%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET624+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 : n004.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 08:32:56 AM UTC 2026
% Result : Theorem 30.94s 4.38s
% Output : CNFRefutation 30.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 76 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 30 ~; 38 |; 1 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 58 ( 4 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(intersect_defn,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ) ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(symmetry_of_intersect,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ) ).
fof(prove_intersect_with_union,conjecture,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[prove_intersect_with_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(sK5(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c4,plain,
( member(sK5(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c6,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c7,plain,
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_intersect]) ).
cnf(c15,plain,
( intersect(sK15,sK17)
| intersect(sK15,sK16)
| intersect(sK15,union(sK16,sK17)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
( ~ intersect(sK15,union(sK16,sK17))
| ~ intersect(sK15,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( ~ intersect(sK15,union(sK16,sK17))
| ~ intersect(sK15,sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( intersect(sK15,sK17)
| intersect(sK15,sK16)
| intersect(union(sK16,sK17),sK15) ),
inference(resolution,[status(thm)],[c7,c15]) ).
cnf(d1,plain,
( ~ intersect(X0,X1)
| intersect(X0,X2)
| ~ member(sK5(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d2,plain,
( ~ member(sK5(X0,X3),X1)
| ~ intersect(X0,X3)
| intersect(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( ~ intersect(X0,X1)
| intersect(X0,union(X1,X2))
| ~ intersect(X0,X1) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( ~ intersect(sK15,sK16)
| ~ intersect(sK15,sK16) ),
inference(resolution,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
( intersect(sK15,sK17)
| intersect(union(sK16,sK17),sK15) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ intersect(X2,X0)
| intersect(X2,union(X1,X0)) ),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d7,plain,
( ~ intersect(sK15,sK17)
| ~ intersect(sK15,sK17) ),
inference(resolution,[status(thm)],[d6,c18]) ).
cnf(d8,plain,
intersect(union(sK16,sK17),sK15),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ intersect(X0,X1)
| intersect(X1,X2)
| ~ member(sK5(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d10,plain,
( member(sK5(union(X0,X1),X2),X0)
| member(sK5(union(X0,X1),X2),X1)
| ~ intersect(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d11,plain,
( ~ intersect(union(X0,X1),X2)
| intersect(X2,X0)
| ~ intersect(union(X0,X1),X2)
| member(sK5(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ intersect(union(X1,X2),X0)
| intersect(X0,X2)
| ~ intersect(union(X1,X2),X0)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( intersect(sK15,sK16)
| intersect(sK15,sK17) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
intersect(sK15,sK17),
inference(resolution,[status(thm)],[d4,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d7,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+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 : n004.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 08:00:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.94/4.38 % SZS status Theorem for theBenchmark.p
% 30.94/4.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------