TSTP Solution File: SET766+4 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET766+4 : TPTP v3.4.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:36:38 EDT 2009
% Result : Theorem 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 233 ( 0 equ)
% Maximal formula atoms : 207 ( 17 avg)
% Number of connectives : 288 ( 68 ~; 166 |; 54 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 62 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-8 aty)
% Number of variables : 22 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(thIII02,plain,
( equivalence(r,e)
& member(a,e)
& ~ member(a,equivalence_class(a,e,r)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET766+4.tptp',unknown),
[] ).
cnf(163112232,plain,
~ member(a,equivalence_class(a,e,r)),
inference(rewrite,[status(thm)],[thIII02]),
[] ).
fof(equivalence_class,plain,
! [A,C,D,B] :
( ( apply(A,C,D)
| ~ member(D,equivalence_class(C,B,A)) )
& ( member(D,B)
| ~ member(D,equivalence_class(C,B,A)) )
& ( member(D,equivalence_class(C,B,A))
| ~ member(D,B)
| ~ apply(A,C,D) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET766+4.tptp',unknown),
[] ).
cnf(162903512,plain,
( member(D,equivalence_class(C,B,A))
| ~ member(D,B)
| ~ apply(A,C,D) ),
inference(rewrite,[status(thm)],[equivalence_class]),
[] ).
cnf(163120320,plain,
member(a,e),
inference(rewrite,[status(thm)],[thIII02]),
[] ).
cnf(176941432,plain,
( member(a,equivalence_class(B,e,A))
| ~ apply(A,B,a) ),
inference(resolution,[status(thm)],[162903512,163120320]),
[] ).
fof(equivalence,plain,
! [D,A,E,B,F,G,H,C] :
( ( ~ member(D,A)
| ~ member(E,A)
| ~ apply(B,D,E)
| apply(B,E,D)
| ~ equivalence(B,A) )
& ( ~ member(F,A)
| ~ member(G,A)
| ~ member(H,A)
| ~ apply(B,F,G)
| ~ apply(B,G,H)
| apply(B,F,H)
| ~ equivalence(B,A) )
& ( ~ member(C,A)
| apply(B,C,C)
| ~ equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| ~ apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| ~ apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| member(x_nn_1(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( ~ apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(x(A,B,C,D,E,F,G,H),A)
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(y(A,B,C,D,E,F,G,H),A)
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) )
& ( member(z(A,B,C,D,E,F,G,H),A)
| member(y_nn_6(A,B,C,D,E,F,G,H),A)
| member(x_nn_2(A,B,C,D,E,F,G,H),A)
| equivalence(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET766+4.tptp',unknown),
[] ).
cnf(162854040,plain,
( ~ member(C,A)
| apply(B,C,C)
| ~ equivalence(B,A) ),
inference(rewrite,[status(thm)],[equivalence]),
[] ).
cnf(176812920,plain,
( apply(A,a,a)
| ~ equivalence(A,e) ),
inference(resolution,[status(thm)],[162854040,163120320]),
[] ).
cnf(163133136,plain,
equivalence(r,e),
inference(rewrite,[status(thm)],[thIII02]),
[] ).
cnf(177340088,plain,
apply(r,a,a),
inference(resolution,[status(thm)],[176812920,163133136]),
[] ).
cnf(178528920,plain,
member(a,equivalence_class(a,e,r)),
inference(resolution,[status(thm)],[176941432,177340088]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[163112232,178528920]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(thIII02,plain,((equivalence(r,e)&member(a,e)&~member(a,equivalence_class(a,e,r)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET766+4.tptp',unknown),[]).
%
% cnf(163112232,plain,(~member(a,equivalence_class(a,e,r))),inference(rewrite,[status(thm)],[thIII02]),[]).
%
% fof(equivalence_class,plain,(((apply(A,C,D)|~member(D,equivalence_class(C,B,A)))&(member(D,B)|~member(D,equivalence_class(C,B,A)))&(member(D,equivalence_class(C,B,A))|~member(D,B)|~apply(A,C,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET766+4.tptp',unknown),[]).
%
% cnf(162903512,plain,(member(D,equivalence_class(C,B,A))|~member(D,B)|~apply(A,C,D)),inference(rewrite,[status(thm)],[equivalence_class]),[]).
%
% cnf(163120320,plain,(member(a,e)),inference(rewrite,[status(thm)],[thIII02]),[]).
%
% cnf(176941432,plain,(member(a,equivalence_class(B,e,A))|~apply(A,B,a)),inference(resolution,[status(thm)],[162903512,163120320]),[]).
%
% fof(equivalence,plain,(((~member(D,A)|~member(E,A)|~apply(B,D,E)|apply(B,E,D)|~equivalence(B,A))&(~member(F,A)|~member(G,A)|~member(H,A)|~apply(B,F,G)|~apply(B,G,H)|apply(B,F,H)|~equivalence(B,A))&(~member(C,A)|apply(B,C,C)|~equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|member(x_nn_1(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(x_nn_1(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(x_nn_1(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|member(x_nn_1(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|member(x_nn_1(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|member(x_nn_1(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|member(y_nn_6(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(y_nn_6(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(y_nn_6(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|member(y_nn_6(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|member(y_nn_6(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|member(y_nn_6(A,B,C,D,E,F,G,H),A)|~apply(B,x_nn_2(A,B,C,D,E,F,G,H),x_nn_2(A,B,C,D,E,F,G,H))|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|apply(B,x_nn_1(A,B,C,D,E,F,G,H),y_nn_6(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|~apply(B,y_nn_6(A,B,C,D,E,F,G,H),x_nn_1(A,B,C,D,E,F,G,H))|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|member(x_nn_1(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(x_nn_1(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(x_nn_1(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|member(x_nn_1(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|member(x_nn_1(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|member(x_nn_1(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,x(A,B,C,D,E,F,G,H),y(A,B,C,D,E,F,G,H))|member(y_nn_6(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(apply(B,y(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(y_nn_6(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(~apply(B,x(A,B,C,D,E,F,G,H),z(A,B,C,D,E,F,G,H))|member(y_nn_6(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(x(A,B,C,D,E,F,G,H),A)|member(y_nn_6(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(y(A,B,C,D,E,F,G,H),A)|member(y_nn_6(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A))&(member(z(A,B,C,D,E,F,G,H),A)|member(y_nn_6(A,B,C,D,E,F,G,H),A)|member(x_nn_2(A,B,C,D,E,F,G,H),A)|equivalence(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET766+4.tptp',unknown),[]).
%
% cnf(162854040,plain,(~member(C,A)|apply(B,C,C)|~equivalence(B,A)),inference(rewrite,[status(thm)],[equivalence]),[]).
%
% cnf(176812920,plain,(apply(A,a,a)|~equivalence(A,e)),inference(resolution,[status(thm)],[162854040,163120320]),[]).
%
% cnf(163133136,plain,(equivalence(r,e)),inference(rewrite,[status(thm)],[thIII02]),[]).
%
% cnf(177340088,plain,(apply(r,a,a)),inference(resolution,[status(thm)],[176812920,163133136]),[]).
%
% cnf(178528920,plain,(member(a,equivalence_class(a,e,r))),inference(resolution,[status(thm)],[176941432,177340088]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[163112232,178528920]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------