%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET605+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 : 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 08:32:52 AM UTC 2026
% Result : Theorem 10.39s 1.79s
% Output : CNFRefutation 10.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 11 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_of_union,axiom,
! [X0,X1] : subset(X0,union(X0,X1)) ).
fof(difference_empty_set,axiom,
! [X0,X1] :
( difference(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(prove_th76,conjecture,
! [X0,X1] : difference(X0,union(X0,X1)) = 'empty$uset' ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : difference(X0,union(X0,X1)) = 'empty$uset',
inference(negate_conjecture,[status(cth)],[prove_th76]) ).
cnf(c0,plain,
subset(X0,union(X0,X1)),
inference(clausification,[status(esa)],[subset_of_union]) ).
cnf(c2,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[difference_empty_set]) ).
cnf(c26,plain,
difference(sK27,union(sK27,sK28)) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
difference(X0,union(X0,X1)) = 'empty$uset',
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
$false,
inference(resolution,[status(thm)],[d0,c26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET605+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:01:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.39/1.79 % SZS status Theorem for theBenchmark.p
% 10.39/1.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------