%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET979+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 08:33:40 AM UTC 2026
% Result : Theorem 11.34s 3.02s
% Output : CNFRefutation 11.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 5 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t120_zfmisc_1,axiom,
! [X0,X1,X2] :
( 'cartesian$uproduct2'(X2,'set$uunion2'(X0,X1)) = 'set$uunion2'('cartesian$uproduct2'(X2,X0),'cartesian$uproduct2'(X2,X1))
& 'cartesian$uproduct2'('set$uunion2'(X0,X1),X2) = 'set$uunion2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2)) ) ).
fof(t41_enumset1,axiom,
! [X0,X1] : 'unordered$upair'(X0,X1) = 'set$uunion2'(singleton(X0),singleton(X1)) ).
fof(t132_zfmisc_1,conjecture,
! [X0,X1,X2] :
( 'cartesian$uproduct2'(X2,'unordered$upair'(X0,X1)) = 'set$uunion2'('cartesian$uproduct2'(X2,singleton(X0)),'cartesian$uproduct2'(X2,singleton(X1)))
& 'cartesian$uproduct2'('unordered$upair'(X0,X1),X2) = 'set$uunion2'('cartesian$uproduct2'(singleton(X0),X2),'cartesian$uproduct2'(singleton(X1),X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'cartesian$uproduct2'(X2,'unordered$upair'(X0,X1)) = 'set$uunion2'('cartesian$uproduct2'(X2,singleton(X0)),'cartesian$uproduct2'(X2,singleton(X1)))
& 'cartesian$uproduct2'('unordered$upair'(X0,X1),X2) = 'set$uunion2'('cartesian$uproduct2'(singleton(X0),X2),'cartesian$uproduct2'(singleton(X1),X2)) ),
inference(negate_conjecture,[status(cth)],[t132_zfmisc_1]) ).
cnf(c7,plain,
'cartesian$uproduct2'('set$uunion2'(X0,X1),X2) = 'set$uunion2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2)),
inference(clausification,[status(esa)],[t120_zfmisc_1]) ).
cnf(c8,plain,
'cartesian$uproduct2'(X0,'set$uunion2'(X1,X2)) = 'set$uunion2'('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X0,X2)),
inference(clausification,[status(esa)],[t120_zfmisc_1]) ).
cnf(c9,plain,
'unordered$upair'(X0,X1) = 'set$uunion2'(singleton(X0),singleton(X1)),
inference(clausification,[status(esa)],[t41_enumset1]) ).
cnf(c10,plain,
( 'cartesian$uproduct2'(sK19,'unordered$upair'(sK17,sK18)) != 'set$uunion2'('cartesian$uproduct2'(sK19,singleton(sK17)),'cartesian$uproduct2'(sK19,singleton(sK18)))
| 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) != 'set$uunion2'('cartesian$uproduct2'(singleton(sK17),sK19),'cartesian$uproduct2'(singleton(sK18),sK19)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'cartesian$uproduct2'(sK19,'unordered$upair'(sK17,sK18)) != 'set$uunion2'('cartesian$uproduct2'(sK19,singleton(sK17)),'cartesian$uproduct2'(sK19,singleton(sK18)))
| 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) != 'cartesian$uproduct2'('set$uunion2'(singleton(sK17),singleton(sK18)),sK19) ),
inference(demodulation,[status(thm)],[c10,c7]) ).
cnf(d1,plain,
( 'cartesian$uproduct2'(sK19,'unordered$upair'(sK17,sK18)) != 'cartesian$uproduct2'(sK19,'set$uunion2'(singleton(sK17),singleton(sK18)))
| 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) != 'cartesian$uproduct2'('set$uunion2'(singleton(sK17),singleton(sK18)),sK19) ),
inference(demodulation,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( 'cartesian$uproduct2'(sK19,'unordered$upair'(sK17,sK18)) != 'cartesian$uproduct2'(sK19,'set$uunion2'(singleton(sK17),singleton(sK18)))
| 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) != 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) ),
inference(demodulation,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( 'cartesian$uproduct2'(sK19,'unordered$upair'(sK17,sK18)) != 'cartesian$uproduct2'(sK19,'unordered$upair'(sK17,sK18))
| 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) != 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) ),
inference(demodulation,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19) != 'cartesian$uproduct2'('unordered$upair'(sK17,sK18),sK19),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
$false,
inference(equality_resolution,[status(thm)],[d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET979+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
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:30:39 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.34/3.02 % SZS status Theorem for theBenchmark.p
% 11.34/3.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------