TSTP Solution File: SET047-5 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET047-5 : TPTP v3.4.2. Released v1.0.0.
% 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 15:25:34 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 26 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_symmetry1,plain,
( set_equal(a,b)
| set_equal(b,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),
[] ).
cnf(143352328,plain,
( set_equal(a,b)
| set_equal(b,a) ),
inference(rewrite,[status(thm)],[prove_symmetry1]),
[] ).
fof(prove_symmetry2,plain,
( ~ set_equal(b,a)
| ~ set_equal(a,b) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),
[] ).
cnf(143362136,plain,
( ~ set_equal(b,a)
| ~ set_equal(a,b) ),
inference(rewrite,[status(thm)],[prove_symmetry2]),
[] ).
fof(clause_3,plain,
! [A,B] :
( element(f(A,B),A)
| element(f(A,B),B)
| set_equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),
[] ).
cnf(143337984,plain,
( element(f(A,B),A)
| element(f(A,B),B)
| set_equal(A,B) ),
inference(rewrite,[status(thm)],[clause_3]),
[] ).
cnf(153764744,plain,
( ~ set_equal(a,b)
| element(f(b,a),b)
| element(f(b,a),a) ),
inference(resolution,[status(thm)],[143362136,143337984]),
[] ).
fof(element_substitution2,plain,
! [A,B,C] :
( ~ set_equal(A,B)
| ~ element(C,B)
| element(C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),
[] ).
cnf(143330424,plain,
( ~ set_equal(A,B)
| ~ element(C,B)
| element(C,A) ),
inference(rewrite,[status(thm)],[element_substitution2]),
[] ).
cnf(153860984,plain,
( ~ element(A,b)
| element(A,a)
| set_equal(b,a) ),
inference(resolution,[status(thm)],[143330424,143352328]),
[] ).
cnf(154346560,plain,
( element(f(b,a),a)
| set_equal(b,a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[143352328,153764744,153860984]),
[] ).
fof(clause_4,plain,
! [A,B] :
( ~ element(f(A,B),B)
| ~ element(f(A,B),A)
| set_equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),
[] ).
cnf(143346216,plain,
( ~ element(f(A,B),B)
| ~ element(f(A,B),A)
| set_equal(A,B) ),
inference(rewrite,[status(thm)],[clause_4]),
[] ).
fof(element_substitution1,plain,
! [A,B,C] :
( ~ set_equal(A,B)
| ~ element(C,A)
| element(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),
[] ).
cnf(143326120,plain,
( ~ set_equal(A,B)
| ~ element(C,A)
| element(C,B) ),
inference(rewrite,[status(thm)],[element_substitution1]),
[] ).
cnf(153806536,plain,
( ~ element(A,a)
| element(A,b)
| set_equal(b,a) ),
inference(resolution,[status(thm)],[143326120,143352328]),
[] ).
cnf(154338800,plain,
( element(f(b,a),b)
| set_equal(b,a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[143352328,153764744,153806536]),
[] ).
cnf(154701680,plain,
set_equal(b,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154346560,143346216,154338800]),
[] ).
cnf(154734576,plain,
( ~ element(A,b)
| element(A,a) ),
inference(resolution,[status(thm)],[154701680,143326120]),
[] ).
cnf(154404312,plain,
( element(f(b,a),a)
| ~ set_equal(a,b) ),
inference(resolution,[status(thm)],[154346560,143362136]),
[] ).
cnf(154362192,plain,
( element(f(b,a),b)
| ~ set_equal(a,b) ),
inference(resolution,[status(thm)],[154338800,143362136]),
[] ).
cnf(154497392,plain,
~ set_equal(a,b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154404312,154362192,143346216,143362136]),
[] ).
cnf(154771248,plain,
~ element(f(a,b),b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[154734576,154497392,143346216]),
[] ).
cnf(154876952,plain,
( element(f(a,b),a)
| set_equal(a,b) ),
inference(resolution,[status(thm)],[154771248,143337984]),
[] ).
cnf(154738848,plain,
( ~ element(A,a)
| element(A,b) ),
inference(resolution,[status(thm)],[154701680,143330424]),
[] ).
cnf(154954968,plain,
~ element(f(a,b),a),
inference(resolution,[status(thm)],[154738848,154771248]),
[] ).
cnf(155064264,plain,
set_equal(a,b),
inference(resolution,[status(thm)],[154876952,154954968]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[155064264,154497392]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_symmetry1,plain,(set_equal(a,b)|set_equal(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),[]).
