%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET766+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:32:38 PM UTC 2025
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 37 ( 11 ~; 8 |; 9 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIII02,plain,
! [E,R,A] :
( ( equivalence(R,E)
& member(A,E) )
=> member(A,equivalence_class(A,E,R)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).
fof(thIII02_negated,plain,
~ ! [E,R,A] :
( ( equivalence(R,E)
& member(A,E) )
=> member(A,equivalence_class(A,E,R)) ),
inference(negate_conjecture,[status(cth)],[thIII02]) ).
cnf(73,plain,
equivalence(sK24,sK23),
inference(cnf,[status(esa)],[thIII02_negated]) ).
cnf(l0,plain,
equivalence(sK24,sK23),
inference(instantiation,[status(thm)],[73]) ).
fof(equivalence,plain,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X] :
( member(X,A)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,A)
& member(Y,A) )
=> ( apply(R,X,Y)
=> apply(R,Y,X) ) )
& ! [X,Y,Z] :
( ( member(X,A)
& member(Y,A)
& member(Z,A) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('Axioms/SET006+2.ax',equivalence) ).
cnf(45,plain,
( ~ member(X0,X1)
| ~ equivalence(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf,[status(esa)],[equivalence]) ).
cnf(l1,plain,
( ~ member(sK25,sK23)
| ~ equivalence(sK24,sK23)
| apply(sK24,sK25,sK25) ),
inference(instantiation,[status(thm)],[45]) ).
fof(equivalence_class,plain,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( member(X,E)
& apply(R,A,X) ) ),
file('Axioms/SET006+2.ax',equivalence_class) ).
cnf(62,plain,
( ~ member(X0,X1)
| ~ apply(X2,X3,X0)
| member(X0,equivalence_class(X3,X1,X2)) ),
inference(cnf,[status(esa)],[equivalence_class]) ).
cnf(l29,plain,
( ~ member(sK25,sK23)
| ~ apply(sK24,sK25,sK25)
| member(sK25,equivalence_class(sK25,sK23,sK24)) ),
inference(instantiation,[status(thm)],[62]) ).
cnf(74,plain,
member(sK25,sK23),
inference(cnf,[status(esa)],[thIII02_negated]) ).
cnf(l2,plain,
member(sK25,sK23),
inference(instantiation,[status(thm)],[74]) ).
cnf(l31,plain,
member(sK25,sK23),
inference(instantiation,[status(thm)],[74]) ).
cnf(75,plain,
~ member(sK25,equivalence_class(sK25,sK23,sK24)),
inference(cnf,[status(esa)],[thIII02_negated]) ).
cnf(l32,plain,
~ member(sK25,equivalence_class(sK25,sK23,sK24)),
inference(instantiation,[status(thm)],[75]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l29,l2,l31,l32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SET766+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.09 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n025.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 22:36:49 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 4
% 0.09/0.29 % launching worker at depth: 5
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 6
% 0.09/0.29 % launching worker at depth: 7
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.30 % launching worker at depth: 9
% 0.14/0.32 % launching worker at depth: 10
% 0.14/0.35 % SZS status Theorem for theBenchmark
% 0.14/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------