%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:31:30 AM UTC 2026
% Result : Theorem 8.93s 1.67s
% Output : CNFRefutation 8.93s
% 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 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_union,axiom,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ) ).
fof(reflexivity_of_subset,axiom,
! [X0] : subset(X0,X0) ).
fof(prove_idempotency_of_union,conjecture,
! [X0] : union(X0,X0) = X0 ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : union(X0,X0) = X0,
inference(negate_conjecture,[status(cth)],[prove_idempotency_of_union]) ).
cnf(c0,plain,
( union(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_union]) ).
cnf(c11,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_of_subset]) ).
cnf(c18,plain,
union(sK18,sK18) != sK18,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
union(X0,X0) = X0,
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d1,plain,
$false,
inference(resolution,[status(thm)],[d0,c18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:47:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.93/1.67 % SZS status Theorem for theBenchmark.p
% 8.93/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------