%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET971+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 : n015.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 11.03s 1.84s
% Output : CNFRefutation 11.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 21 unt; 0 def)
% Number of atoms : 31 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(idempotence_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X0) = X0 ).
fof(t123_zfmisc_1,axiom,
! [X0,X1,X2,X3] : 'cartesian$uproduct2'('set$uintersection2'(X0,X1),'set$uintersection2'(X2,X3)) = 'set$uintersection2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3)) ).
fof(t28_xboole_1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uintersection2'(X0,X1) = X0 ) ).
fof(t124_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> 'set$uintersection2'('cartesian$uproduct2'(X0,X3),'cartesian$uproduct2'(X1,X2)) = 'cartesian$uproduct2'(X0,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> 'set$uintersection2'('cartesian$uproduct2'(X0,X3),'cartesian$uproduct2'(X1,X2)) = 'cartesian$uproduct2'(X0,X2) ),
inference(negate_conjecture,[status(cth)],[t124_zfmisc_1]) ).
cnf(c0,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c1,plain,
'set$uintersection2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(c5,plain,
'cartesian$uproduct2'('set$uintersection2'(X0,X1),'set$uintersection2'(X2,X3)) = 'set$uintersection2'('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3)),
inference(clausification,[status(esa)],[t123_zfmisc_1]) ).
cnf(c6,plain,
( 'set$uintersection2'(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t28_xboole_1]) ).
cnf(c7,plain,
subset(sK14,sK15),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
subset(sK16,sK17),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
'set$uintersection2'('cartesian$uproduct2'(sK14,sK17),'cartesian$uproduct2'(sK15,sK16)) != 'cartesian$uproduct2'(sK14,sK16),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'set$uintersection2'(sK16,sK17) = sK16,
inference(resolution,[status(thm)],[c6,c8]) ).
cnf(d1,plain,
'set$uintersection2'(sK14,sK15) = sK14,
inference(resolution,[status(thm)],[c6,c7]) ).
cnf(d2,plain,
'cartesian$uproduct2'(sK14,'set$uintersection2'(X0,X1)) = 'set$uintersection2'('cartesian$uproduct2'(sK14,X0),'cartesian$uproduct2'(sK15,X1)),
inference(superposition,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
'cartesian$uproduct2'(sK14,'set$uintersection2'(sK17,sK16)) != 'cartesian$uproduct2'(sK14,sK16),
inference(demodulation,[status(thm)],[c9,d2]) ).
cnf(d4,plain,
'cartesian$uproduct2'(sK14,'set$uintersection2'(sK16,sK17)) != 'cartesian$uproduct2'(sK14,sK16),
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
'cartesian$uproduct2'(sK14,sK16) != 'cartesian$uproduct2'(sK14,sK16),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
'cartesian$uproduct2'(X0,'set$uintersection2'(X1,X2)) = 'set$uintersection2'('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X0,X2)),
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d7,plain,
'cartesian$uproduct2'('set$uintersection2'(X0,X1),sK16) = 'set$uintersection2'('cartesian$uproduct2'(X0,sK16),'cartesian$uproduct2'(X1,sK17)),
inference(superposition,[status(thm)],[d0,c5]) ).
cnf(d8,plain,
'cartesian$uproduct2'(X0,'set$uintersection2'(sK16,sK17)) = 'cartesian$uproduct2'('set$uintersection2'(X0,X0),sK16),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
'cartesian$uproduct2'(X0,sK16) = 'cartesian$uproduct2'('set$uintersection2'(X0,X0),sK16),
inference(demodulation,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
'cartesian$uproduct2'(X0,sK16) = 'cartesian$uproduct2'(X0,sK16),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:31:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.03/1.84 % SZS status Theorem for theBenchmark.p
% 11.03/1.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------