TSTP Solution File: SET008-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET008-1 : 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 15:22:56 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 2 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersection_axiom2,plain,
! [A,B,C] :
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
[] ).
cnf(161774536,plain,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),B) ),
inference(rewrite,[status(thm)],[intersection_axiom2]),
[] ).
fof(prove_aI_bDa_is_empty,plain,
! [A] : ~ member(A,ai_bda),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
[] ).
cnf(161855992,plain,
~ member(A,ai_bda),
inference(rewrite,[status(thm)],[prove_aI_bDa_is_empty]),
[] ).
cnf(172547944,plain,
( intersection(A,B,ai_bda)
| member(h(A,B,ai_bda),B) ),
inference(resolution,[status(thm)],[161774536,161855992]),
[] ).
fof(a_intersection_bDa,plain,
~ intersection(a,bda,ai_bda),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
[] ).
cnf(161847792,plain,
~ intersection(a,bda,ai_bda),
inference(rewrite,[status(thm)],[a_intersection_bDa]),
[] ).
cnf(172725448,plain,
member(h(a,bda,ai_bda),bda),
inference(resolution,[status(thm)],[172547944,161847792]),
[] ).
fof(not_member_of_difference,plain,
! [A,B,C,D] :
( ~ member(A,B)
| ~ member(A,C)
| ~ difference(D,B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
[] ).
cnf(161802456,plain,
( ~ member(A,B)
| ~ member(A,C)
| ~ difference(D,B,C) ),
inference(rewrite,[status(thm)],[not_member_of_difference]),
[] ).
fof(b_minus_a,plain,
difference(b,a,bda),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
[] ).
cnf(161843672,plain,
difference(b,a,bda),
inference(rewrite,[status(thm)],[b_minus_a]),
[] ).
cnf(172340664,plain,
( ~ member(A,a)
| ~ member(A,bda) ),
inference(resolution,[status(thm)],[161802456,161843672]),
[] ).
fof(intersection_axiom1,plain,
! [A,B,C] :
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
[] ).
cnf(161770208,plain,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),A) ),
inference(rewrite,[status(thm)],[intersection_axiom1]),
[] ).
cnf(172514984,plain,
( intersection(A,B,ai_bda)
| member(h(A,B,ai_bda),A) ),
inference(resolution,[status(thm)],[161770208,161855992]),
[] ).
cnf(172711768,plain,
member(h(a,bda,ai_bda),a),
inference(resolution,[status(thm)],[172514984,161847792]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[172725448,172340664,172711768]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(intersection_axiom2,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
%
% cnf(161774536,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B)),inference(rewrite,[status(thm)],[intersection_axiom2]),[]).
%
% fof(prove_aI_bDa_is_empty,plain,(~member(A,ai_bda)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
%
% cnf(161855992,plain,(~member(A,ai_bda)),inference(rewrite,[status(thm)],[prove_aI_bDa_is_empty]),[]).
%
% cnf(172547944,plain,(intersection(A,B,ai_bda)|member(h(A,B,ai_bda),B)),inference(resolution,[status(thm)],[161774536,161855992]),[]).
%
% fof(a_intersection_bDa,plain,(~intersection(a,bda,ai_bda)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
%
% cnf(161847792,plain,(~intersection(a,bda,ai_bda)),inference(rewrite,[status(thm)],[a_intersection_bDa]),[]).
%
% cnf(172725448,plain,(member(h(a,bda,ai_bda),bda)),inference(resolution,[status(thm)],[172547944,161847792]),[]).
%
% fof(not_member_of_difference,plain,(~member(A,B)|~member(A,C)|~difference(D,B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
%
% cnf(161802456,plain,(~member(A,B)|~member(A,C)|~difference(D,B,C)),inference(rewrite,[status(thm)],[not_member_of_difference]),[]).
%
% fof(b_minus_a,plain,(difference(b,a,bda)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
%
% cnf(161843672,plain,(difference(b,a,bda)),inference(rewrite,[status(thm)],[b_minus_a]),[]).
%
% cnf(172340664,plain,(~member(A,a)|~member(A,bda)),inference(resolution,[status(thm)],[161802456,161843672]),[]).
%
% fof(intersection_axiom1,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
%
% cnf(161770208,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A)),inference(rewrite,[status(thm)],[intersection_axiom1]),[]).
%
% cnf(172514984,plain,(intersection(A,B,ai_bda)|member(h(A,B,ai_bda),A)),inference(resolution,[status(thm)],[161770208,161855992]),[]).
%
% cnf(172711768,plain,(member(h(a,bda,ai_bda),a)),inference(resolution,[status(thm)],[172514984,161847792]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172725448,172340664,172711768]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------