%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET692+4 : 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 : 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 08:33:06 AM UTC 2026
% Result : Theorem 15.57s 3.13s
% Output : CNFRefutation 15.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 4 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 28 ~; 53 |; 2 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 5 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(equal_set,axiom,
! [X0,X1] :
( 'equal$uset'(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(intersection,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ) ).
fof(union,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ) ).
fof(thI19,conjecture,
! [X0,X1] :
( 'equal$uset'(X0,intersection(X0,X1))
<=> subset(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'equal$uset'(X0,intersection(X0,X1))
<=> subset(X0,X1) ),
inference(negate_conjecture,[status(cth)],[thI19]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c3,plain,
( subset(X0,X1)
| ~ 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c8,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c9,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c10,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c11,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union]) ).
cnf(c13,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union]) ).
cnf(c30,plain,
( subset(sK31,sK32)
| 'equal$uset'(sK31,intersection(sK31,sK32)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
( ~ 'equal$uset'(sK31,intersection(sK31,sK32))
| ~ subset(sK31,sK32) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(X0,intersection(X1,X2))
| ~ member(sK3(X0,intersection(X1,X2)),X1)
| ~ member(sK3(X0,intersection(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d1,plain,
( subset(X0,intersection(X0,X1))
| ~ member(sK3(X0,intersection(X0,X1)),X1)
| subset(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( member(sK3(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d3,plain,
( member(sK3(X0,X3),X1)
| member(sK3(X0,X3),X2)
| subset(X0,X3)
| ~ subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
( subset(X0,union(X1,X2))
| ~ member(sK3(X0,union(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d5,plain,
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
( member(sK3(X0,X2),X3)
| ~ subset(X1,X3)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d7,plain,
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d8,plain,
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( subset(sK31,sK32)
| subset(sK31,intersection(sK31,sK32)) ),
inference(resolution,[status(thm)],[c3,c30]) ).
cnf(d10,plain,
( subset(sK31,sK32)
| member(sK3(sK31,X1),X0)
| subset(sK31,X1)
| ~ subset(intersection(sK31,sK32),X0) ),
inference(resolution,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
( member(sK3(sK31,X0),sK32)
| subset(sK31,sK32)
| subset(sK31,X0) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( subset(sK31,sK32)
| subset(sK31,sK32)
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( member(sK3(sK31,X1),X0)
| subset(sK31,X1)
| ~ subset(sK32,X0) ),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( subset(sK31,X0)
| ~ subset(sK32,X0)
| subset(sK31,X0) ),
inference(resolution,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
subset(sK31,union(X0,sK32)),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
( member(sK3(sK31,X0),X1)
| member(sK3(sK31,X0),sK32)
| subset(sK31,X0) ),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
( subset(sK31,X0)
| member(sK3(sK31,X0),sK32)
| subset(sK31,X0) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
( subset(sK31,intersection(sK31,sK32))
| subset(sK31,intersection(sK31,sK32)) ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( 'equal$uset'(sK31,intersection(sK31,sK32))
| ~ subset(intersection(sK31,sK32),sK31) ),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d21,plain,
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
'equal$uset'(sK31,intersection(sK31,sK32)),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
~ 'equal$uset'(sK31,intersection(sK31,sK32)),
inference(resolution,[status(thm)],[d12,c31]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET692+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n014.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 08:06:01 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.57/3.13 % SZS status Theorem for theBenchmark.p
% 15.57/3.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------