%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:33:40 AM UTC 2026
% Result : Theorem 16.88s 2.67s
% Output : CNFRefutation 16.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 4 unt; 0 def)
% Number of atoms : 54 ( 18 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 21 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 4 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
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(t128_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
inference(negate_conjecture,[status(cth)],[t128_zfmisc_1]) ).
cnf(c2,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c3,plain,
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c10,plain,
( in(X0,X2)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c11,plain,
( in(X1,X3)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c12,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c16,plain,
( sK18 = sK20
| in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK20),sK21)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
( in(sK19,sK21)
| in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK20),sK21)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( ~ in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK20),sK21))
| ~ in(sK19,sK21)
| sK18 != sK20 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d1,plain,
( sK18 = sK20
| in(sK18,singleton(sK20)) ),
inference(resolution,[status(thm)],[c10,c16]) ).
cnf(d2,plain,
( sK18 = sK20
| sK18 = sK20 ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( in(sK19,sK21)
| in(sK19,sK21) ),
inference(resolution,[status(thm)],[c11,c17]) ).
cnf(d4,plain,
( ~ in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK20),sK21))
| sK18 != sK20 ),
inference(resolution,[status(thm)],[d3,c18]) ).
cnf(d5,plain,
( ~ in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK20),sK21))
| sK18 != sK18 ),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK18),sK21))
| sK18 != sK18 ),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
~ in('ordered$upair'(sK18,sK19),'cartesian$uproduct2'(singleton(sK18),sK21)),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
( ~ in(sK19,sK21)
| ~ in(sK18,singleton(sK18)) ),
inference(resolution,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
~ in(sK18,singleton(sK18)),
inference(resolution,[status(thm)],[d3,d8]) ).
cnf(d10,plain,
( in(X0,singleton(X1))
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(d11,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n006.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:28:11 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.88/2.67 % SZS status Theorem for theBenchmark.p
% 16.88/2.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------