%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET162+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 : 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 08:32:12 AM UTC 2026
% Result : Theorem 12.88s 2.07s
% Output : CNFRefutation 12.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 45 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 13 ~; 15 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(prove_union_empty_set,conjecture,
! [X0] : union(X0,'empty$uset') = X0 ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : union(X0,'empty$uset') = X0,
inference(negate_conjecture,[status(cth)],[prove_union_empty_set]) ).
cnf(c0,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c3,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c6,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c7,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c9,plain,
( member(sK11(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c10,plain,
( ~ member(sK11(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c20,plain,
union(sK20,'empty$uset') != sK20,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(sK11(union(X0,X1),X2),X0)
| member(sK11(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d1,plain,
( subset(union(X0,X1),X1)
| subset(union(X0,X1),X1)
| member(sK11(union(X0,X1),X1),X0) ),
inference(resolution,[status(thm)],[d0,c10]) ).
cnf(d2,plain,
subset(union('empty$uset',X0),X0),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ member(sK11(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d4,plain,
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( ~ subset(union(X1,X0),X0)
| X0 = union(X1,X0) ),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
X0 = union('empty$uset',X0),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
union('empty$uset',sK20) != sK20,
inference(demodulation,[status(thm)],[c20,c7]) ).
cnf(d8,plain,
sK20 != sK20,
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
$false,
inference(equality_resolution,[status(thm)],[d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET162+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
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:15:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.88/2.07 % SZS status Theorem for theBenchmark.p
% 12.88/2.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------