%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU321+1 : 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 : n002.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 08:41:39 AM UTC 2026
% Result : Theorem 23.88s 3.61s
% Output : CNFRefutation 23.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 105 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 49 ~; 35 |; 13 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 4 sgn 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t5_subset,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ) ).
fof(t8_boole,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ) ).
fof(existence_m1_subset_1,axiom,
! [X0] :
? [X1] : element(X1,X0) ).
fof(fc1_struct_0,axiom,
! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ~ empty('the$ucarrier'(X0)) ) ).
fof(fc6_membered,axiom,
( 'v5$umembered'('empty$uset')
& 'v4$umembered'('empty$uset')
& 'v3$umembered'('empty$uset')
& 'v2$umembered'('empty$uset')
& 'v1$umembered'('empty$uset')
& empty('empty$uset') ) ).
fof(t50_subset_1,axiom,
! [X0] :
( X0 != 'empty$uset'
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,'subset$ucomplement'(X0,X1)) ) ) ) ) ).
fof(t54_subset_1,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,'subset$ucomplement'(X0,X2)) ) ) ).
fof(l40_tops_1,conjecture,
! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( in(X2,'subset$ucomplement'('the$ucarrier'(X0),X1))
<=> ~ in(X2,X1) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'one$usorted$ustr'(X0)
& ~ 'empty$ucarrier'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ! [X2] :
( element(X2,'the$ucarrier'(X0))
=> ( in(X2,'subset$ucomplement'('the$ucarrier'(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(negate_conjecture,[status(cth)],[l40_tops_1]) ).
cnf(c51,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c52,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t5_subset]) ).
cnf(c53,plain,
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t8_boole]) ).
cnf(c57,plain,
element(sK46(X0),X0),
inference(clausification,[status(esa)],[existence_m1_subset_1]) ).
cnf(c61,plain,
( ~ empty('the$ucarrier'(X0))
| ~ 'one$usorted$ustr'(X0)
| 'empty$ucarrier'(X0) ),
inference(clausification,[status(esa)],[fc1_struct_0]) ).
cnf(c62,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc6_membered]) ).
cnf(c74,plain,
( X1 = 'empty$uset'
| in(X0,X2)
| ~ element(X2,powerset(X1))
| in(X0,'subset$ucomplement'(X1,X2))
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t50_subset_1]) ).
cnf(c75,plain,
( ~ in(X2,X0)
| ~ in(X2,'subset$ucomplement'(X1,X0))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t54_subset_1]) ).
cnf(c76,plain,
~ 'empty$ucarrier'(sK67),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c77,plain,
'one$usorted$ustr'(sK67),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c78,plain,
element(sK68,powerset('the$ucarrier'(sK67))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c79,plain,
element(sK69,'the$ucarrier'(sK67)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c81,plain,
( ~ in(sK69,sK68)
| in(sK69,'subset$ucomplement'('the$ucarrier'(sK67),sK68)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
( ~ in(sK69,'subset$ucomplement'('the$ucarrier'(sK67),sK68))
| in(sK69,sK68) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ empty(X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[c53,c62]) ).
cnf(d1,plain,
( in(sK46(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[c57,c51]) ).
cnf(d2,plain,
( in(sK69,sK68)
| in(sK69,sK68)
| ~ element(sK69,'the$ucarrier'(sK67))
| ~ element(sK68,powerset('the$ucarrier'(sK67)))
| 'the$ucarrier'(sK67) = 'empty$uset' ),
inference(resolution,[status(thm)],[c74,c82]) ).
cnf(d3,plain,
( in(sK69,sK68)
| ~ element(sK68,powerset('the$ucarrier'(sK67)))
| 'the$ucarrier'(sK67) = 'empty$uset' ),
inference(resolution,[status(thm)],[c79,d2]) ).
cnf(d4,plain,
( in(sK69,sK68)
| 'the$ucarrier'(sK67) = 'empty$uset' ),
inference(resolution,[status(thm)],[c78,d3]) ).
cnf(d5,plain,
( ~ in(sK69,sK68)
| ~ in(sK69,sK68)
| ~ element(sK68,powerset('the$ucarrier'(sK67))) ),
inference(resolution,[status(thm)],[c75,c81]) ).
cnf(d6,plain,
~ in(sK69,sK68),
inference(resolution,[status(thm)],[c78,d5]) ).
cnf(d7,plain,
'the$ucarrier'(sK67) = 'empty$uset',
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( ~ in(X0,sK68)
| ~ empty('the$ucarrier'(sK67)) ),
inference(resolution,[status(thm)],[c52,c78]) ).
cnf(d9,plain,
( ~ in(X0,sK68)
| ~ empty('empty$uset') ),
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
~ in(X0,sK68),
inference(resolution,[status(thm)],[c62,d9]) ).
cnf(d11,plain,
empty(sK68),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
'empty$uset' = sK68,
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( 'empty$ucarrier'(sK67)
| ~ 'one$usorted$ustr'(sK67)
| ~ empty('empty$uset') ),
inference(superposition,[status(thm)],[d7,c61]) ).
cnf(d14,plain,
( ~ empty(sK68)
| 'empty$ucarrier'(sK67)
| ~ 'one$usorted$ustr'(sK67) ),
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ empty(sK68)
| ~ 'one$usorted$ustr'(sK67) ),
inference(resolution,[status(thm)],[c76,d14]) ).
cnf(d16,plain,
~ empty(sK68),
inference(resolution,[status(thm)],[c77,d15]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d11,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU321+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n002.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 09:14:50 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.88/3.61 % SZS status Theorem for theBenchmark.p
% 23.88/3.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------