%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET173+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 : 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 08:32:14 AM UTC 2026
% Result : Theorem 11.84s 4.44s
% Output : CNFRefutation 11.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 73 ( 13 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 20 ~; 30 |; 2 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(reflexivity_of_subset,axiom,
! [X0] : subset(X0,X0) ).
fof(prove_absorbtion_for_intersection,conjecture,
! [X0,X1] : intersection(X0,union(X0,X1)) = X0 ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
inference(negate_conjecture,[status(cth)],[prove_absorbtion_for_intersection]) ).
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(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c5,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c8,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c12,plain,
( member(sK15(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c13,plain,
( ~ member(sK15(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c14,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_of_subset]) ).
cnf(c21,plain,
intersection(sK21,union(sK21,sK22)) != sK21,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(sK15(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(d1,plain,
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
( ~ subset(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
( ~ member(sK15(X0,intersection(X1,X2)),X1)
| ~ member(sK15(X0,intersection(X1,X2)),X2)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[c13,c5]) ).
cnf(d4,plain,
( subset(X0,intersection(X0,X1))
| subset(X0,intersection(X0,X1))
| ~ member(sK15(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
( ~ member(sK15(X0,intersection(X0,union(X1,X2))),X1)
| subset(X0,intersection(X0,union(X1,X2))) ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
( subset(X0,intersection(X0,union(X0,X1)))
| subset(X0,intersection(X0,union(X0,X1))) ),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d7,plain,
X0 = intersection(X0,union(X0,X1)),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
sK21 != sK21,
inference(demodulation,[status(thm)],[c21,d7]) ).
cnf(d9,plain,
( ~ member(sK15(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c13,c1]) ).
cnf(d10,plain,
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[d9,c12]) ).
cnf(d11,plain,
( ~ subset(union(X0,X1),X0)
| union(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d10,c8]) ).
cnf(d12,plain,
( member(sK15(union(X0,X1),X2),X0)
| member(sK15(union(X0,X1),X2),X1)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d13,plain,
( subset(union(X0,X1),X1)
| subset(union(X0,X1),X1)
| member(sK15(union(X0,X1),X1),X0) ),
inference(resolution,[status(thm)],[d12,c13]) ).
cnf(d14,plain,
( subset(union(X0,X0),X0)
| subset(union(X0,X0),X0) ),
inference(resolution,[status(thm)],[d13,c13]) ).
cnf(d15,plain,
union(X0,X0) = X0,
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( union(X0,X0) = X0
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( ~ subset(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
X0 = X0,
inference(resolution,[status(thm)],[c14,d17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET173+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
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 07:16:29 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.84/4.44 % SZS status Theorem for theBenchmark.p
% 11.84/4.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------