%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:41:08 AM UTC 2026
% Result : Theorem 84.38s 29.33s
% Output : CNFRefutation 84.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 45 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 41 ( 18 ~; 14 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 47 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t118_zfmisc_1,lemma,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset('cartesian$uproduct2'(X2,X0),'cartesian$uproduct2'(X2,X1))
& subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2)) ) ) ).
fof(t1_xboole_1,lemma,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ).
fof(t33_xboole_1,lemma,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset('set$udifference'(X0,X2),'set$udifference'(X1,X2)) ) ).
fof(t3_boole,axiom,
! [X0] : 'set$udifference'(X0,'empty$uset') = X0 ).
fof(t119_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3)) ),
inference(negate_conjecture,[status(cth)],[t119_zfmisc_1]) ).
cnf(c112,plain,
( subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X2))
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t118_zfmisc_1]) ).
cnf(c113,plain,
( subset('cartesian$uproduct2'(X2,X0),'cartesian$uproduct2'(X2,X1))
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t118_zfmisc_1]) ).
cnf(c118,plain,
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t1_xboole_1]) ).
cnf(c128,plain,
( subset('set$udifference'(X0,X2),'set$udifference'(X1,X2))
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t33_xboole_1]) ).
cnf(c143,plain,
'set$udifference'(X0,'empty$uset') = X0,
inference(clausification,[status(esa)],[t3_boole]) ).
cnf(c172,plain,
subset(sK224,sK225),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c173,plain,
subset(sK222,sK223),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c174,plain,
~ subset('cartesian$uproduct2'(sK222,sK224),'cartesian$uproduct2'(sK223,sK225)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset(X3,X0)
| subset('cartesian$uproduct2'(X3,X1),X2)
| ~ subset('cartesian$uproduct2'(X0,X1),X2) ),
inference(resolution,[status(thm)],[c118,c112]) ).
cnf(d1,plain,
( ~ subset(X2,X3)
| subset('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[d0,c113]) ).
cnf(d2,plain,
( ~ subset(X0,X1)
| subset(X0,'set$udifference'(X1,'empty$uset')) ),
inference(superposition,[status(thm)],[c143,c128]) ).
cnf(d3,plain,
( subset(X1,X0)
| ~ subset(X1,X0) ),
inference(demodulation,[status(thm)],[d2,c143]) ).
cnf(d4,plain,
( ~ subset(X0,X2)
| ~ subset(X1,X3)
| subset('cartesian$uproduct2'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ subset(sK222,sK223)
| ~ subset(sK224,sK225) ),
inference(resolution,[status(thm)],[d4,c174]) ).
cnf(d6,plain,
~ subset(sK222,sK223),
inference(resolution,[status(thm)],[c172,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c173,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:43:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 84.38/29.33 % SZS status Theorem for theBenchmark.p
% 84.38/29.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------