%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET628+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 : n014.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 08:32:57 AM UTC 2026
% Result : Theorem 9.62s 1.66s
% Output : CNFRefutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 59 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 20 ~; 21 |; 1 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 4 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(equal_member_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ) ).
fof(not_equal_defn,axiom,
! [X0,X1] :
( 'not$uequal'(X0,X1)
<=> X0 != X1 ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th110,conjecture,
! [X0] :
( intersect(X0,X0)
<=> 'not$uequal'(X0,'empty$uset') ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( intersect(X0,X0)
<=> 'not$uequal'(X0,'empty$uset') ),
inference(negate_conjecture,[status(cth)],[prove_th110]) ).
cnf(c1,plain,
( member(sK2(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c3,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c7,plain,
( member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_member_defn]) ).
cnf(c10,plain,
( X0 != X1
| ~ 'not$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[not_equal_defn]) ).
cnf(c11,plain,
( X0 = X1
| 'not$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[not_equal_defn]) ).
cnf(c13,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c14,plain,
( member(sK15(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c16,plain,
( 'not$uequal'(sK16,'empty$uset')
| intersect(sK16,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
( ~ intersect(sK16,sK16)
| ~ 'not$uequal'(sK16,'empty$uset') ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(sK8(X0,'empty$uset'),X0)
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d1,plain,
( ~ empty(X0)
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
( ~ intersect(sK16,sK16)
| sK16 = 'empty$uset' ),
inference(resolution,[status(thm)],[c11,c17]) ).
cnf(d3,plain,
( ~ member(sK15(X0),X1)
| intersect(X0,X1)
| empty(X0) ),
inference(resolution,[status(thm)],[c14,c2]) ).
cnf(d4,plain,
( empty(X0)
| empty(X0)
| intersect(X0,X0) ),
inference(resolution,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
( sK16 = 'empty$uset'
| empty(sK16) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( sK16 = 'empty$uset'
| sK16 = 'empty$uset' ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'not$uequal'(sK16,sK16)
| intersect(sK16,sK16) ),
inference(demodulation,[status(thm)],[c16,d6]) ).
cnf(d8,plain,
~ 'not$uequal'(X0,X0),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(d9,plain,
intersect(sK16,sK16),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
~ intersect(X0,'empty$uset'),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d11,plain,
~ intersect(X0,sK16),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:01:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.62/1.66 % SZS status Theorem for theBenchmark.p
% 9.62/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------