%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:33:12 AM UTC 2026
% Result : Theorem 15.48s 2.63s
% Output : CNFRefutation 15.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 35 ( 11 ~; 6 |; 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 : 26 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equivalence,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X0)
& member(X2,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) ) ) ) ).
fof(equivalence_class,axiom,
! [X0,X1,X2,X3] :
( member(X3,'equivalence$uclass'(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ) ).
fof(thIII02,conjecture,
! [X0,X1,X2] :
( ( member(X2,X0)
& equivalence(X1,X0) )
=> member(X2,'equivalence$uclass'(X2,X0,X1)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X2,X0)
& equivalence(X1,X0) )
=> member(X2,'equivalence$uclass'(X2,X0,X1)) ),
inference(negate_conjecture,[status(cth)],[thIII02]) ).
cnf(c48,plain,
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ equivalence(X0,X1) ),
inference(clausification,[status(esa)],[equivalence]) ).
cnf(c67,plain,
( ~ apply(X3,X1,X0)
| ~ member(X0,X2)
| member(X0,'equivalence$uclass'(X1,X2,X3)) ),
inference(clausification,[status(esa)],[equivalence_class]) ).
cnf(c79,plain,
equivalence(sK83,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c80,plain,
member(sK84,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c81,plain,
~ member(sK84,'equivalence$uclass'(sK84,sK82,sK83)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( apply(sK83,X0,X0)
| ~ member(X0,sK82) ),
inference(resolution,[status(thm)],[c48,c79]) ).
cnf(d1,plain,
( ~ apply(sK83,sK84,sK84)
| ~ member(sK84,sK82) ),
inference(resolution,[status(thm)],[c67,c81]) ).
cnf(d2,plain,
~ apply(sK83,sK84,sK84),
inference(resolution,[status(thm)],[c80,d1]) ).
cnf(d3,plain,
~ member(sK84,sK82),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c80,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:13:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.48/2.63 % SZS status Theorem for theBenchmark.p
% 15.48/2.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------