%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET143+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 : n012.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 08:32:09 AM UTC 2026
% Result : Theorem 92.46s 31.18s
% Output : CNFRefutation 92.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 85 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 26 ~; 39 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 114 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(prove_associativity_of_intersection,conjecture,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(negate_conjecture,[status(cth)],[prove_associativity_of_intersection]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c2,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c6,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
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,
intersection(sK16,intersection(sK17,sK18)) != intersection(intersection(sK16,sK17),sK18),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
intersection(sK16,intersection(sK17,sK18)) != intersection(sK18,intersection(sK16,sK17)),
inference(demodulation,[status(thm)],[c17,c6]) ).
cnf(d1,plain,
( member(sK10(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d2,plain,
( member(sK10(intersection(X0,intersection(X1,X2)),X3),X2)
| subset(intersection(X0,intersection(X1,X2)),X3) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( member(sK10(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d4,plain,
( ~ member(sK10(X0,intersection(X1,X2)),X2)
| ~ member(sK10(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(d5,plain,
( subset(intersection(X0,X1),intersection(X0,X2))
| subset(intersection(X0,X1),intersection(X0,X2))
| ~ member(sK10(intersection(X0,X1),intersection(X0,X2)),X2) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( subset(intersection(X0,intersection(X1,X2)),intersection(X0,X2))
| subset(intersection(X0,intersection(X1,X2)),intersection(X0,X2)) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
subset(intersection(X0,intersection(X2,X1)),intersection(X1,X0)),
inference(superposition,[status(thm)],[c6,d6]) ).
cnf(d8,plain,
( ~ subset(intersection(X2,X0),intersection(X0,intersection(X1,X2)))
| intersection(X0,intersection(X1,X2)) = intersection(X2,X0) ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
( subset(intersection(X0,X1),intersection(X1,X2))
| subset(intersection(X0,X1),intersection(X1,X2))
| ~ member(sK10(intersection(X0,X1),intersection(X1,X2)),X2) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d10,plain,
( ~ member(sK10(intersection(X0,X1),intersection(X1,intersection(X2,X3))),X3)
| ~ member(sK10(intersection(X0,X1),intersection(X1,intersection(X2,X3))),X2)
| subset(intersection(X0,X1),intersection(X1,intersection(X2,X3))) ),
inference(resolution,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
( subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X1,X2),intersection(X2,X3)))
| subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X1,X2),intersection(X2,X3)))
| ~ member(sK10(intersection(X0,intersection(X1,X2)),intersection(intersection(X1,X2),intersection(X2,X3))),X3) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X1,X2),intersection(X2,X0)))
| subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X1,X2),intersection(X2,X0))) ),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
intersection(intersection(X0,X1),intersection(X1,X2)) = intersection(X2,intersection(X0,X1)),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( member(sK10(intersection(intersection(X0,X1),X2),X3),X0)
| subset(intersection(intersection(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d15,plain,
( subset(intersection(intersection(X0,X1),X2),intersection(X0,X3))
| ~ member(sK10(intersection(intersection(X0,X1),X2),intersection(X0,X3)),X3)
| subset(intersection(intersection(X0,X1),X2),intersection(X0,X3)) ),
inference(resolution,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
( subset(intersection(intersection(X0,X1),X2),intersection(X0,X2))
| subset(intersection(intersection(X0,X1),X2),intersection(X0,X2)) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ subset(intersection(X0,X2),intersection(intersection(X0,X1),X2))
| intersection(intersection(X0,X1),X2) = intersection(X0,X2) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
( member(sK10(intersection(X0,intersection(X1,X2)),X3),X1)
| subset(intersection(X0,intersection(X1,X2)),X3) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d19,plain,
( ~ member(sK10(X0,intersection(intersection(X1,X2),X3)),X2)
| ~ member(sK10(X0,intersection(intersection(X1,X2),X3)),X1)
| subset(X0,intersection(intersection(X1,X2),X3))
| ~ member(sK10(X0,intersection(intersection(X1,X2),X3)),X3) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d20,plain,
( subset(intersection(X0,X1),intersection(intersection(X0,X2),X3))
| subset(intersection(X0,X1),intersection(intersection(X0,X2),X3))
| ~ member(sK10(intersection(X0,X1),intersection(intersection(X0,X2),X3)),X2)
| ~ member(sK10(intersection(X0,X1),intersection(intersection(X0,X2),X3)),X3) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
( subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X0,X1),X3))
| subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X0,X1),X3))
| ~ member(sK10(intersection(X0,intersection(X1,X2)),intersection(intersection(X0,X1),X3)),X3) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X0,X1),intersection(X1,X2)))
| subset(intersection(X0,intersection(X1,X2)),intersection(intersection(X0,X1),intersection(X1,X2))) ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
intersection(intersection(X0,X1),intersection(X1,X2)) = intersection(X0,intersection(X1,X2)),
inference(resolution,[status(thm)],[d22,d17]) ).
cnf(d24,plain,
intersection(X0,intersection(X1,X2)) = intersection(X2,intersection(X0,X1)),
inference(superposition,[status(thm)],[d23,d13]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 07:12:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.46/31.18 % SZS status Theorem for theBenchmark.p
% 92.46/31.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------