TSTP Solution File: SET662+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET662+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:34:58 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 124 ( 57 ~; 58 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 8 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p20,plain,
! [A] : ilf_type(A,set_type),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(173126024,plain,
ilf_type(A,set_type),
inference(rewrite,[status(thm)],[p20]),
[] ).
fof(p12,plain,
! [A,B,C] :
( ( ~ member(A,power_set(B))
| ~ ilf_type(C,set_type)
| ~ member(C,A)
| member(C,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( member(d(A,B,C),A)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ~ member(d(A,B,C),B)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(d(A,B,C),set_type)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(172944536,plain,
( member(d(A,B,C),A)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p12]),
[] ).
cnf(181216560,plain,
( member(d(A,B,C),A)
| member(A,power_set(B)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172944536,173126024]),
[] ).
fof(p4,plain,
! [A] :
( ~ ilf_type(A,set_type)
| ~ member(A,empty_set) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(172747392,plain,
( ~ ilf_type(A,set_type)
| ~ member(A,empty_set) ),
inference(rewrite,[status(thm)],[p4]),
[] ).
cnf(181113856,plain,
~ member(A,empty_set),
inference(resolution,[status(thm)],[172747392,173126024]),
[] ).
cnf(181951256,plain,
member(empty_set,power_set(A)),
inference(resolution,[status(thm)],[181216560,181113856]),
[] ).
fof(p14,plain,
! [A,B] :
( ( ~ ilf_type(A,member_type(B))
| member(A,B)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(A,member_type(B))
| ~ member(A,B)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(172992928,plain,
( ilf_type(A,member_type(B))
| ~ member(A,B)
| empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p14]),
[] ).
cnf(181225888,plain,
( ilf_type(A,member_type(B))
| ~ member(A,B)
| empty(B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172992928,173126024]),
[] ).
cnf(182045240,plain,
( ilf_type(empty_set,member_type(power_set(A)))
| empty(power_set(A)) ),
inference(resolution,[status(thm)],[181951256,181225888]),
[] ).
fof(p13,plain,
! [A] :
( ( ilf_type(power_set(A),set_type)
| ~ ilf_type(A,set_type) )
& ( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(172971432,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p13]),
[] ).
cnf(181123112,plain,
~ empty(power_set(A)),
inference(resolution,[status(thm)],[172971432,173126024]),
[] ).
cnf(182149760,plain,
ilf_type(empty_set,member_type(power_set(A))),
inference(resolution,[status(thm)],[182045240,181123112]),
[] ).
fof(p7,plain,
! [B,A] :
( ( ~ ilf_type(B,subset_type(A))
| ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ilf_type(B,subset_type(A))
| ~ ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(172800824,plain,
( ilf_type(B,subset_type(A))
| ~ ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p7]),
[] ).
cnf(181201632,plain,
( ilf_type(B,subset_type(A))
| ~ ilf_type(B,member_type(power_set(A))) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172800824,173126024]),
[] ).
cnf(182163360,plain,
ilf_type(empty_set,subset_type(A)),
inference(resolution,[status(thm)],[182149760,181201632]),
[] ).
fof(p2,plain,
! [C,A,B,D] :
( ( ~ ilf_type(C,subset_type(cross_product(A,B)))
| ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) )
& ( ~ ilf_type(D,relation_type(A,B))
| ilf_type(D,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(172737680,plain,
( ~ ilf_type(C,subset_type(cross_product(A,B)))
| ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(rewrite,[status(thm)],[p2]),
[] ).
cnf(181250000,plain,
( ~ ilf_type(C,subset_type(cross_product(A,B)))
| ilf_type(C,relation_type(A,B)) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172737680,173126024]),
[] ).
fof(prove_relset_1_25,plain,
( ilf_type(b,set_type)
& ilf_type(c,set_type)
& ~ ilf_type(empty_set,relation_type(b,c)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),
[] ).
cnf(173177408,plain,
~ ilf_type(empty_set,relation_type(b,c)),
inference(rewrite,[status(thm)],[prove_relset_1_25]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[182163360,181250000,173177408]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(p20,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(173126024,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p20]),[]).
%
% fof(p12,plain,(((~member(A,power_set(B))|~ilf_type(C,set_type)|~member(C,A)|member(C,B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(member(d(A,B,C),A)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(~member(d(A,B,C),B)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(d(A,B,C),set_type)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(172944536,plain,(member(d(A,B,C),A)|member(A,power_set(B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p12]),[]).
%
% cnf(181216560,plain,(member(d(A,B,C),A)|member(A,power_set(B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172944536,173126024]),[]).
%
% fof(p4,plain,(~ilf_type(A,set_type)|~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(172747392,plain,(~ilf_type(A,set_type)|~member(A,empty_set)),inference(rewrite,[status(thm)],[p4]),[]).
%
% cnf(181113856,plain,(~member(A,empty_set)),inference(resolution,[status(thm)],[172747392,173126024]),[]).
%
% cnf(181951256,plain,(member(empty_set,power_set(A))),inference(resolution,[status(thm)],[181216560,181113856]),[]).
%
% fof(p14,plain,(((~ilf_type(A,member_type(B))|member(A,B)|empty(B)|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(A,member_type(B))|~member(A,B)|empty(B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(172992928,plain,(ilf_type(A,member_type(B))|~member(A,B)|empty(B)|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p14]),[]).
%
% cnf(181225888,plain,(ilf_type(A,member_type(B))|~member(A,B)|empty(B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172992928,173126024]),[]).
%
% cnf(182045240,plain,(ilf_type(empty_set,member_type(power_set(A)))|empty(power_set(A))),inference(resolution,[status(thm)],[181951256,181225888]),[]).
%
% fof(p13,plain,(((ilf_type(power_set(A),set_type)|~ilf_type(A,set_type))&(~empty(power_set(A))|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(172971432,plain,(~empty(power_set(A))|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p13]),[]).
%
% cnf(181123112,plain,(~empty(power_set(A))),inference(resolution,[status(thm)],[172971432,173126024]),[]).
%
% cnf(182149760,plain,(ilf_type(empty_set,member_type(power_set(A)))),inference(resolution,[status(thm)],[182045240,181123112]),[]).
%
% fof(p7,plain,(((~ilf_type(B,subset_type(A))|ilf_type(B,member_type(power_set(A)))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(172800824,plain,(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p7]),[]).
%
% cnf(181201632,plain,(ilf_type(B,subset_type(A))|~ilf_type(B,member_type(power_set(A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172800824,173126024]),[]).
%
% cnf(182163360,plain,(ilf_type(empty_set,subset_type(A))),inference(resolution,[status(thm)],[182149760,181201632]),[]).
%
% fof(p2,plain,(((~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type))&(~ilf_type(D,relation_type(A,B))|ilf_type(D,subset_type(cross_product(A,B)))|~ilf_type(B,set_type)|~ilf_type(A,set_type)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(172737680,plain,(~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))|~ilf_type(B,set_type)|~ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p2]),[]).
%
% cnf(181250000,plain,(~ilf_type(C,subset_type(cross_product(A,B)))|ilf_type(C,relation_type(A,B))),inference(forward_subsumption_resolution__resolution,[status(thm)],[173126024,172737680,173126024]),[]).
%
% fof(prove_relset_1_25,plain,((ilf_type(b,set_type)&ilf_type(c,set_type)&~ilf_type(empty_set,relation_type(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET662+3.tptp',unknown),[]).
%
% cnf(173177408,plain,(~ilf_type(empty_set,relation_type(b,c))),inference(rewrite,[status(thm)],[prove_relset_1_25]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182163360,181250000,173177408]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------