%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET637+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 : n019.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 08:32:58 AM UTC 2026
% Result : Theorem 20.73s 3.09s
% Output : CNFRefutation 20.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 101 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 96 ( 42 ~; 43 |; 2 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 4 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
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(symmetry_of_intersect,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th119,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> 'not$uequal'(intersection(X0,X1),'empty$uset') ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> 'not$uequal'(intersection(X0,X1),'empty$uset') ),
inference(negate_conjecture,[status(cth)],[prove_th119]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
( member(sK5(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c4,plain,
( member(sK5(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c6,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c10,plain,
( member(sK11(X0,X1),X1)
| member(sK11(X0,X1),X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_member_defn]) ).
cnf(c13,plain,
( X0 != X1
| ~ 'not$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[not_equal_defn]) ).
cnf(c14,plain,
( X0 = X1
| 'not$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[not_equal_defn]) ).
cnf(c16,plain,
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_intersect]) ).
cnf(c17,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c18,plain,
( member(sK20(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c20,plain,
( 'not$uequal'(intersection(sK21,sK22),'empty$uset')
| intersect(sK21,sK22) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
( ~ intersect(sK21,sK22)
| ~ 'not$uequal'(intersection(sK21,sK22),'empty$uset') ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c17,c2]) ).
cnf(d1,plain,
( ~ intersect(sK21,sK22)
| intersection(sK21,sK22) = 'empty$uset' ),
inference(resolution,[status(thm)],[c14,c21]) ).
cnf(d2,plain,
( intersect(X1,X2)
| ~ member(sK11(X0,X1),X2)
| member(sK11(X0,X1),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c10,c5]) ).
cnf(d3,plain,
( member(sK11(X0,X1),X0)
| X0 = X1
| intersect(X1,X1)
| member(sK11(X0,X1),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
( intersect(X0,X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( member(sK5(intersection(X0,X1),X2),X1)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d6,plain,
( member(sK5(intersection(X0,X1),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d7,plain,
( intersect(X0,X3)
| ~ member(sK5(intersection(X0,X1),X2),X3)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
( ~ intersect(intersection(X0,X1),X2)
| ~ intersect(intersection(X0,X1),X2)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( 'empty$uset' = intersection(X0,X1)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( intersection(sK21,sK22) = 'empty$uset'
| 'empty$uset' = intersection(sK21,sK22) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( 'empty$uset' = intersection(sK21,sK22)
| 'empty$uset' != 'empty$uset' ),
inference(equality_factoring,[status(thm)],[d10]) ).
cnf(d12,plain,
'empty$uset' = intersection(sK21,sK22),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( ~ member(X0,sK21)
| ~ member(X0,sK22)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
empty('empty$uset'),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d15,plain,
( ~ member(X0,sK22)
| ~ member(X0,sK21) ),
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
( ~ intersect(sK22,X0)
| ~ member(sK5(sK22,X0),sK21) ),
inference(resolution,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
( ~ intersect(sK22,sK21)
| ~ intersect(sK22,sK21) ),
inference(resolution,[status(thm)],[d16,c4]) ).
cnf(d18,plain,
( 'not$uequal'('empty$uset','empty$uset')
| intersect(sK21,sK22) ),
inference(demodulation,[status(thm)],[c20,d12]) ).
cnf(d19,plain,
~ 'not$uequal'(X0,X0),
inference(equality_resolution,[status(thm)],[c13]) ).
cnf(d20,plain,
intersect(sK21,sK22),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
intersect(sK22,sK21),
inference(resolution,[status(thm)],[d20,c16]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+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 : n019.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 08:02:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.73/3.09 % SZS status Theorem for theBenchmark.p
% 20.73/3.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------