%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET636+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 : n007.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 11.04s 3.11s
% Output : CNFRefutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 110 ( 20 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 105 ( 48 ~; 45 |; 3 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 6 sgn 21 !; 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$uset') ).
fof(disjoint_defn,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ) ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th118,conjecture,
! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[prove_th118]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
( member(sK5(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c4,plain,
( member(sK5(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c6,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c7,plain,
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[disjoint_defn]) ).
cnf(c8,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[disjoint_defn]) ).
cnf(c11,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c12,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c15,plain,
( member(sK19(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c18,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c19,plain,
( member(sK23(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c27,plain,
( intersection(sK28,sK29) = 'empty$uset'
| disjoint(sK28,sK29) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c28,plain,
( ~ disjoint(sK28,sK29)
| intersection(sK28,sK29) != 'empty$uset' ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c18,c2]) ).
cnf(d1,plain,
( intersection(sK28,sK29) = 'empty$uset'
| ~ intersect(sK28,sK29) ),
inference(resolution,[status(thm)],[c7,c27]) ).
cnf(d2,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d3,plain,
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c15,c18]) ).
cnf(d4,plain,
( ~ subset(X1,X0)
| X1 = X0
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
( ~ empty(X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( member(sK5(intersection(X0,X1),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d7,plain,
( ~ intersect(X0,X1)
| intersect(X1,X2)
| ~ member(sK5(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d8,plain,
( ~ intersect(intersection(X1,X2),X0)
| ~ intersect(intersection(X1,X2),X0)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( intersect(X0,X1)
| ~ member(sK23(X0),X1)
| empty(X0) ),
inference(resolution,[status(thm)],[c19,c5]) ).
cnf(d10,plain,
( member(sK23(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(d11,plain,
( empty(intersection(X0,X1))
| intersect(intersection(X0,X1),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( intersect(X1,X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( 'empty$uset' = intersection(X1,X0)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( intersection(sK28,sK29) = 'empty$uset'
| 'empty$uset' = intersection(sK29,sK28) ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( 'empty$uset' = intersection(sK28,sK29)
| intersection(sK28,sK29) = 'empty$uset' ),
inference(demodulation,[status(thm)],[d14,c12]) ).
cnf(d16,plain,
( 'empty$uset' = intersection(sK28,sK29)
| 'empty$uset' != 'empty$uset' ),
inference(equality_factoring,[status(thm)],[d15]) ).
cnf(d17,plain,
'empty$uset' = intersection(sK28,sK29),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ member(X0,sK28)
| ~ member(X0,sK29)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
empty('empty$uset'),
inference(resolution,[status(thm)],[c19,c6]) ).
cnf(d20,plain,
( ~ member(X0,sK29)
| ~ member(X0,sK28) ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ intersect(X0,sK29)
| ~ member(sK5(X0,sK29),sK28) ),
inference(resolution,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
( ~ intersect(sK28,sK29)
| ~ intersect(sK28,sK29) ),
inference(resolution,[status(thm)],[d21,c3]) ).
cnf(d23,plain,
( ~ disjoint(sK28,sK29)
| 'empty$uset' != 'empty$uset' ),
inference(demodulation,[status(thm)],[c28,d17]) ).
cnf(d24,plain,
~ disjoint(sK28,sK29),
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
intersect(sK28,sK29),
inference(resolution,[status(thm)],[d24,c8]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.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 08:00:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.04/3.11 % SZS status Theorem for theBenchmark.p
% 11.04/3.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------