%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET968+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 : n002.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 13.86s 2.98s
% Output : CNFRefutation 13.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 24 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 10 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X0) = X0 ).
fof(t120_zfmisc_1,axiom,
! [X0,X1,X2] :
( 'cartesian$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$uproduct2'(X1,X2)) ) ).
fof(t4_xboole_1,axiom,
! [X0,X1,X2] : 'set$uunion2'('set$uunion2'(X0,X1),X2) = 'set$uunion2'(X0,'set$uunion2'(X1,X2)) ).
fof(t121_zfmisc_1,conjecture,
! [X0,X1,X2,X3] : 'cartesian$uproduct2'('set$uunion2'(X0,X1),'set$uunion2'(X2,X3)) = 'set$uunion2'('set$uunion2'('set$uunion2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X0,X3)),'cartesian$uproduct2'(X1,X2)),'cartesian$uproduct2'(X1,X3)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] : 'cartesian$uproduct2'('set$uunion2'(X0,X1),'set$uunion2'(X2,X3)) = 'set$uunion2'('set$uunion2'('set$uunion2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X0,X3)),'cartesian$uproduct2'(X1,X2)),'cartesian$uproduct2'(X1,X3)),
inference(negate_conjecture,[status(cth)],[t121_zfmisc_1]) ).
cnf(c0,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c3,plain,
'set$uunion2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(c6,plain,
'cartesian$uproduct2'('set$uunion2'(X0,X1),X2) = 'set$uunion2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2)),
inference(clausification,[status(esa)],[t120_zfmisc_1]) ).
cnf(c7,plain,
'cartesian$uproduct2'(X0,'set$uunion2'(X1,X2)) = 'set$uunion2'('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X0,X2)),
inference(clausification,[status(esa)],[t120_zfmisc_1]) ).
cnf(c8,plain,
'set$uunion2'('set$uunion2'(X0,X1),X2) = 'set$uunion2'(X0,'set$uunion2'(X1,X2)),
inference(clausification,[status(esa)],[t4_xboole_1]) ).
cnf(c9,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('set$uunion2'('set$uunion2'('cartesian$uproduct2'(sK16,sK18),'cartesian$uproduct2'(sK16,sK19)),'cartesian$uproduct2'(sK17,sK18)),'cartesian$uproduct2'(sK17,sK19)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'set$uunion2'('cartesian$uproduct2'(X0,'set$uunion2'(X1,X2)),X3) = 'set$uunion2'('cartesian$uproduct2'(X0,X1),'set$uunion2'('cartesian$uproduct2'(X0,X2),X3)),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d1,plain,
'set$uunion2'(X2,'set$uunion2'(X0,X1)) = 'set$uunion2'(X0,'set$uunion2'(X1,X2)),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(d2,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('cartesian$uproduct2'(sK17,sK19),'set$uunion2'('set$uunion2'('cartesian$uproduct2'(sK16,sK18),'cartesian$uproduct2'(sK16,sK19)),'cartesian$uproduct2'(sK17,sK18))),
inference(demodulation,[status(thm)],[c9,c0]) ).
cnf(d3,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('cartesian$uproduct2'(sK17,sK19),'set$uunion2'('cartesian$uproduct2'(sK17,sK18),'set$uunion2'('cartesian$uproduct2'(sK16,sK18),'cartesian$uproduct2'(sK16,sK19)))),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('cartesian$uproduct2'(sK17,sK19),'set$uunion2'('cartesian$uproduct2'(sK17,sK18),'cartesian$uproduct2'(sK16,'set$uunion2'(sK18,sK19)))),
inference(demodulation,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('cartesian$uproduct2'(sK17,sK18),'set$uunion2'('cartesian$uproduct2'(sK16,'set$uunion2'(sK18,sK19)),'cartesian$uproduct2'(sK17,sK19))),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('cartesian$uproduct2'(sK17,sK18),'set$uunion2'('cartesian$uproduct2'(sK17,sK19),'cartesian$uproduct2'(sK16,'set$uunion2'(sK18,sK19)))),
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'set$uunion2'('cartesian$uproduct2'(sK17,'set$uunion2'(sK18,sK19)),'cartesian$uproduct2'(sK16,'set$uunion2'(sK18,sK19))),
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'cartesian$uproduct2'('set$uunion2'(sK17,sK16),'set$uunion2'(sK18,sK19)),
inference(demodulation,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)) != 'cartesian$uproduct2'('set$uunion2'(sK16,sK17),'set$uunion2'(sK18,sK19)),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
'cartesian$uproduct2'('set$uunion2'(X0,X0),X1) = 'cartesian$uproduct2'(X0,X1),
inference(superposition,[status(thm)],[c6,c3]) ).
cnf(d11,plain,
'cartesian$uproduct2'(X0,X1) = 'cartesian$uproduct2'(X0,X1),
inference(demodulation,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.58 % Computer : n002.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sat Sep 26 08:30:53 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.86/2.98 % SZS status Theorem for theBenchmark.p
% 13.86/2.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------