%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% 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 08:41:00 AM UTC 2026
% Result : Theorem 25.90s 27.68s
% Output : CNFRefutation 25.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 60 ( 39 unt; 0 def)
% Number of atoms : 91 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 18 ~; 20 |; 2 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 9 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(d10_xboole_0,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(d4_xboole_0,axiom,
! [X0,X1,X2] :
( X2 = 'set$udifference'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ) ).
fof(l2_zfmisc_1,lemma,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t12_xboole_1,lemma,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uunion2'(X0,X1) = X1 ) ).
fof(t17_xboole_1,lemma,
! [X0,X1] : subset('set$uintersection2'(X0,X1),X0) ).
fof(t28_xboole_1,lemma,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uintersection2'(X0,X1) = X0 ) ).
fof(t33_xboole_1,lemma,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset('set$udifference'(X0,X2),'set$udifference'(X1,X2)) ) ).
fof(t36_xboole_1,lemma,
! [X0,X1] : subset('set$udifference'(X0,X1),X0) ).
fof(t39_xboole_1,lemma,
! [X0,X1] : 'set$uunion2'(X0,'set$udifference'(X1,X0)) = 'set$uunion2'(X0,X1) ).
fof(t40_xboole_1,lemma,
! [X0,X1] : 'set$udifference'('set$uunion2'(X0,X1),X1) = 'set$udifference'(X0,X1) ).
fof(t48_xboole_1,lemma,
! [X0,X1] : 'set$udifference'(X0,'set$udifference'(X0,X1)) = 'set$uintersection2'(X0,X1) ).
fof(t7_xboole_1,lemma,
! [X0,X1] : subset(X0,'set$uunion2'(X0,X1)) ).
fof(l3_zfmisc_1,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,'set$udifference'(X1,singleton(X2)))
| in(X2,X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,'set$udifference'(X1,singleton(X2)))
| in(X2,X0) ) ),
inference(negate_conjecture,[status(cth)],[l3_zfmisc_1]) ).
cnf(c3,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c4,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c7,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[d10_xboole_0]) ).
cnf(c45,plain,
( ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c63,plain,
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l2_zfmisc_1]) ).
cnf(c64,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(clausification,[status(esa)],[l2_zfmisc_1]) ).
cnf(c69,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c71,plain,
( 'set$uunion2'(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t12_xboole_1]) ).
cnf(c72,plain,
subset('set$uintersection2'(X0,X1),X0),
inference(clausification,[status(esa)],[t17_xboole_1]) ).
cnf(c77,plain,
( 'set$uintersection2'(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t28_xboole_1]) ).
cnf(c84,plain,
( subset('set$udifference'(X0,X2),'set$udifference'(X1,X2))
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t33_xboole_1]) ).
cnf(c85,plain,
subset('set$udifference'(X0,X1),X0),
inference(clausification,[status(esa)],[t36_xboole_1]) ).
cnf(c88,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X0,'set$udifference'(X1,X0)),
inference(clausification,[status(esa)],[t39_xboole_1]) ).
cnf(c94,plain,
'set$udifference'(X0,X1) = 'set$udifference'('set$uunion2'(X0,X1),X1),
inference(clausification,[status(esa)],[t40_xboole_1]) ).
cnf(c96,plain,
'set$uintersection2'(X0,X1) = 'set$udifference'(X0,'set$udifference'(X0,X1)),
inference(clausification,[status(esa)],[t48_xboole_1]) ).
cnf(c105,plain,
subset(X0,'set$uunion2'(X0,X1)),
inference(clausification,[status(esa)],[t7_xboole_1]) ).
cnf(c110,plain,
subset(sK137,sK138),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c111,plain,
~ subset(sK137,'set$udifference'(sK138,singleton(sK139))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c112,plain,
~ in(sK139,sK137),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset('set$uintersection2'(X1,X0),X0),
inference(superposition,[status(thm)],[c4,c72]) ).
cnf(d1,plain,
( 'set$uintersection2'('set$udifference'(X0,X2),'set$udifference'(X1,X2)) = 'set$udifference'(X0,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c84,c77]) ).
cnf(d2,plain,
'set$uintersection2'('set$udifference'(sK137,X0),'set$udifference'(sK138,X0)) = 'set$udifference'(sK137,X0),
inference(resolution,[status(thm)],[d1,c110]) ).
cnf(d3,plain,
subset('set$udifference'(sK137,X0),'set$udifference'(sK138,X0)),
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
subset(X0,'set$uunion2'(X1,X0)),
inference(superposition,[status(thm)],[c3,c105]) ).
cnf(d5,plain,
'set$uintersection2'(X0,'set$uunion2'(X1,X0)) = X0,
inference(resolution,[status(thm)],[c77,d4]) ).
cnf(d6,plain,
'set$uintersection2'('set$uunion2'(X0,X1),X1) = 'set$udifference'('set$uunion2'(X0,X1),'set$udifference'(X0,X1)),
inference(superposition,[status(thm)],[c94,c96]) ).
cnf(d7,plain,
'set$uintersection2'(X1,'set$uunion2'(X0,X1)) = 'set$udifference'('set$uunion2'(X0,X1),'set$udifference'(X0,X1)),
inference(demodulation,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
X0 = 'set$udifference'('set$uunion2'(X1,X0),'set$udifference'(X1,X0)),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
'set$uunion2'(X0,'set$uunion2'(X1,X0)) = 'set$uunion2'(X1,X0),
inference(resolution,[status(thm)],[c71,d4]) ).
cnf(d10,plain,
'set$uunion2'(X1,'set$uunion2'(X0,X1)) = 'set$uunion2'(X1,'set$udifference'(X0,X1)),
inference(superposition,[status(thm)],[c94,c88]) ).
cnf(d11,plain,
'set$uunion2'(X1,X0) = 'set$uunion2'(X0,'set$udifference'(X1,X0)),
inference(demodulation,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
'set$udifference'(X0,'set$udifference'(X1,X0)) = 'set$udifference'('set$uunion2'(X1,X0),'set$udifference'(X1,X0)),
inference(superposition,[status(thm)],[d11,c94]) ).
cnf(d13,plain,
'set$udifference'(X1,'set$udifference'(X0,X1)) = X1,
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
subset(sK137,'set$udifference'(sK138,'set$udifference'(X0,sK137))),
inference(superposition,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,'set$udifference'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c45]) ).
cnf(d16,plain,
( ~ subset(X0,'set$udifference'(X0,X1))
| 'set$udifference'(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c7,c85]) ).
cnf(d17,plain,
( ~ in(X0,'set$udifference'(singleton(X0),X1))
| 'set$udifference'(singleton(X0),X1) = singleton(X0) ),
inference(resolution,[status(thm)],[d16,c64]) ).
cnf(d18,plain,
( ~ in(X0,singleton(X0))
| in(X0,X1)
| 'set$udifference'(singleton(X0),X1) = singleton(X0) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
in(X0,singleton(X0)),
inference(resolution,[status(thm)],[c63,c69]) ).
cnf(d20,plain,
( in(X0,X1)
| 'set$udifference'(singleton(X0),X1) = singleton(X0) ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
'set$udifference'(singleton(sK139),sK137) = singleton(sK139),
inference(resolution,[status(thm)],[d20,c112]) ).
cnf(d22,plain,
subset(sK137,'set$udifference'(sK138,singleton(sK139))),
inference(superposition,[status(thm)],[d21,d14]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[c111,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n015.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sat Sep 26 08:43:48 UTC 2026
% 0.18/5.47 % CPUTime :
% 0.18/5.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.90/27.68 % SZS status Theorem for theBenchmark.p
% 25.90/27.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------