%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET185+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 : n003.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 08:32:16 AM UTC 2026
% Result : Theorem 14.31s 3.91s
% Output : CNFRefutation 14.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 54 ( 10 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 40 ( 13 ~; 20 |; 1 &)
% ( 3 <=>; 3 =>; 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 : 45 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
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(prove_subset_union,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
inference(negate_conjecture,[status(cth)],[prove_subset_union]) ).
cnf(c0,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c4,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c5,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c8,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c9,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c17,plain,
subset(sK16,sK17),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
union(sK16,sK17) != sK17,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,sK16)
| member(X0,sK17) ),
inference(resolution,[status(thm)],[c3,c17]) ).
cnf(d1,plain,
( member(sK6(union(X0,X1),X2),X0)
| member(sK6(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d2,plain,
( subset(union(X0,X1),X1)
| subset(union(X0,X1),X1)
| member(sK6(union(X0,X1),X1),X0) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( member(sK6(union(sK16,X0),X0),sK17)
| subset(union(sK16,X0),X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( subset(union(sK16,sK17),sK17)
| subset(union(sK16,sK17),sK17) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
subset(union(sK17,sK16),sK17),
inference(demodulation,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
( ~ member(sK6(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d7,plain,
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( ~ subset(union(X0,X1),X0)
| union(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
union(sK17,sK16) = sK17,
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
union(sK17,sK16) != sK17,
inference(demodulation,[status(thm)],[c18,c9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET185+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 07:19:40 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.31/3.91 % SZS status Theorem for theBenchmark.p
% 14.31/3.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------