%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET956+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 : 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 08:33:38 AM UTC 2026
% Result : Theorem 9.78s 2.05s
% Output : CNFRefutation 9.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 41 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 33 ( 11 ~; 10 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(t103_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( X3 = 'ordered$upair'(X4,X5)
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,'cartesian$uproduct2'(X1,X2)) ) ).
fof(t109_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( in('ordered$upair'(X4,X5),X0)
=> in('ordered$upair'(X4,X5),X3) )
& subset(X0,'cartesian$uproduct2'(X1,X2)) )
=> subset(X0,X3) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ! [X4,X5] :
( in('ordered$upair'(X4,X5),X0)
=> in('ordered$upair'(X4,X5),X3) )
& subset(X0,'cartesian$uproduct2'(X1,X2)) )
=> subset(X0,X3) ),
inference(negate_conjecture,[status(cth)],[t109_zfmisc_1]) ).
cnf(c3,plain,
( in(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c4,plain,
( ~ in(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c12,plain,
( X3 = 'ordered$upair'(sK20(X1,X2,X3),sK21(X1,X2,X3))
| ~ in(X3,X0)
| ~ subset(X0,'cartesian$uproduct2'(X1,X2)) ),
inference(clausification,[status(esa)],[t103_zfmisc_1]) ).
cnf(c13,plain,
subset(sK22,'cartesian$uproduct2'(sK23,sK24)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( in('ordered$upair'(X0,X1),sK25)
| ~ in('ordered$upair'(X0,X1),sK22) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
~ subset(sK22,sK25),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,sK22)
| X0 = 'ordered$upair'(sK20(sK23,sK24,X0),sK21(sK23,sK24,X0)) ),
inference(resolution,[status(thm)],[c12,c13]) ).
cnf(d1,plain,
( subset(sK22,X0)
| sK7(sK22,X0) = 'ordered$upair'(sK20(sK23,sK24,sK7(sK22,X0)),sK21(sK23,sK24,sK7(sK22,X0))) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
sK7(sK22,sK25) = 'ordered$upair'(sK20(sK23,sK24,sK7(sK22,sK25)),sK21(sK23,sK24,sK7(sK22,sK25))),
inference(resolution,[status(thm)],[d1,c15]) ).
cnf(d3,plain,
( in('ordered$upair'(sK20(sK23,sK24,sK7(sK22,sK25)),sK21(sK23,sK24,sK7(sK22,sK25))),sK25)
| ~ in(sK7(sK22,sK25),sK22) ),
inference(superposition,[status(thm)],[d2,c14]) ).
cnf(d4,plain,
( in(sK7(sK22,sK25),sK25)
| ~ in(sK7(sK22,sK25),sK22) ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( subset(sK22,sK25)
| in(sK7(sK22,sK25),sK25) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
in(sK7(sK22,sK25),sK25),
inference(resolution,[status(thm)],[c15,d5]) ).
cnf(d7,plain,
subset(sK22,sK25),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c15,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:25:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.78/2.05 % SZS status Theorem for theBenchmark.p
% 9.78/2.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------