%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET701+4 : 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 : n016.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 08:33:07 AM UTC 2026
% Result : Theorem 32.67s 29.76s
% Output : CNFRefutation 32.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 4 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 118 ( 42 ~; 64 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 3 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(intersection,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ) ).
fof(difference,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ) ).
fof(thI35,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(negate_conjecture,[status(cth)],[thI35]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c8,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c9,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c10,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c16,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference]) ).
cnf(c17,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference]) ).
cnf(c30,plain,
subset(sK31,sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c32,plain,
( subset(intersection(sK31,difference(sK34,sK32)),intersection(sK33,difference(sK34,sK33)))
| subset(sK31,sK32) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c33,plain,
( ~ subset(sK31,sK32)
| ~ subset(intersection(sK31,difference(sK34,sK32)),intersection(sK33,difference(sK34,sK33))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(sK3(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( member(X0,X3)
| ~ subset(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(d2,plain,
( subset(sK31,sK32)
| ~ member(X0,difference(sK34,sK32))
| ~ member(X0,sK31)
| member(X0,intersection(sK33,difference(sK34,sK33))) ),
inference(resolution,[status(thm)],[d1,c32]) ).
cnf(d3,plain,
( member(X0,difference(sK34,sK33))
| ~ member(X0,sK31)
| ~ member(X0,difference(sK34,sK32))
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
( ~ member(X0,sK34)
| member(X0,sK32)
| ~ member(X0,sK31)
| member(X0,difference(sK34,sK33))
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d3,c17]) ).
cnf(d5,plain,
( ~ member(X0,sK33)
| ~ member(X0,sK31)
| ~ member(X0,sK34)
| member(X0,sK32)
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d4,c16]) ).
cnf(d6,plain,
( member(X0,sK33)
| ~ member(X0,sK31)
| ~ member(X0,difference(sK34,sK32))
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d7,plain,
( ~ member(X0,sK34)
| member(X0,sK32)
| member(X0,sK33)
| ~ member(X0,sK31)
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d6,c17]) ).
cnf(d8,plain,
( ~ member(X0,sK31)
| ~ member(X0,sK34)
| member(X0,sK32)
| subset(sK31,sK32)
| ~ member(X0,sK31)
| ~ member(X0,sK34)
| member(X0,sK32)
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( subset(sK31,X0)
| ~ member(sK3(sK31,X0),sK34)
| member(sK3(sK31,X0),sK32)
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( subset(sK31,X0)
| ~ subset(sK31,sK34)
| member(sK3(sK31,X0),sK32)
| subset(sK31,sK32)
| subset(sK31,X0) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( member(sK3(sK31,X0),sK32)
| subset(sK31,sK32)
| subset(sK31,X0) ),
inference(resolution,[status(thm)],[c30,d10]) ).
cnf(d12,plain,
( subset(sK31,sK32)
| subset(sK31,sK32)
| subset(sK31,sK32) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
~ subset(intersection(sK31,difference(sK34,sK32)),intersection(sK33,difference(sK34,sK33))),
inference(resolution,[status(thm)],[d12,c33]) ).
cnf(d14,plain,
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d15,plain,
( member(sK3(intersection(X0,X1),X2),X3)
| ~ subset(X0,X3)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d17,plain,
( ~ member(sK3(intersection(X0,difference(X1,X2)),X3),X2)
| subset(intersection(X0,difference(X1,X2)),X3) ),
inference(resolution,[status(thm)],[d16,c16]) ).
cnf(d18,plain,
( subset(intersection(X0,difference(X1,X2)),X3)
| ~ subset(X0,X2)
| subset(intersection(X0,difference(X1,X2)),X3) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
~ subset(sK31,sK32),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d12,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET701+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n016.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 08:11:38 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.67/29.76 % SZS status Theorem for theBenchmark.p
% 32.67/29.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------