%
% cnf(143352328,plain,(set_equal(a,b)|set_equal(b,a)),inference(rewrite,[status(thm)],[prove_symmetry1]),[]).
%
% fof(prove_symmetry2,plain,(~set_equal(b,a)|~set_equal(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),[]).
%
% cnf(143362136,plain,(~set_equal(b,a)|~set_equal(a,b)),inference(rewrite,[status(thm)],[prove_symmetry2]),[]).
%
% fof(clause_3,plain,(element(f(A,B),A)|element(f(A,B),B)|set_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),[]).
%
% cnf(143337984,plain,(element(f(A,B),A)|element(f(A,B),B)|set_equal(A,B)),inference(rewrite,[status(thm)],[clause_3]),[]).
%
% cnf(153764744,plain,(~set_equal(a,b)|element(f(b,a),b)|element(f(b,a),a)),inference(resolution,[status(thm)],[143362136,143337984]),[]).
%
% fof(element_substitution2,plain,(~set_equal(A,B)|~element(C,B)|element(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),[]).
%
% cnf(143330424,plain,(~set_equal(A,B)|~element(C,B)|element(C,A)),inference(rewrite,[status(thm)],[element_substitution2]),[]).
%
% cnf(153860984,plain,(~element(A,b)|element(A,a)|set_equal(b,a)),inference(resolution,[status(thm)],[143330424,143352328]),[]).
%
% cnf(154346560,plain,(element(f(b,a),a)|set_equal(b,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[143352328,153764744,153860984]),[]).
%
% fof(clause_4,plain,(~element(f(A,B),B)|~element(f(A,B),A)|set_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),[]).
%
% cnf(143346216,plain,(~element(f(A,B),B)|~element(f(A,B),A)|set_equal(A,B)),inference(rewrite,[status(thm)],[clause_4]),[]).
%
% fof(element_substitution1,plain,(~set_equal(A,B)|~element(C,A)|element(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET047-5.tptp',unknown),[]).
%
% cnf(143326120,plain,(~set_equal(A,B)|~element(C,A)|element(C,B)),inference(rewrite,[status(thm)],[element_substitution1]),[]).
%
% cnf(153806536,plain,(~element(A,a)|element(A,b)|set_equal(b,a)),inference(resolution,[status(thm)],[143326120,143352328]),[]).
%
% cnf(154338800,plain,(element(f(b,a),b)|set_equal(b,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[143352328,153764744,153806536]),[]).
%
% cnf(154701680,plain,(set_equal(b,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154346560,143346216,154338800]),[]).
%
% cnf(154734576,plain,(~element(A,b)|element(A,a)),inference(resolution,[status(thm)],[154701680,143326120]),[]).
%
% cnf(154404312,plain,(element(f(b,a),a)|~set_equal(a,b)),inference(resolution,[status(thm)],[154346560,143362136]),[]).
%
% cnf(154362192,plain,(element(f(b,a),b)|~set_equal(a,b)),inference(resolution,[status(thm)],[154338800,143362136]),[]).
%
% cnf(154497392,plain,(~set_equal(a,b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154404312,154362192,143346216,143362136]),[]).
%
% cnf(154771248,plain,(~element(f(a,b),b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154734576,154497392,143346216]),[]).
%
% cnf(154876952,plain,(element(f(a,b),a)|set_equal(a,b)),inference(resolution,[status(thm)],[154771248,143337984]),[]).
%
% cnf(154738848,plain,(~element(A,a)|element(A,b)),inference(resolution,[status(thm)],[154701680,143330424]),[]).
%
% cnf(154954968,plain,(~element(f(a,b),a)),inference(resolution,[status(thm)],[154738848,154771248]),[]).
%
% cnf(155064264,plain,(set_equal(a,b)),inference(resolution,[status(thm)],[154876952,154954968]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[155064264,154497392]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------