%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET984+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 : 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 08:33:41 AM UTC 2026
% Result : Theorem 7.50s 3.45s
% Output : CNFRefutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 17 unt; 0 def)
% Number of atoms : 82 ( 64 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 60 ( 16 ~; 36 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 5 con; 0-2 aty)
% Number of variables : 54 ( 8 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(t113_zfmisc_1,axiom,
! [X0,X1] :
( 'cartesian$uproduct2'(X0,X1) = 'empty$uset'
<=> ( X1 = 'empty$uset'
| X0 = 'empty$uset' ) ) ).
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(t134_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( 'cartesian$uproduct2'(X0,X1) = 'cartesian$uproduct2'(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| X1 = 'empty$uset'
| X0 = 'empty$uset' ) ) ).
fof(t17_xboole_1,axiom,
! [X0,X1] : subset('set$uintersection2'(X0,X1),X0) ).
fof(t28_xboole_1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uintersection2'(X0,X1) = X0 ) ).
fof(t138_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t138_zfmisc_1]) ).
cnf(c0,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c7,plain,
( X0 != 'empty$uset'
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[t113_zfmisc_1]) ).
cnf(c8,plain,
( X1 != 'empty$uset'
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[t113_zfmisc_1]) ).
cnf(c9,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(c10,plain,
( X0 = X2
| X1 = 'empty$uset'
| X0 = 'empty$uset'
| 'cartesian$uproduct2'(X0,X1) != 'cartesian$uproduct2'(X2,X3) ),
inference(clausification,[status(esa)],[t134_zfmisc_1]) ).
cnf(c11,plain,
( X1 = X3
| X1 = 'empty$uset'
| X0 = 'empty$uset'
| 'cartesian$uproduct2'(X0,X1) != 'cartesian$uproduct2'(X2,X3) ),
inference(clausification,[status(esa)],[t134_zfmisc_1]) ).
cnf(c12,plain,
subset('set$uintersection2'(X0,X1),X0),
inference(clausification,[status(esa)],[t17_xboole_1]) ).
cnf(c13,plain,
( 'set$uintersection2'(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t28_xboole_1]) ).
cnf(c14,plain,
subset('cartesian$uproduct2'(sK22,sK23),'cartesian$uproduct2'(sK24,sK25)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
'cartesian$uproduct2'(sK22,sK23) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
( ~ subset(sK23,sK25)
| ~ subset(sK22,sK24) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'cartesian$uproduct2'('empty$uset',X0) = 'empty$uset',
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d1,plain,
'cartesian$uproduct2'(X0,'empty$uset') = 'empty$uset',
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d2,plain,
subset('set$uintersection2'(X1,X0),X0),
inference(superposition,[status(thm)],[c0,c12]) ).
cnf(d3,plain,
'set$uintersection2'('cartesian$uproduct2'(sK22,sK23),'cartesian$uproduct2'(sK24,sK25)) = 'cartesian$uproduct2'(sK22,sK23),
inference(resolution,[status(thm)],[c13,c14]) ).
cnf(d4,plain,
'cartesian$uproduct2'('set$uintersection2'(sK22,sK24),'set$uintersection2'(sK23,sK25)) = 'cartesian$uproduct2'(sK22,sK23),
inference(demodulation,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( X0 = 'empty$uset'
| X1 = 'empty$uset'
| X1 = 'set$uintersection2'(sK23,sK25)
| 'cartesian$uproduct2'(X0,X1) != 'cartesian$uproduct2'(sK22,sK23) ),
inference(superposition,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( sK22 = 'empty$uset'
| sK23 = 'empty$uset'
| sK23 = 'set$uintersection2'(sK23,sK25) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( sK23 = 'empty$uset'
| sK22 = 'empty$uset'
| subset(sK23,sK25) ),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( ~ subset(sK22,sK24)
| sK23 = 'empty$uset'
| sK22 = 'empty$uset' ),
inference(resolution,[status(thm)],[d7,c16]) ).
cnf(d9,plain,
( X0 = 'empty$uset'
| X0 = 'set$uintersection2'(sK22,sK24)
| X1 = 'empty$uset'
| 'cartesian$uproduct2'(X0,X1) != 'cartesian$uproduct2'(sK22,sK23) ),
inference(superposition,[status(thm)],[d4,c10]) ).
cnf(d10,plain,
( sK22 = 'empty$uset'
| sK22 = 'set$uintersection2'(sK22,sK24)
| sK23 = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( sK23 = 'empty$uset'
| sK22 = 'empty$uset'
| subset(sK22,sK24) ),
inference(superposition,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( sK23 = 'empty$uset'
| sK22 = 'empty$uset'
| sK23 = 'empty$uset'
| sK22 = 'empty$uset' ),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( sK22 = 'empty$uset'
| 'cartesian$uproduct2'(sK22,'empty$uset') != 'empty$uset' ),
inference(superposition,[status(thm)],[d12,c15]) ).
cnf(d14,plain,
( sK22 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
sK22 = 'empty$uset',
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
'cartesian$uproduct2'('empty$uset',sK23) != 'empty$uset',
inference(demodulation,[status(thm)],[c15,d15]) ).
cnf(d17,plain,
'empty$uset' != 'empty$uset',
inference(demodulation,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
$false,
inference(equality_resolution,[status(thm)],[d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET984+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
% 0.16/0.44 % Computer : n015.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 08:31:58 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.50/3.45 % SZS status Theorem for theBenchmark.p
% 7.50/3.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------