%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET578+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 : n011.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 11.27s 2.75s
% Output : CNFRefutation 11.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 90 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 24 ~; 35 |; 4 &)
% ( 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 : 61 ( 2 sgn 19 !; 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(reflexivity_of_subset,axiom,
! [X0] : subset(X0,X0) ).
fof(prove_th19,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
=> X0 = intersection(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
& member(X3,X1) ) )
=> X0 = intersection(X1,X2) ),
inference(negate_conjecture,[status(cth)],[prove_th19]) ).
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,X2)
| ~ member(X0,X1)
| 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(c10,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_of_subset]) ).
cnf(c17,plain,
( member(X0,sK17)
| ~ member(X0,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( member(X0,sK18)
| ~ member(X0,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
( ~ member(X0,sK18)
| ~ member(X0,sK17)
| member(X0,sK16) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
sK16 != intersection(sK17,sK18),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(sK10(sK16,X0),sK17)
| subset(sK16,X0) ),
inference(resolution,[status(thm)],[c8,c17]) ).
cnf(d1,plain,
( member(sK10(sK16,X0),sK18)
| subset(sK16,X0) ),
inference(resolution,[status(thm)],[c8,c18]) ).
cnf(d2,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(d3,plain,
( subset(sK16,intersection(sK18,X0))
| subset(sK16,intersection(sK18,X0))
| ~ member(sK10(sK16,intersection(sK18,X0)),X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( subset(sK16,intersection(sK18,sK17))
| subset(sK16,intersection(sK18,sK17)) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
subset(sK16,intersection(sK17,sK18)),
inference(demodulation,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
( ~ subset(intersection(sK17,sK18),sK16)
| intersection(sK17,sK18) = sK16 ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( member(sK10(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d8,plain,
( member(sK10(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d9,plain,
( ~ member(sK10(intersection(X0,sK18),X1),sK17)
| member(sK10(intersection(X0,sK18),X1),sK16)
| subset(intersection(X0,sK18),X1) ),
inference(resolution,[status(thm)],[d8,c19]) ).
cnf(d10,plain,
( subset(intersection(sK17,sK18),X0)
| subset(intersection(sK17,sK18),X0)
| member(sK10(intersection(sK17,sK18),X0),sK16) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( subset(intersection(sK17,sK18),sK16)
| subset(intersection(sK17,sK18),sK16) ),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
intersection(sK17,sK18) = sK16,
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
sK16 != sK16,
inference(demodulation,[status(thm)],[c20,d12]) ).
cnf(d14,plain,
( subset(X0,intersection(X0,X1))
| subset(X0,intersection(X0,X1))
| ~ member(sK10(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d15,plain,
( subset(sK16,intersection(sK16,sK18))
| subset(sK16,intersection(sK16,sK18)) ),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d7,c9]) ).
cnf(d17,plain,
( ~ subset(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
sK16 = intersection(sK16,sK18),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( ~ subset(intersection(sK16,sK18),sK16)
| intersection(sK16,sK18) = sK16 ),
inference(resolution,[status(thm)],[d15,c5]) ).
cnf(d20,plain,
( ~ subset(intersection(sK16,sK18),sK16)
| sK16 = sK16 ),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ subset(sK16,sK16)
| sK16 = sK16 ),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
sK16 = sK16,
inference(resolution,[status(thm)],[c10,d21]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d22,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:56:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.27/2.75 % SZS status Theorem for theBenchmark.p
% 11.27/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------