%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET200+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 : n009.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 08:32:18 AM UTC 2026
% Result : Theorem 15.08s 2.35s
% Output : CNFRefutation 15.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 57 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 41 ( 12 ~; 22 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 3 sgn 16 !; 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(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(prove_th34,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(union(X0,X2),union(X1,X3)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(union(X0,X2),union(X1,X3)) ),
inference(negate_conjecture,[status(cth)],[prove_th34]) ).
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(c6,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c14,plain,
subset(sK14,sK15),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
subset(sK16,sK17),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
~ subset(union(sK14,sK16),union(sK15,sK17)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,sK16)
| member(X0,sK17) ),
inference(resolution,[status(thm)],[c3,c15]) ).
cnf(d1,plain,
( subset(sK16,X0)
| member(sK6(sK16,X0),sK17) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ member(sK6(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d3,plain,
( subset(sK16,union(sK17,X0))
| subset(sK16,union(sK17,X0)) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
subset(sK16,union(X0,sK17)),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
( ~ member(X0,sK16)
| member(X0,union(X1,sK17)) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
( subset(X0,union(X1,sK17))
| ~ member(sK6(X0,union(X1,sK17)),sK16) ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( ~ member(X0,sK14)
| member(X0,sK15) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(d8,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(d9,plain,
( member(sK6(union(X0,sK14),X1),sK15)
| subset(union(X0,sK14),X1)
| member(sK6(union(X0,sK14),X1),X0) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( subset(union(X0,sK14),union(sK15,X1))
| subset(union(X0,sK14),union(sK15,X1))
| member(sK6(union(X0,sK14),union(sK15,X1)),X0) ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( subset(union(sK16,sK14),union(sK15,sK17))
| subset(union(sK16,sK14),union(sK15,sK17)) ),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
subset(union(sK14,sK16),union(sK15,sK17)),
inference(demodulation,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c16,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET200+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
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 07:19:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.08/2.35 % SZS status Theorem for theBenchmark.p
% 15.08/2.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------