%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET809+4 : TPTP v3.4.2. Released v3.2.0.
% 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 15:37:40 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 84 ( 8 avg)
% Number of connectives : 169 ( 46 ~; 88 |; 35 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-7 aty)
% Number of variables : 26 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(thV2,plain,
( member(a,on)
& member(a,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),
[] ).
cnf(152050968,plain,
member(a,on),
inference(rewrite,[status(thm)],[thV2]),
[] ).
fof(ordinal_number,plain,
! [A,B] :
( ( strict_well_order(member_predicate,A)
| ~ member(A,on) )
& ( ~ member(B,A)
| subset(B,A)
| ~ member(A,on) )
& ( set(A)
| ~ member(A,on) )
& ( ~ subset(x(A,B),A)
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ( member(x(A,B),A)
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),
[] ).
cnf(152054616,plain,
( strict_well_order(member_predicate,A)
| ~ member(A,on) ),
inference(rewrite,[status(thm)],[ordinal_number]),
[] ).
fof(strict_well_order,plain,
! [C,B,D,A,H] :
( ( ~ subset(C,B)
| ~ member(D,C)
| least(y_nn_2(A,B,C,D),A,C)
| ~ strict_well_order(A,B) )
& ( strict_order(A,B)
| ~ strict_well_order(A,B) )
& ( subset(a(A,B,C,D),B)
| ~ strict_order(A,B)
| strict_well_order(A,B) )
& ( member(x(A,B,C,D),a(A,B,C,D))
| ~ strict_order(A,B)
| strict_well_order(A,B) )
& ( ~ least(H,A,a(A,B,C,D))
| ~ strict_order(A,B)
| strict_well_order(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),
[] ).
cnf(152413728,plain,
( strict_order(A,B)
| ~ strict_well_order(A,B) ),
inference(rewrite,[status(thm)],[strict_well_order]),
[] ).
fof(rel_member,plain,
! [A,B] :
( ( ~ apply(member_predicate,A,B)
| member(A,B) )
& ( apply(member_predicate,A,B)
| ~ member(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),
[] ).
cnf(152516152,plain,
( apply(member_predicate,A,B)
| ~ member(A,B) ),
inference(rewrite,[status(thm)],[rel_member]),
[] ).
cnf(152863416,plain,
member(a,a),
inference(rewrite,[status(thm)],[thV2]),
[] ).
cnf(163543648,plain,
apply(member_predicate,a,a),
inference(resolution,[status(thm)],[152516152,152863416]),
[] ).
fof(strict_order,plain,
! [E,B,F,G,A,C,D] :
( ( ~ member(E,B)
| ~ member(F,B)
| ~ member(G,B)
| ~ apply(A,E,F)
| ~ apply(A,F,G)
| apply(A,E,G)
| ~ strict_order(A,B) )
& ( ~ member(C,B)
| ~ member(D,B)
| ~ apply(A,C,D)
| ~ apply(A,D,C)
| ~ strict_order(A,B) )
& ( apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))
| apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( ~ apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( member(x(A,B,C,D,E,F,G),B)
| apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( member(y(A,B,C,D,E,F,G),B)
| apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( member(z(A,B,C,D,E,F,G),B)
| apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))
| apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( ~ apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( member(x(A,B,C,D,E,F,G),B)
| apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( member(y(A,B,C,D,E,F,G),B)
| apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( member(z(A,B,C,D,E,F,G),B)
| apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))
| strict_order(A,B) )
& ( apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))
| member(x_nn_1(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| member(x_nn_1(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( ~ apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| member(x_nn_1(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( member(x(A,B,C,D,E,F,G),B)
| member(x_nn_1(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( member(y(A,B,C,D,E,F,G),B)
| member(x_nn_1(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( member(z(A,B,C,D,E,F,G),B)
| member(x_nn_1(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))
| member(y_nn_4(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| member(y_nn_4(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( ~ apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))
| member(y_nn_4(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( member(x(A,B,C,D,E,F,G),B)
| member(y_nn_4(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( member(y(A,B,C,D,E,F,G),B)
| member(y_nn_4(A,B,C,D,E,F,G),B)
| strict_order(A,B) )
& ( member(z(A,B,C,D,E,F,G),B)
| member(y_nn_4(A,B,C,D,E,F,G),B)
| strict_order(A,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),
[] ).
cnf(152720152,plain,
( ~ member(C,B)
| ~ member(D,B)
| ~ apply(A,C,D)
| ~ apply(A,D,C)
| ~ strict_order(A,B) ),
inference(rewrite,[status(thm)],[strict_order]),
[] ).
cnf(164537136,plain,
( ~ member(a,A)
| ~ strict_order(member_predicate,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[163543648,152720152,163543648]),
[] ).
cnf(164551456,plain,
~ strict_order(member_predicate,a),
inference(resolution,[status(thm)],[164537136,152863416]),
[] ).
cnf(164694120,plain,
~ strict_well_order(member_predicate,a),
inference(resolution,[status(thm)],[152413728,164551456]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[152050968,152054616,164694120]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(thV2,plain,((member(a,on)&member(a,a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),[]).
%
% cnf(152050968,plain,(member(a,on)),inference(rewrite,[status(thm)],[thV2]),[]).
