%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:12:37 AM UTC 2026
% Result : Theorem 11.11s 1.95s
% Output : CNFRefutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 63 ( 3 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 27 ~; 20 |; 7 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 40 ( 5 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ) ).
fof(fc12_relat_1,axiom,
( 'relation$uempty$uyielding'('empty$uset')
& relation('empty$uset')
& empty('empty$uset') ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ) ).
fof(t4_subset,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ) ).
fof(t5_subset,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ) ).
fof(t6_boole,axiom,
! [X0] :
( empty(X0)
=> X0 = 'empty$uset' ) ).
fof(t7_ordinal1,conjecture,
! [X0,X1] :
~ ( subset(X1,X0)
& in(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
~ ( subset(X1,X0)
& in(X0,X1) ),
inference(negate_conjecture,[status(cth)],[t7_ordinal1]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_r2_hidden]) ).
cnf(c7,plain,
empty('empty$uset'),
inference(clausification,[status(esa)],[fc12_relat_1]) ).
cnf(c37,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c39,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c40,plain,
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t4_subset]) ).
cnf(c41,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t5_subset]) ).
cnf(c42,plain,
( X0 = 'empty$uset'
| ~ empty(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c45,plain,
in(sK36,sK37),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c46,plain,
subset(sK37,sK36),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c40,c39]) ).
cnf(d1,plain,
( element(X0,sK36)
| ~ in(X0,sK37) ),
inference(resolution,[status(thm)],[d0,c46]) ).
cnf(d2,plain,
element(sK36,sK36),
inference(resolution,[status(thm)],[d1,c45]) ).
cnf(d3,plain,
( empty(sK36)
| in(sK36,sK36) ),
inference(resolution,[status(thm)],[d2,c37]) ).
cnf(d4,plain,
( ~ in(sK36,sK36)
| empty(sK36) ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( empty(sK36)
| empty(sK36) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
sK36 = 'empty$uset',
inference(resolution,[status(thm)],[d5,c42]) ).
cnf(d7,plain,
in('empty$uset',sK37),
inference(demodulation,[status(thm)],[c45,d6]) ).
cnf(d8,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c41,c39]) ).
cnf(d9,plain,
( ~ empty(sK36)
| ~ in(X0,sK37) ),
inference(resolution,[status(thm)],[d8,c46]) ).
cnf(d10,plain,
( ~ empty('empty$uset')
| ~ in(X0,sK37) ),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
~ in(X0,sK37),
inference(resolution,[status(thm)],[c7,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n007.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 02:35:40 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.11/1.95 % SZS status Theorem for theBenchmark.p
% 11.11/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------