TSTP Solution File: SYN074-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SYN074-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 16:41:12 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 63 ( 26 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 5 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clause_8,plain,
! [B,A] :
( ~ $equal(g(B),A)
| big_f(f(B),A)
| $equal(f(B),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154416112,plain,
( ~ $equal(g(B),A)
| big_f(f(B),A)
| $equal(f(B),B) ),
inference(rewrite,[status(thm)],[clause_8]),
[] ).
cnf(180791680,plain,
( big_f(f(A),g(A))
| $equal(f(A),A) ),
inference(equality_resolution,[status(thm)],[154416112]),
[] ).
fof(clause_3,plain,
! [A,B] :
( ~ $equal(a,A)
| ~ $equal(b,B)
| big_f(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154369000,plain,
( ~ $equal(a,A)
| ~ $equal(b,B)
| big_f(A,B) ),
inference(rewrite,[status(thm)],[clause_3]),
[] ).
fof(clause_1,plain,
! [A,B] :
( ~ big_f(A,B)
| $equal(a,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154347832,plain,
( ~ big_f(A,B)
| $equal(a,A) ),
inference(rewrite,[status(thm)],[clause_1]),
[] ).
cnf(180598192,plain,
( ~ $equal(b,B)
| big_f(A,B)
| ~ big_f(A,C) ),
inference(resolution,[status(thm)],[154369000,154347832]),
[] ).
cnf(180638080,plain,
( big_f(A,b)
| ~ big_f(A,B) ),
inference(equality_resolution,[status(thm)],[180598192]),
[] ).
cnf(180893904,plain,
( $equal(f(A),A)
| big_f(f(A),b) ),
inference(resolution,[status(thm)],[180791680,180638080]),
[] ).
fof(clause_4,plain,
! [A,B] :
( ~ big_f(f(A),B)
| $equal(g(A),B)
| $equal(f(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154376360,plain,
( ~ big_f(f(A),B)
| $equal(g(A),B)
| $equal(f(A),A) ),
inference(rewrite,[status(thm)],[clause_4]),
[] ).
cnf(181057720,plain,
( $equal(f(A),A)
| $equal(g(A),b) ),
inference(resolution,[status(thm)],[180893904,154376360]),
[] ).
cnf(180864576,plain,
( $equal(f(A),A)
| $equal(a,f(A)) ),
inference(resolution,[status(thm)],[180791680,154347832]),
[] ).
cnf(180946776,plain,
( $equal(f(A),A)
| ~ big_f(B,C)
| $equal(f(A),B) ),
inference(paramodulation,[status(thm)],[180864576,154347832,theory(equality)]),
[] ).
cnf(180591720,plain,
big_f(a,b),
inference(equality_resolution,[status(thm)],[154369000]),
[] ).
cnf(181335232,plain,
( $equal(f(A),A)
| $equal(f(A),a) ),
inference(resolution,[status(thm)],[180946776,180591720]),
[] ).
fof(clause_10,plain,
! [A,B] :
( ~ $equal(f(A),A)
| big_f(f(A),h(A,B))
| $equal(h(A,B),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154433912,plain,
( ~ $equal(f(A),A)
| big_f(f(A),h(A,B))
| $equal(h(A,B),B) ),
inference(rewrite,[status(thm)],[clause_10]),
[] ).
cnf(182018120,plain,
( big_f(f(a),h(a,A))
| $equal(h(a,A),A) ),
inference(resolution,[status(thm)],[154433912,181335232]),
[] ).
fof(clause_11,plain,
! [A,B] :
( ~ $equal(f(A),A)
| ~ $equal(h(A,B),B)
| ~ big_f(f(A),h(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154440448,plain,
( ~ $equal(f(A),A)
| ~ $equal(h(A,B),B)
| ~ big_f(f(A),h(A,B)) ),
inference(rewrite,[status(thm)],[clause_11]),
[] ).
fof(clause_2,plain,
! [A,B] :
( ~ big_f(A,B)
| $equal(b,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),
[] ).
cnf(154356864,plain,
( ~ big_f(A,B)
| $equal(b,B) ),
inference(rewrite,[status(thm)],[clause_2]),
[] ).
cnf(182530880,plain,
( $equal(h(a,A),A)
| $equal(b,h(a,A)) ),
inference(resolution,[status(thm)],[182018120,154356864]),
[] ).
cnf(185513968,plain,
( ~ $equal(b,A)
| $equal(h(a,A),A) ),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[182018120,181335232,154440448,182530880,theory(equality)]),
[] ).
cnf(185584648,plain,
$equal(h(a,b),b),
inference(equality_resolution,[status(thm)],[185513968]),
[] ).
cnf(186057216,plain,
~ big_f(f(a),b),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[181335232,185584648,185584648,154440448,theory(equality)]),
[] ).
cnf(186211496,plain,
$equal(f(a),a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[181057720,186057216,154416112]),
[] ).
cnf(186348928,plain,
big_f(f(a),b),
inference(paramodulation,[status(thm)],[186211496,180591720,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[186348928,186057216]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(clause_8,plain,(~$equal(g(B),A)|big_f(f(B),A)|$equal(f(B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154416112,plain,(~$equal(g(B),A)|big_f(f(B),A)|$equal(f(B),B)),inference(rewrite,[status(thm)],[clause_8]),[]).
