912,plain,(k4(c)|~q3(e,b)|~n3(e)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_274,159742984]),[]).
%
% fof(rule_236,plain,(m3(A,A,A)|~n2(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(162619832,plain,(m3(A,A,A)|~n2(A)),inference(rewrite,[status(thm)],[rule_236]),[]).
%
% fof(rule_137,plain,(n2(A)|~p1(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(161250896,plain,(n2(A)|~p1(B,C,A)),inference(rewrite,[status(thm)],[rule_137]),[]).
%
% fof(rule_075,plain,(p1(a,a,a)|~p0(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% fof(axiom_14,plain,(p0(b,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(159647944,plain,(p0(b,A)),inference(rewrite,[status(thm)],[axiom_14]),[]).
%
% cnf(160580592,plain,(p1(a,a,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[rule_075,159647944]),[]).
%
% cnf(175840632,plain,(n2(a)),inference(resolution,[status(thm)],[161250896,160580592]),[]).
%
% cnf(175892224,plain,(m3(a,a,a)),inference(resolution,[status(thm)],[162619832,175840632]),[]).
%
% fof(rule_284,plain,(n4(A,A)|~k4(B)|~m3(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(163280152,plain,(n4(A,A)|~k4(B)|~m3(A,A,A)),inference(rewrite,[status(thm)],[rule_284]),[]).
%
% fof(prove_this,plain,(~n4(A,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(163944296,plain,(~n4(A,a)),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(176055488,plain,(~k4(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175892224,163280152,163944296]),[]).
%
% cnf(176088200,plain,(~q3(e,b)|~n3(e)),inference(resolution,[status(thm)],[163155912,176055488]),[]).
%
% fof(rule_240,plain,(n3(A)|~p2(B,C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(162667464,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/SYN155-1.tptp',unknown),[]).
%
% cnf(161560000,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/SYN155-1.tptp',unknown),[]).
%
% cnf(159768208,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/SYN155-1.tptp',unknown),[]).
%
% cnf(159578368,plain,(n0(d,e)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(173110712,plain,(k1(e)),inference(resolution,[status(thm)],[159768208,159578368]),[]).
%
% cnf(173235960,plain,(p2(e,e,e)),inference(resolution,[status(thm)],[161560000,173110712]),[]).
%
% cnf(176280560,plain,(n3(e)),inference(resolution,[status(thm)],[162667464,173235960]),[]).
%
% cnf(178753368,plain,(~q3(e,b)),inference(resolution,[status(thm)],[176088200,176280560]),[]).
%
% cnf(196232016,plain,(~q2(e,e,b)),inference(resolution,[status(thm)],[195274592,178753368]),[]).
%
% fof(rule_186,plain,(q2(A,A,B)|~l1(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN155-1.tptp',unknown),[]).
%
% cnf(161925448,plain,(q2(A,A,B)|~l1(B,A)),inference(rewrite,[status(thm)],[rule_186]),[]).
%
% cnf(196313664,plain,(~l1(b,e)),inference(resolution,[status(thm)],[196232016,161925448]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[200585952,196313664]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------