TSTP Solution File: SET628+3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET628+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 15:33:37 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 94 ( 40 ~; 42 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 34 ( 7 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersect_defn,plain,
! [A,B,D] :
( ( member(d_nn_1(A,B),B)
| ~ intersect(A,B) )
& ( member(d_nn_1(A,B),A)
| ~ intersect(A,B) )
& ( intersect(A,B)
| ~ member(D,A)
| ~ member(D,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
[] ).
cnf(169824616,plain,
( intersect(A,B)
| ~ member(D,A)
| ~ member(D,B) ),
inference(rewrite,[status(thm)],[intersect_defn]),
[] ).
fof(equal_member_defn,plain,
! [C,A,B] :
( ( member(C,A)
| ~ member(C,B)
| ~ $equal(B,A) )
& ( ~ member(C,A)
| member(C,B)
| ~ $equal(B,A) )
& ( member(d(A,B,C),B)
| ~ member(d(A,B,C),B)
| $equal(B,A) )
& ( ~ member(d(A,B,C),A)
| ~ member(d(A,B,C),B)
| $equal(B,A) )
& ( member(d(A,B,C),B)
| member(d(A,B,C),A)
| $equal(B,A) )
& ( ~ member(d(A,B,C),A)
| member(d(A,B,C),A)
| $equal(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
[] ).
cnf(169856440,plain,
( member(d(A,B,C),B)
| member(d(A,B,C),A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[equal_member_defn]),
[] ).
fof(empty_set_defn,plain,
! [A] : ~ member(A,empty_set),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
[] ).
cnf(169841448,plain,
~ member(A,empty_set),
inference(rewrite,[status(thm)],[empty_set_defn]),
[] ).
cnf(180502392,plain,
( member(d(A,empty_set,B),A)
| $equal(empty_set,A) ),
inference(resolution,[status(thm)],[169856440,169841448]),
[] ).
fof(prove_th110,plain,
( ( not_equal(b,empty_set)
| intersect(b,b) )
& ( ~ intersect(b,b)
| intersect(b,b) )
& ( not_equal(b,empty_set)
| ~ not_equal(b,empty_set) )
& ( ~ intersect(b,b)
| ~ not_equal(b,empty_set) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
[] ).
cnf(169978224,plain,
( ~ intersect(b,b)
| ~ not_equal(b,empty_set) ),
inference(rewrite,[status(thm)],[prove_th110]),
[] ).
fof(not_equal_defn,plain,
! [A,B] :
( ( ~ not_equal(A,B)
| ~ $equal(B,A) )
& ( not_equal(A,B)
| $equal(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
[] ).
cnf(169888880,plain,
( not_equal(A,B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[not_equal_defn]),
[] ).
cnf(180623296,plain,
( ~ intersect(b,b)
| $equal(empty_set,b) ),
inference(resolution,[status(thm)],[169978224,169888880]),
[] ).
fof(empty_defn,plain,
! [A,B] :
( ( ~ empty(A)
| ~ member(B,A) )
& ( empty(A)
| member(c(A,B),A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
[] ).
cnf(169912360,plain,
( empty(A)
| member(c(A,B),A) ),
inference(rewrite,[status(thm)],[empty_defn]),
[] ).
cnf(180429240,plain,
empty(empty_set),
inference(resolution,[status(thm)],[169912360,169841448]),
[] ).
cnf(180643288,plain,
( ~ intersect(b,b)
| empty(b) ),
inference(paramodulation,[status(thm)],[180623296,180429240,theory(equality)]),
[] ).
cnf(169811488,plain,
( ~ not_equal(A,B)
| ~ $equal(B,A) ),
inference(rewrite,[status(thm)],[not_equal_defn]),
[] ).
cnf(169988264,plain,
( not_equal(b,empty_set)
| intersect(b,b) ),
inference(rewrite,[status(thm)],[prove_th110]),
[] ).
cnf(180580456,plain,
( ~ $equal(empty_set,b)
| intersect(b,b) ),
inference(resolution,[status(thm)],[169811488,169988264]),
[] ).
cnf(180674544,plain,
( empty(b)
| ~ $equal(empty_set,b) ),
inference(resolution,[status(thm)],[180643288,180580456]),
[] ).
cnf(169831296,plain,
( member(d_nn_1(A,B),A)
| ~ intersect(A,B) ),
inference(rewrite,[status(thm)],[intersect_defn]),
[] ).
cnf(169918944,plain,
( ~ empty(A)
| ~ member(B,A) ),
inference(rewrite,[status(thm)],[empty_defn]),
[] ).
cnf(180787248,plain,
( ~ intersect(A,B)
| ~ empty(A) ),
inference(resolution,[status(thm)],[169831296,169918944]),
[] ).
cnf(180849536,plain,
~ $equal(empty_set,b),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180674544,180787248,180580456]),
[] ).
cnf(181081184,plain,
member(d(b,empty_set,A),b),
inference(resolution,[status(thm)],[180502392,180849536]),
[] ).
cnf(181142888,plain,
~ empty(b),
inference(resolution,[status(thm)],[181081184,169918944]),
[] ).
cnf(181164560,plain,
member(c(b,A),b),
inference(resolution,[status(thm)],[181142888,169912360]),
[] ).
cnf(181624320,plain,
intersect(b,b),
inference(resolution,[status(thm)],[169824616,181164560]),
[] ).
