%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET688+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 : n002.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 08:33:06 AM UTC 2026
% Result : Theorem 2.83s 3.54s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 17 |; 7 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(equal_set,axiom,
! [X0,X1] :
( 'equal$uset'(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(thI04,conjecture,
! [X0,X1,X2] :
( ( ~ 'equal$uset'(X1,X2)
& subset(X1,X2)
& ~ 'equal$uset'(X0,X1)
& subset(X0,X1) )
=> ~ 'equal$uset'(X0,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ 'equal$uset'(X1,X2)
& subset(X1,X2)
& ~ 'equal$uset'(X0,X1)
& subset(X0,X1) )
=> ~ 'equal$uset'(X0,X2) ),
inference(negate_conjecture,[status(cth)],[thI04]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c4,plain,
( subset(X1,X0)
| ~ 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c29,plain,
subset(sK31,sK32),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
~ 'equal$uset'(sK31,sK32),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
subset(sK32,sK33),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c33,plain,
'equal$uset'(sK31,sK33),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset(sK33,sK31),
inference(resolution,[status(thm)],[c4,c33]) ).
cnf(d1,plain,
( member(sK3(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d2,plain,
( member(sK3(X0,X2),X3)
| ~ subset(X1,X3)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( member(sK3(sK32,X1),X0)
| subset(sK32,X1)
| ~ subset(sK33,X0) ),
inference(resolution,[status(thm)],[d2,c31]) ).
cnf(d4,plain,
( subset(sK32,X0)
| ~ subset(sK33,X0)
| subset(sK32,X0) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
subset(sK32,sK31),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( 'equal$uset'(sK31,sK32)
| ~ subset(sK32,sK31) ),
inference(resolution,[status(thm)],[c5,c29]) ).
cnf(d7,plain,
~ subset(sK32,sK31),
inference(resolution,[status(thm)],[c30,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET688+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
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:08:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.83/3.54 % SZS status Theorem for theBenchmark.p
% 2.83/3.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------