TSTP Solution File: SET002-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET002-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 15:22:29 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(member_of_set1_is_member_of_union,plain,
! [A,B,C,D] :
( ~ union(A,B,C)
| ~ member(D,A)
| member(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165702976,plain,
( ~ union(A,B,C)
| ~ member(D,A)
| member(D,C) ),
inference(rewrite,[status(thm)],[member_of_set1_is_member_of_union]),
[] ).
fof(a_union_a_is_aUa,plain,
union(a,a,aua),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165738784,plain,
union(a,a,aua),
inference(rewrite,[status(thm)],[a_union_a_is_aUa]),
[] ).
cnf(173548888,plain,
( ~ member(A,a)
| member(A,aua) ),
inference(resolution,[status(thm)],[165702976,165738784]),
[] ).
fof(subsets_axiom1,plain,
! [A,B] :
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165656664,plain,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
inference(rewrite,[status(thm)],[subsets_axiom1]),
[] ).
cnf(174318496,plain,
( member(member_of_1_not_of_2(a,A),aua)
| subset(a,A) ),
inference(resolution,[status(thm)],[173548888,165656664]),
[] ).
fof(subsets_axiom2,plain,
! [A,B] :
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165666608,plain,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subsets_axiom2]),
[] ).
cnf(174589600,plain,
subset(a,aua),
inference(resolution,[status(thm)],[174318496,165666608]),
[] ).
fof(subsets_are_set_equal_sets,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_sets(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165688832,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_sets(B,A) ),
inference(rewrite,[status(thm)],[subsets_are_set_equal_sets]),
[] ).
fof(prove_a_equals_aUa,plain,
~ equal_sets(aua,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165742752,plain,
~ equal_sets(aua,a),
inference(rewrite,[status(thm)],[prove_a_equals_aUa]),
[] ).
cnf(173582608,plain,
( ~ subset(a,aua)
| ~ subset(aua,a) ),
inference(resolution,[status(thm)],[165688832,165742752]),
[] ).
cnf(173852832,plain,
( ~ subset(a,aua)
| member(member_of_1_not_of_2(aua,a),aua) ),
inference(resolution,[status(thm)],[173582608,165656664]),
[] ).
cnf(174662456,plain,
member(member_of_1_not_of_2(aua,a),aua),
inference(resolution,[status(thm)],[174589600,173852832]),
[] ).
fof(member_of_union_is_member_of_one_set,plain,
! [A,B,C,D] :
( ~ union(A,B,C)
| ~ member(D,C)
| member(D,A)
| member(D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),
[] ).
cnf(165698632,plain,
( ~ union(A,B,C)
| ~ member(D,C)
| member(D,A)
| member(D,B) ),
inference(rewrite,[status(thm)],[member_of_union_is_member_of_one_set]),
[] ).
cnf(173560304,plain,
( ~ member(A,aua)
| member(A,a) ),
inference(resolution,[status(thm)],[165698632,165738784]),
[] ).
cnf(174656520,plain,
~ subset(aua,a),
inference(resolution,[status(thm)],[174589600,173582608]),
[] ).
cnf(174672144,plain,
~ member(member_of_1_not_of_2(aua,a),a),
inference(resolution,[status(thm)],[174656520,165666608]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[174662456,173560304,174672144]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(member_of_set1_is_member_of_union,plain,(~union(A,B,C)|~member(D,A)|member(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165702976,plain,(~union(A,B,C)|~member(D,A)|member(D,C)),inference(rewrite,[status(thm)],[member_of_set1_is_member_of_union]),[]).
%
% fof(a_union_a_is_aUa,plain,(union(a,a,aua)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165738784,plain,(union(a,a,aua)),inference(rewrite,[status(thm)],[a_union_a_is_aUa]),[]).
%
% cnf(173548888,plain,(~member(A,a)|member(A,aua)),inference(resolution,[status(thm)],[165702976,165738784]),[]).
%
% fof(subsets_axiom1,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165656664,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),inference(rewrite,[status(thm)],[subsets_axiom1]),[]).
%
% cnf(174318496,plain,(member(member_of_1_not_of_2(a,A),aua)|subset(a,A)),inference(resolution,[status(thm)],[173548888,165656664]),[]).
%
% fof(subsets_axiom2,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165666608,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),inference(rewrite,[status(thm)],[subsets_axiom2]),[]).
%
% cnf(174589600,plain,(subset(a,aua)),inference(resolution,[status(thm)],[174318496,165666608]),[]).
%
% fof(subsets_are_set_equal_sets,plain,(~subset(A,B)|~subset(B,A)|equal_sets(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165688832,plain,(~subset(A,B)|~subset(B,A)|equal_sets(B,A)),inference(rewrite,[status(thm)],[subsets_are_set_equal_sets]),[]).
%
% fof(prove_a_equals_aUa,plain,(~equal_sets(aua,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165742752,plain,(~equal_sets(aua,a)),inference(rewrite,[status(thm)],[prove_a_equals_aUa]),[]).
%
% cnf(173582608,plain,(~subset(a,aua)|~subset(aua,a)),inference(resolution,[status(thm)],[165688832,165742752]),[]).
%
% cnf(173852832,plain,(~subset(a,aua)|member(member_of_1_not_of_2(aua,a),aua)),inference(resolution,[status(thm)],[173582608,165656664]),[]).
%
% cnf(174662456,plain,(member(member_of_1_not_of_2(aua,a),aua)),inference(resolution,[status(thm)],[174589600,173852832]),[]).
%
% fof(member_of_union_is_member_of_one_set,plain,(~union(A,B,C)|~member(D,C)|member(D,A)|member(D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET002-1.tptp',unknown),[]).
%
% cnf(165698632,plain,(~union(A,B,C)|~member(D,C)|member(D,A)|member(D,B)),inference(rewrite,[status(thm)],[member_of_union_is_member_of_one_set]),[]).
%
% cnf(173560304,plain,(~member(A,aua)|member(A,a)),inference(resolution,[status(thm)],[165698632,165738784]),[]).
%
% cnf(174656520,plain,(~subset(aua,a)),inference(resolution,[status(thm)],[174589600,173582608]),[]).
%
% cnf(174672144,plain,(~member(member_of_1_not_of_2(aua,a),a)),inference(resolution,[status(thm)],[174656520,165666608]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[174662456,173560304,174672144]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------