%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET581+3 : 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 : n012.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 08:32:48 AM UTC 2026
% Result : Theorem 10.15s 1.62s
% Output : CNFRefutation 10.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 29 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 6 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(not_equal_defn,axiom,
! [X0,X1] :
( 'not$uequal'(X0,X1)
<=> X0 != X1 ) ).
fof(prove_th24,conjecture,
! [X0,X1,X2] :
( ( member(X0,X2)
& member(X0,X1) )
=> 'not$uequal'(intersection(X1,X2),'empty$uset') ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X0,X2)
& member(X0,X1) )
=> 'not$uequal'(intersection(X1,X2),'empty$uset') ),
inference(negate_conjecture,[status(cth)],[prove_th24]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c11,plain,
( X0 = X1
| 'not$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[not_equal_defn]) ).
cnf(c15,plain,
member(sK15,sK16),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
member(sK15,sK17),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
~ 'not$uequal'(intersection(sK16,sK17),'empty$uset'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
intersection(sK16,sK17) = 'empty$uset',
inference(resolution,[status(thm)],[c11,c17]) ).
cnf(d1,plain,
( ~ member(X0,sK17)
| ~ member(X0,sK16)
| member(X0,'empty$uset') ),
inference(superposition,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( ~ member(X0,sK17)
| ~ member(X0,sK16) ),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d3,plain,
~ member(sK15,sK16),
inference(resolution,[status(thm)],[d2,c16]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c15,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 07:57:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.15/1.62 % SZS status Theorem for theBenchmark.p
% 10.15/1.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------