%
% cnf(180791680,plain,(big_f(f(A),g(A))|$equal(f(A),A)),inference(equality_resolution,[status(thm)],[154416112]),[]).
%
% fof(clause_3,plain,(~$equal(a,A)|~$equal(b,B)|big_f(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154369000,plain,(~$equal(a,A)|~$equal(b,B)|big_f(A,B)),inference(rewrite,[status(thm)],[clause_3]),[]).
%
% fof(clause_1,plain,(~big_f(A,B)|$equal(a,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154347832,plain,(~big_f(A,B)|$equal(a,A)),inference(rewrite,[status(thm)],[clause_1]),[]).
%
% cnf(180598192,plain,(~$equal(b,B)|big_f(A,B)|~big_f(A,C)),inference(resolution,[status(thm)],[154369000,154347832]),[]).
%
% cnf(180638080,plain,(big_f(A,b)|~big_f(A,B)),inference(equality_resolution,[status(thm)],[180598192]),[]).
%
% cnf(180893904,plain,($equal(f(A),A)|big_f(f(A),b)),inference(resolution,[status(thm)],[180791680,180638080]),[]).
%
% fof(clause_4,plain,(~big_f(f(A),B)|$equal(g(A),B)|$equal(f(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154376360,plain,(~big_f(f(A),B)|$equal(g(A),B)|$equal(f(A),A)),inference(rewrite,[status(thm)],[clause_4]),[]).
%
% cnf(181057720,plain,($equal(f(A),A)|$equal(g(A),b)),inference(resolution,[status(thm)],[180893904,154376360]),[]).
%
% cnf(180864576,plain,($equal(f(A),A)|$equal(a,f(A))),inference(resolution,[status(thm)],[180791680,154347832]),[]).
%
% cnf(180946776,plain,($equal(f(A),A)|~big_f(B,C)|$equal(f(A),B)),inference(paramodulation,[status(thm)],[180864576,154347832,theory(equality)]),[]).
%
% cnf(180591720,plain,(big_f(a,b)),inference(equality_resolution,[status(thm)],[154369000]),[]).
%
% cnf(181335232,plain,($equal(f(A),A)|$equal(f(A),a)),inference(resolution,[status(thm)],[180946776,180591720]),[]).
%
% fof(clause_10,plain,(~$equal(f(A),A)|big_f(f(A),h(A,B))|$equal(h(A,B),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154433912,plain,(~$equal(f(A),A)|big_f(f(A),h(A,B))|$equal(h(A,B),B)),inference(rewrite,[status(thm)],[clause_10]),[]).
%
% cnf(182018120,plain,(big_f(f(a),h(a,A))|$equal(h(a,A),A)),inference(resolution,[status(thm)],[154433912,181335232]),[]).
%
% fof(clause_11,plain,(~$equal(f(A),A)|~$equal(h(A,B),B)|~big_f(f(A),h(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154440448,plain,(~$equal(f(A),A)|~$equal(h(A,B),B)|~big_f(f(A),h(A,B))),inference(rewrite,[status(thm)],[clause_11]),[]).
%
% fof(clause_2,plain,(~big_f(A,B)|$equal(b,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SYN/SYN074-1.tptp',unknown),[]).
%
% cnf(154356864,plain,(~big_f(A,B)|$equal(b,B)),inference(rewrite,[status(thm)],[clause_2]),[]).
%
% cnf(182530880,plain,($equal(h(a,A),A)|$equal(b,h(a,A))),inference(resolution,[status(thm)],[182018120,154356864]),[]).
%
% cnf(185513968,plain,(~$equal(b,A)|$equal(h(a,A),A)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[182018120,181335232,154440448,182530880,theory(equality)]),[]).
%
% cnf(185584648,plain,($equal(h(a,b),b)),inference(equality_resolution,[status(thm)],[185513968]),[]).
%
% cnf(186057216,plain,(~big_f(f(a),b)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[181335232,185584648,185584648,154440448,theory(equality)]),[]).
%
% cnf(186211496,plain,($equal(f(a),a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[181057720,186057216,154416112]),[]).
%
% cnf(186348928,plain,(big_f(f(a),b)),inference(paramodulation,[status(thm)],[186211496,180591720,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[186348928,186057216]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------