%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET002+4 : 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 : n015.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 16.52s 8.31s
% Output : CNFRefutation 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 30 ( 9 ~; 16 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(equal_set,axiom,
! [X0,X1] :
( 'equal$uset'(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(union,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ) ).
fof(thI14,conjecture,
! [X0] : 'equal$uset'(union(X0,X0),X0) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : 'equal$uset'(union(X0,X0),X0),
inference(negate_conjecture,[status(cth)],[thI14]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c11,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union]) ).
cnf(c12,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union]) ).
cnf(c29,plain,
~ 'equal$uset'(union(sK31,sK31),sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(union(X0,X1),X2)
| member(sK3(union(X0,X1),X2),X0)
| member(sK3(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c11,c1]) ).
cnf(d1,plain,
( subset(union(X0,X1),X1)
| member(sK3(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( subset(union(X0,X0),X0)
| subset(union(X0,X0),X0) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( 'equal$uset'(union(X0,X0),X0)
| ~ subset(X0,union(X0,X0)) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( subset(X0,union(X1,X2))
| ~ member(sK3(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d5,plain,
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
'equal$uset'(union(X0,X0),X0),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:50:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.52/8.31 % SZS status Theorem for theBenchmark.p
% 16.52/8.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------