%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET577+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 : n010.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 08:32:47 AM UTC 2026
% Result : Theorem 6.30s 2.52s
% Output : CNFRefutation 6.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 71 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 16 ~; 30 |; 1 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
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_th18,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
=> X0 = union(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
=> X0 = union(X1,X2) ),
inference(negate_conjecture,[status(cth)],[prove_th18]) ).
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(c2,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c6,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c8,plain,
( member(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c9,plain,
( ~ member(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c17,plain,
( member(X0,sK18)
| member(X0,sK17)
| ~ member(X0,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( ~ member(X0,sK17)
| member(X0,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
( ~ member(X0,sK18)
| member(X0,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
sK16 != union(sK17,sK18),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(sK10(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(d1,plain,
( member(sK10(sK16,X0),sK17)
| member(sK10(sK16,X0),sK18)
| subset(sK16,X0) ),
inference(resolution,[status(thm)],[c8,c17]) ).
cnf(d2,plain,
( ~ member(sK10(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d3,plain,
( subset(sK16,union(sK17,X0))
| member(sK10(sK16,union(sK17,X0)),sK18)
| subset(sK16,union(sK17,X0)) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( subset(sK16,union(sK17,sK18))
| subset(sK16,union(sK17,sK18)) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
subset(sK16,union(sK18,sK17)),
inference(demodulation,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
( ~ subset(union(sK18,sK17),sK16)
| union(sK18,sK17) = sK16 ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( member(sK10(union(X0,X1),X2),X0)
| member(sK10(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d8,plain,
( member(sK10(union(X0,sK17),X1),sK16)
| subset(union(X0,sK17),X1)
| member(sK10(union(X0,sK17),X1),X0) ),
inference(resolution,[status(thm)],[d7,c18]) ).
cnf(d9,plain,
( member(sK10(union(sK18,sK17),X0),sK16)
| subset(union(sK18,sK17),X0)
| member(sK10(union(sK18,sK17),X0),sK16) ),
inference(resolution,[status(thm)],[d8,c19]) ).
cnf(d10,plain,
( subset(union(sK18,sK17),sK16)
| subset(union(sK18,sK17),sK16) ),
inference(resolution,[status(thm)],[d9,c9]) ).
cnf(d11,plain,
union(sK18,sK17) = sK16,
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
sK16 != union(sK18,sK17),
inference(demodulation,[status(thm)],[c20,c6]) ).
cnf(d13,plain,
sK16 != sK16,
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
$false,
inference(equality_resolution,[status(thm)],[d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET577+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
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:57:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.30/2.52 % SZS status Theorem for theBenchmark.p
% 6.30/2.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------