%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 08:32:51 AM UTC 2026
% Result : Theorem 16.85s 2.68s
% Output : CNFRefutation 16.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 23 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 4 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
! [X0] :
( subset(X0,'empty$uset')
=> X0 = 'empty$uset' ) ).
fof(intersection_of_subset,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(intersection(X0,X2),intersection(X1,X2)) ) ).
fof(prove_th55,conjecture,
! [X0,X1,X2] :
( ( intersection(X1,X2) = 'empty$uset'
& subset(X0,X1) )
=> intersection(X0,X2) = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( intersection(X1,X2) = 'empty$uset'
& subset(X0,X1) )
=> intersection(X0,X2) = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[prove_th55]) ).
cnf(c0,plain,
( X0 = 'empty$uset'
| ~ subset(X0,'empty$uset') ),
inference(clausification,[status(esa)],[subset_of_empty_set_is_empty_set]) ).
cnf(c1,plain,
( subset(intersection(X0,X2),intersection(X1,X2))
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[intersection_of_subset]) ).
cnf(c22,plain,
subset(sK24,sK25),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c23,plain,
intersection(sK25,sK26) = 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c24,plain,
intersection(sK24,sK26) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset(X0,sK25)
| subset(intersection(X0,sK26),'empty$uset') ),
inference(superposition,[status(thm)],[c23,c1]) ).
cnf(d1,plain,
( intersection(X0,sK26) = 'empty$uset'
| ~ subset(X0,sK25) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
intersection(sK24,sK26) = 'empty$uset',
inference(resolution,[status(thm)],[d1,c22]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c24,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n005.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:58:16 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.85/2.68 % SZS status Theorem for theBenchmark.p
% 16.85/2.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------