%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET985+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 : 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 08:33:41 AM UTC 2026
% Result : Theorem 9.42s 2.93s
% Output : CNFRefutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 61 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 12 ~; 28 |; 1 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_xboole_0,axiom,
empty('empty$uset') ).
fof(t113_zfmisc_1,axiom,
! [X0,X1] :
( 'cartesian$uproduct2'(X0,X1) = 'empty$uset'
<=> ( X1 = 'empty$uset'
| X0 = 'empty$uset' ) ) ).
fof(t138_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset' ) ) ).
fof(t2_xboole_1,axiom,
! [X0] : subset('empty$uset',X0) ).
fof(t139_zfmisc_1,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset('cartesian$uproduct2'(X1,X0),'cartesian$uproduct2'(X3,X2))
| subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3)) )
=> subset(X1,X3) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset('cartesian$uproduct2'(X1,X0),'cartesian$uproduct2'(X3,X2))
| subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3)) )
=> subset(X1,X3) ) ),
inference(negate_conjecture,[status(cth)],[t139_zfmisc_1]) ).
cnf(c0,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c4,plain,
( X1 = 'empty$uset'
| X0 = 'empty$uset'
| 'cartesian$uproduct2'(X0,X1) != 'empty$uset' ),
inference(clausification,[status(esa)],[t113_zfmisc_1]) ).
cnf(c7,plain,
( subset(X0,X2)
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset'
| ~ subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[t138_zfmisc_1]) ).
cnf(c8,plain,
( subset(X1,X3)
| 'cartesian$uproduct2'(X0,X1) = 'empty$uset'
| ~ subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[t138_zfmisc_1]) ).
cnf(c9,plain,
subset('empty$uset',X0),
inference(clausification,[status(esa)],[t2_xboole_1]) ).
cnf(c10,plain,
~ empty(sK11),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
( subset('cartesian$uproduct2'(sK12,sK11),'cartesian$uproduct2'(sK14,sK13))
| subset('cartesian$uproduct2'(sK11,sK12),'cartesian$uproduct2'(sK13,sK14)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
~ subset(sK12,sK14),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset('cartesian$uproduct2'(sK11,sK12),'cartesian$uproduct2'(sK13,sK14))
| subset(sK12,sK14)
| 'cartesian$uproduct2'(sK12,sK11) = 'empty$uset' ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d1,plain,
( subset('cartesian$uproduct2'(sK11,sK12),'cartesian$uproduct2'(sK13,sK14))
| 'cartesian$uproduct2'(sK12,sK11) = 'empty$uset' ),
inference(resolution,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
( 'cartesian$uproduct2'(sK12,sK11) = 'empty$uset'
| subset(sK12,sK14)
| 'cartesian$uproduct2'(sK11,sK12) = 'empty$uset' ),
inference(resolution,[status(thm)],[c8,d1]) ).
cnf(d3,plain,
( 'cartesian$uproduct2'(sK12,sK11) = 'empty$uset'
| 'cartesian$uproduct2'(sK11,sK12) = 'empty$uset' ),
inference(resolution,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
( 'cartesian$uproduct2'(sK11,sK12) = 'empty$uset'
| sK12 = 'empty$uset'
| sK11 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( sK12 = 'empty$uset'
| sK11 = 'empty$uset'
| 'cartesian$uproduct2'(sK11,sK12) = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( sK12 = 'empty$uset'
| sK11 = 'empty$uset'
| sK11 = 'empty$uset'
| sK12 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( sK12 = 'empty$uset'
| sK11 = 'empty$uset' ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
( sK11 = 'empty$uset'
| ~ subset('empty$uset',sK14) ),
inference(superposition,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
sK11 = 'empty$uset',
inference(resolution,[status(thm)],[c9,d8]) ).
cnf(d10,plain,
~ empty('empty$uset'),
inference(demodulation,[status(thm)],[c10,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c0,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET985+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
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:31:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.42/2.93 % SZS status Theorem for theBenchmark.p
% 9.42/2.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------