%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:33:39 AM UTC 2026
% Result : Theorem 4.44s 3.62s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 4 unt; 0 def)
% Number of atoms : 80 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 30 ~; 40 |; 5 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 7 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(l55_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t117_zfmisc_1,conjecture,
! [X0,X1,X2] :
~ ( ~ subset(X1,X2)
& ( subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X0,X2))
| subset('cartesian$uproduct2'(X1,X0),'cartesian$uproduct2'(X2,X0)) )
& X0 != 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ subset(X1,X2)
& ( subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X0,X2))
| subset('cartesian$uproduct2'(X1,X0),'cartesian$uproduct2'(X2,X0)) )
& X0 != 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[t117_zfmisc_1]) ).
cnf(c3,plain,
( in(sK6(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c18,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c19,plain,
( in(sK24(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c20,plain,
( ~ in(sK24(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c24,plain,
( in(X0,X2)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c25,plain,
( in(X1,X3)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c26,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c30,plain,
sK37 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
( subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| subset('cartesian$uproduct2'(sK38,sK37),'cartesian$uproduct2'(sK39,sK37)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c32,plain,
~ subset(sK38,sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| ~ in(X0,'cartesian$uproduct2'(sK38,sK37))
| in(X0,'cartesian$uproduct2'(sK39,sK37)) ),
inference(resolution,[status(thm)],[c18,c31]) ).
cnf(d1,plain,
( subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK39,sK37))
| ~ in(X1,sK37)
| ~ in(X0,sK38) ),
inference(resolution,[status(thm)],[c26,d0]) ).
cnf(d2,plain,
( in(X1,sK39)
| subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| ~ in(X1,sK38)
| ~ in(X0,sK37) ),
inference(resolution,[status(thm)],[d1,c24]) ).
cnf(d3,plain,
( sK37 = 'empty$uset'
| subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| in(X0,sK39)
| ~ in(X0,sK38) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| in(X0,sK39)
| ~ in(X0,sK38) ),
inference(resolution,[status(thm)],[c30,d3]) ).
cnf(d5,plain,
( subset(sK38,X0)
| subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39))
| in(sK24(sK38,X0),sK39) ),
inference(resolution,[status(thm)],[d4,c19]) ).
cnf(d6,plain,
( subset(sK38,sK39)
| subset(sK38,sK39)
| subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39)) ),
inference(resolution,[status(thm)],[d5,c20]) ).
cnf(d7,plain,
subset('cartesian$uproduct2'(sK37,sK38),'cartesian$uproduct2'(sK37,sK39)),
inference(resolution,[status(thm)],[c32,d6]) ).
cnf(d8,plain,
( ~ in(X0,'cartesian$uproduct2'(sK37,sK38))
| in(X0,'cartesian$uproduct2'(sK37,sK39)) ),
inference(resolution,[status(thm)],[d7,c18]) ).
cnf(d9,plain,
( ~ in(X1,sK38)
| ~ in(X0,sK37)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK37,sK39)) ),
inference(resolution,[status(thm)],[d8,c26]) ).
cnf(d10,plain,
( in(X0,sK39)
| ~ in(X1,sK37)
| ~ in(X0,sK38) ),
inference(resolution,[status(thm)],[d9,c25]) ).
cnf(d11,plain,
( subset(sK38,X1)
| in(sK24(sK38,X1),sK39)
| ~ in(X0,sK37) ),
inference(resolution,[status(thm)],[d10,c19]) ).
cnf(d12,plain,
( sK37 = 'empty$uset'
| subset(sK38,X0)
| in(sK24(sK38,X0),sK39) ),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d13,plain,
( subset(sK38,X0)
| in(sK24(sK38,X0),sK39) ),
inference(resolution,[status(thm)],[c30,d12]) ).
cnf(d14,plain,
( subset(sK38,sK39)
| subset(sK38,sK39) ),
inference(resolution,[status(thm)],[d13,c20]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c32,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:29:55 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.44/3.62 % SZS status Theorem for theBenchmark.p
% 4.44/3.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------