%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU171+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 : n014.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 08:41:09 AM UTC 2026
% Result : Theorem 41.28s 9.44s
% Output : CNFRefutation 41.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 23 unt; 0 def)
% Number of atoms : 116 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 37 ~; 30 |; 5 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(d2_subset_1,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ) ).
fof(d4_xboole_0,axiom,
! [X0,X1,X2] :
( X2 = 'set$udifference'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ) ).
fof(d5_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,X1) = 'set$udifference'(X0,X1) ) ).
fof(l32_xboole_1,lemma,
! [X0,X1] :
( 'set$udifference'(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(l3_subset_1,lemma,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ) ).
fof(t1_xboole_1,lemma,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ).
fof(t36_xboole_1,lemma,
! [X0,X1] : subset('set$udifference'(X0,X1),X0) ).
fof(t4_boole,axiom,
! [X0] : 'set$udifference'('empty$uset',X0) = 'empty$uset' ).
fof(t7_boole,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ) ).
fof(t50_subset_1,conjecture,
! [X0] :
( X0 != 'empty$uset'
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,'subset$ucomplement'(X0,X1)) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( X0 != 'empty$uset'
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,'subset$ucomplement'(X0,X1)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t50_subset_1]) ).
cnf(c7,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[d10_xboole_0]) ).
cnf(c15,plain,
( in(sK18(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c22,plain,
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(clausification,[status(esa)],[d2_subset_1]) ).
cnf(c53,plain,
( in(sK54(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c54,plain,
( ~ in(sK54(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c73,plain,
( ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2)
| 'set$udifference'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d4_xboole_0]) ).
cnf(c79,plain,
( 'set$udifference'(X1,X0) = 'subset$ucomplement'(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[d5_subset_1]) ).
cnf(c104,plain,
( ~ subset(X0,X1)
| 'set$udifference'(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[l32_xboole_1]) ).
cnf(c105,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[l3_subset_1]) ).
cnf(c137,plain,
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t1_xboole_1]) ).
cnf(c150,plain,
subset('set$udifference'(X0,X1),X0),
inference(clausification,[status(esa)],[t36_xboole_1]) ).
cnf(c173,plain,
'set$udifference'('empty$uset',X0) = 'empty$uset',
inference(clausification,[status(esa)],[t4_boole]) ).
cnf(c183,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t7_boole]) ).
cnf(c198,plain,
sK261 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c199,plain,
element(sK262,powerset(sK261)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c200,plain,
element(sK263,sK261),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c201,plain,
~ in(sK263,'subset$ucomplement'(sK261,sK262)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c202,plain,
~ in(sK263,sK262),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,sK262)
| in(X0,sK261) ),
inference(resolution,[status(thm)],[c105,c199]) ).
cnf(d1,plain,
( sK262 = 'empty$uset'
| in(sK18(sK262),sK261) ),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
( ~ empty(sK261)
| sK262 = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c183]) ).
cnf(d3,plain,
( empty(sK261)
| in(sK263,sK261) ),
inference(resolution,[status(thm)],[c22,c200]) ).
cnf(d4,plain,
'set$udifference'(sK261,sK262) = 'subset$ucomplement'(sK261,sK262),
inference(resolution,[status(thm)],[c79,c199]) ).
cnf(d5,plain,
~ in(sK263,'set$udifference'(sK261,sK262)),
inference(demodulation,[status(thm)],[c201,d4]) ).
cnf(d6,plain,
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,'set$udifference'(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c73]) ).
cnf(d7,plain,
( ~ in(sK263,sK261)
| in(sK263,sK262) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
~ in(sK263,sK261),
inference(resolution,[status(thm)],[c202,d7]) ).
cnf(d9,plain,
empty(sK261),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
sK262 = 'empty$uset',
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( subset(sK262,X0)
| in(sK54(sK262,X0),sK261) ),
inference(resolution,[status(thm)],[d0,c53]) ).
cnf(d12,plain,
( subset(sK262,sK261)
| subset(sK262,sK261) ),
inference(resolution,[status(thm)],[d11,c54]) ).
cnf(d13,plain,
( ~ subset(sK261,sK262)
| sK262 = sK261 ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c53,c183]) ).
cnf(d15,plain,
( sK262 = sK261
| ~ empty(sK261) ),
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
sK262 = sK261,
inference(resolution,[status(thm)],[d9,d15]) ).
cnf(d17,plain,
'empty$uset' = sK261,
inference(demodulation,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
'empty$uset' != 'empty$uset',
inference(demodulation,[status(thm)],[c198,d17]) ).
cnf(d19,plain,
( ~ subset(X0,sK262)
| subset(X0,sK261) ),
inference(resolution,[status(thm)],[c137,d12]) ).
cnf(d20,plain,
subset('set$udifference'(sK262,X0),sK261),
inference(resolution,[status(thm)],[d19,c150]) ).
cnf(d21,plain,
'set$udifference'('set$udifference'(sK262,X0),sK261) = 'empty$uset',
inference(resolution,[status(thm)],[d20,c104]) ).
cnf(d22,plain,
'set$udifference'(sK262,sK261) = 'empty$uset',
inference(resolution,[status(thm)],[d12,c104]) ).
cnf(d23,plain,
'set$udifference'('empty$uset',sK261) = 'empty$uset',
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
'empty$uset' = 'empty$uset',
inference(demodulation,[status(thm)],[d23,c173]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU171+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:44:17 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.28/9.44 % SZS status Theorem for theBenchmark.p
% 41.28/9.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------