cnf(180667392,plain,
( empty(b)
| not_equal(b,empty_set) ),
inference(resolution,[status(thm)],[180643288,169988264]),
[] ).
cnf(180828408,plain,
not_equal(b,empty_set),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180667392,180787248,169988264]),
[] ).
cnf(180856696,plain,
~ intersect(b,b),
inference(resolution,[status(thm)],[180828408,169978224]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[181624320,180856696]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(intersect_defn,plain,(((member(d_nn_1(A,B),B)|~intersect(A,B))&(member(d_nn_1(A,B),A)|~intersect(A,B))&(intersect(A,B)|~member(D,A)|~member(D,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
%
% cnf(169824616,plain,(intersect(A,B)|~member(D,A)|~member(D,B)),inference(rewrite,[status(thm)],[intersect_defn]),[]).
%
% fof(equal_member_defn,plain,(((member(C,A)|~member(C,B)|~$equal(B,A))&(~member(C,A)|member(C,B)|~$equal(B,A))&(member(d(A,B,C),B)|~member(d(A,B,C),B)|$equal(B,A))&(~member(d(A,B,C),A)|~member(d(A,B,C),B)|$equal(B,A))&(member(d(A,B,C),B)|member(d(A,B,C),A)|$equal(B,A))&(~member(d(A,B,C),A)|member(d(A,B,C),A)|$equal(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
%
% cnf(169856440,plain,(member(d(A,B,C),B)|member(d(A,B,C),A)|$equal(B,A)),inference(rewrite,[status(thm)],[equal_member_defn]),[]).
%
% fof(empty_set_defn,plain,(~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
%
% cnf(169841448,plain,(~member(A,empty_set)),inference(rewrite,[status(thm)],[empty_set_defn]),[]).
%
% cnf(180502392,plain,(member(d(A,empty_set,B),A)|$equal(empty_set,A)),inference(resolution,[status(thm)],[169856440,169841448]),[]).
%
% fof(prove_th110,plain,(((not_equal(b,empty_set)|intersect(b,b))&(~intersect(b,b)|intersect(b,b))&(not_equal(b,empty_set)|~not_equal(b,empty_set))&(~intersect(b,b)|~not_equal(b,empty_set)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
%
% cnf(169978224,plain,(~intersect(b,b)|~not_equal(b,empty_set)),inference(rewrite,[status(thm)],[prove_th110]),[]).
%
% fof(not_equal_defn,plain,(((~not_equal(A,B)|~$equal(B,A))&(not_equal(A,B)|$equal(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
%
% cnf(169888880,plain,(not_equal(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[not_equal_defn]),[]).
%
% cnf(180623296,plain,(~intersect(b,b)|$equal(empty_set,b)),inference(resolution,[status(thm)],[169978224,169888880]),[]).
%
% fof(empty_defn,plain,(((~empty(A)|~member(B,A))&(empty(A)|member(c(A,B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
%
% cnf(169912360,plain,(empty(A)|member(c(A,B),A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
%
% cnf(180429240,plain,(empty(empty_set)),inference(resolution,[status(thm)],[169912360,169841448]),[]).
%
% cnf(180643288,plain,(~intersect(b,b)|empty(b)),inference(paramodulation,[status(thm)],[180623296,180429240,theory(equality)]),[]).
%
% cnf(169811488,plain,(~not_equal(A,B)|~$equal(B,A)),inference(rewrite,[status(thm)],[not_equal_defn]),[]).
%
% cnf(169988264,plain,(not_equal(b,empty_set)|intersect(b,b)),inference(rewrite,[status(thm)],[prove_th110]),[]).
%
% cnf(180580456,plain,(~$equal(empty_set,b)|intersect(b,b)),inference(resolution,[status(thm)],[169811488,169988264]),[]).
%
% cnf(180674544,plain,(empty(b)|~$equal(empty_set,b)),inference(resolution,[status(thm)],[180643288,180580456]),[]).
%
% cnf(169831296,plain,(member(d_nn_1(A,B),A)|~intersect(A,B)),inference(rewrite,[status(thm)],[intersect_defn]),[]).
%
% cnf(169918944,plain,(~empty(A)|~member(B,A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
%
% cnf(180787248,plain,(~intersect(A,B)|~empty(A)),inference(resolution,[status(thm)],[169831296,169918944]),[]).
%
% cnf(180849536,plain,(~$equal(empty_set,b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180674544,180787248,180580456]),[]).
%
% cnf(181081184,plain,(member(d(b,empty_set,A),b)),inference(resolution,[status(thm)],[180502392,180849536]),[]).
%
% cnf(181142888,plain,(~empty(b)),inference(resolution,[status(thm)],[181081184,169918944]),[]).
%
% cnf(181164560,plain,(member(c(b,A),b)),inference(resolution,[status(thm)],[181142888,169912360]),[]).
%
% cnf(181624320,plain,(intersect(b,b)),inference(resolution,[status(thm)],[169824616,181164560]),[]).
%
% cnf(180667392,plain,(empty(b)|not_equal(b,empty_set)),inference(resolution,[status(thm)],[180643288,169988264]),[]).
%
% cnf(180828408,plain,(not_equal(b,empty_set)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180667392,180787248,169988264]),[]).
%
% cnf(180856696,plain,(~intersect(b,b)),inference(resolution,[status(thm)],[180828408,169978224]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[181624320,180856696]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------