%
% fof(ordinal_number,plain,(((strict_well_order(member_predicate,A)|~member(A,on))&(~member(B,A)|subset(B,A)|~member(A,on))&(set(A)|~member(A,on))&(~subset(x(A,B),A)|~strict_well_order(member_predicate,A)|~set(A)|member(A,on))&(member(x(A,B),A)|~strict_well_order(member_predicate,A)|~set(A)|member(A,on)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),[]).
%
% cnf(152054616,plain,(strict_well_order(member_predicate,A)|~member(A,on)),inference(rewrite,[status(thm)],[ordinal_number]),[]).
%
% fof(strict_well_order,plain,(((~subset(C,B)|~member(D,C)|least(y_nn_2(A,B,C,D),A,C)|~strict_well_order(A,B))&(strict_order(A,B)|~strict_well_order(A,B))&(subset(a(A,B,C,D),B)|~strict_order(A,B)|strict_well_order(A,B))&(member(x(A,B,C,D),a(A,B,C,D))|~strict_order(A,B)|strict_well_order(A,B))&(~least(H,A,a(A,B,C,D))|~strict_order(A,B)|strict_well_order(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),[]).
%
% cnf(152413728,plain,(strict_order(A,B)|~strict_well_order(A,B)),inference(rewrite,[status(thm)],[strict_well_order]),[]).
%
% fof(rel_member,plain,(((~apply(member_predicate,A,B)|member(A,B))&(apply(member_predicate,A,B)|~member(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),[]).
%
% cnf(152516152,plain,(apply(member_predicate,A,B)|~member(A,B)),inference(rewrite,[status(thm)],[rel_member]),[]).
%
% cnf(152863416,plain,(member(a,a)),inference(rewrite,[status(thm)],[thV2]),[]).
%
% cnf(163543648,plain,(apply(member_predicate,a,a)),inference(resolution,[status(thm)],[152516152,152863416]),[]).
%
% fof(strict_order,plain,(((~member(E,B)|~member(F,B)|~member(G,B)|~apply(A,E,F)|~apply(A,F,G)|apply(A,E,G)|~strict_order(A,B))&(~member(C,B)|~member(D,B)|~apply(A,C,D)|~apply(A,D,C)|~strict_order(A,B))&(apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))|apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))|strict_order(A,B))&(apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))|strict_order(A,B))&(~apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))|strict_order(A,B))&(member(x(A,B,C,D,E,F,G),B)|apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))|strict_order(A,B))&(member(y(A,B,C,D,E,F,G),B)|apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))|strict_order(A,B))&(member(z(A,B,C,D,E,F,G),B)|apply(A,x_nn_1(A,B,C,D,E,F,G),y_nn_4(A,B,C,D,E,F,G))|strict_order(A,B))&(apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))|apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))|strict_order(A,B))&(apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))|strict_order(A,B))&(~apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))|strict_order(A,B))&(member(x(A,B,C,D,E,F,G),B)|apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))|strict_order(A,B))&(member(y(A,B,C,D,E,F,G),B)|apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))|strict_order(A,B))&(member(z(A,B,C,D,E,F,G),B)|apply(A,y_nn_4(A,B,C,D,E,F,G),x_nn_1(A,B,C,D,E,F,G))|strict_order(A,B))&(apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))|member(x_nn_1(A,B,C,D,E,F,G),B)|strict_order(A,B))&(apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|member(x_nn_1(A,B,C,D,E,F,G),B)|strict_order(A,B))&(~apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|member(x_nn_1(A,B,C,D,E,F,G),B)|strict_order(A,B))&(member(x(A,B,C,D,E,F,G),B)|member(x_nn_1(A,B,C,D,E,F,G),B)|strict_order(A,B))&(member(y(A,B,C,D,E,F,G),B)|member(x_nn_1(A,B,C,D,E,F,G),B)|strict_order(A,B))&(member(z(A,B,C,D,E,F,G),B)|member(x_nn_1(A,B,C,D,E,F,G),B)|strict_order(A,B))&(apply(A,x(A,B,C,D,E,F,G),y(A,B,C,D,E,F,G))|member(y_nn_4(A,B,C,D,E,F,G),B)|strict_order(A,B))&(apply(A,y(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|member(y_nn_4(A,B,C,D,E,F,G),B)|strict_order(A,B))&(~apply(A,x(A,B,C,D,E,F,G),z(A,B,C,D,E,F,G))|member(y_nn_4(A,B,C,D,E,F,G),B)|strict_order(A,B))&(member(x(A,B,C,D,E,F,G),B)|member(y_nn_4(A,B,C,D,E,F,G),B)|strict_order(A,B))&(member(y(A,B,C,D,E,F,G),B)|member(y_nn_4(A,B,C,D,E,F,G),B)|strict_order(A,B))&(member(z(A,B,C,D,E,F,G),B)|member(y_nn_4(A,B,C,D,E,F,G),B)|strict_order(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET809+4.tptp',unknown),[]).
%
% cnf(152720152,plain,(~member(C,B)|~member(D,B)|~apply(A,C,D)|~apply(A,D,C)|~strict_order(A,B)),inference(rewrite,[status(thm)],[strict_order]),[]).
%
% cnf(164537136,plain,(~member(a,A)|~strict_order(member_predicate,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163543648,152720152,163543648]),[]).
%
% cnf(164551456,plain,(~strict_order(member_predicate,a)),inference(resolution,[status(thm)],[164537136,152863416]),[]).
%
% cnf(164694120,plain,(~strict_well_order(member_predicate,a)),inference(resolution,[status(thm)],[152413728,164551456]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[152050968,152054616,164694120]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------