%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 6.62s 3.32s
% Output : CNFRefutation 6.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 100 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 40 |; 6 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 5 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
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$uset') ).
fof(disjoint_defn,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ) ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(symmetry_of_intersect,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th114,conjecture,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X2)
& subset(X0,X1) )
=> X0 = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X2)
& subset(X0,X1) )
=> X0 = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[prove_th114]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c3,plain,
( member(sK6(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c4,plain,
( member(sK6(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c6,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c7,plain,
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[disjoint_defn]) ).
cnf(c11,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c12,plain,
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_intersect]) ).
cnf(c14,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c15,plain,
( member(sK18(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c16,plain,
subset(sK19,sK20),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
subset(sK19,sK21),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
disjoint(sK20,sK21),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
sK19 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c14,c1]) ).
cnf(d2,plain,
( ~ subset(X1,X0)
| X0 = X1
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( ~ empty(X0)
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( member(sK18(X0),X1)
| ~ subset(X0,X1)
| empty(X0) ),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d5,plain,
( empty(X0)
| ~ subset(X0,'empty$uset') ),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
( member(sK3(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d7,plain,
( subset(X0,X1)
| intersect(X0,X2)
| ~ member(sK3(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d8,plain,
( subset(X0,X1)
| ~ subset(X0,X2)
| intersect(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( intersect(sK19,sK21)
| subset(sK19,X0) ),
inference(resolution,[status(thm)],[d8,c17]) ).
cnf(d10,plain,
( empty(sK19)
| intersect(sK19,sK21) ),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( member(sK6(X0,X1),X2)
| ~ subset(X0,X2)
| ~ intersect(X0,X1) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d12,plain,
( ~ intersect(X0,X1)
| intersect(X1,X2)
| ~ member(sK6(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d13,plain,
( ~ intersect(X2,X0)
| ~ subset(X2,X1)
| ~ intersect(X2,X0)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( empty(sK19)
| intersect(sK21,X0)
| ~ subset(sK19,X0) ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( empty(sK19)
| intersect(sK21,sK20) ),
inference(resolution,[status(thm)],[d14,c16]) ).
cnf(d16,plain,
( intersect(sK20,sK21)
| empty(sK19) ),
inference(resolution,[status(thm)],[d15,c12]) ).
cnf(d17,plain,
~ intersect(sK20,sK21),
inference(resolution,[status(thm)],[c7,c18]) ).
cnf(d18,plain,
empty(sK19),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
sK19 = 'empty$uset',
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c19,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.64 % Computer : n017.cluster.edu
% 0.16/0.64 % Model : x86_64 x86_64
% 0.16/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.64 % Memory : 8046.5625MB
% 0.16/0.64 % OS : Linux 6.8.0-71-generic
% 0.16/0.64 % CPULimit : 300
% 0.16/0.64 % WCLimit : 300
% 0.16/0.64 % DateTime : Sat Sep 26 07:57:19 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.65 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.62/3.32 % SZS status Theorem for theBenchmark.p
% 6.62/3.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------