%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:33:15 AM UTC 2026
% Result : Theorem 24.88s 3.68s
% Output : CNFRefutation 24.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 38 ( 12 ~; 12 |; 4 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(lower_bound,axiom,
! [X0,X1,X2] :
( 'lower$ubound'(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ).
fof(thIV10,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4] :
( 'lower$ubound'(X4,X0,X3)
=> 'lower$ubound'(X4,X0,X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4] :
( 'lower$ubound'(X4,X0,X3)
=> 'lower$ubound'(X4,X0,X2) ) ) ),
inference(negate_conjecture,[status(cth)],[thIV10]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c60,plain,
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ 'lower$ubound'(X0,X1,X2) ),
inference(clausification,[status(esa)],[lower_bound]) ).
cnf(c61,plain,
( member(sK64(X1,X2,X0),X2)
| 'lower$ubound'(X0,X1,X2) ),
inference(clausification,[status(esa)],[lower_bound]) ).
cnf(c62,plain,
( ~ apply(X1,X0,sK64(X1,X2,X0))
| 'lower$ubound'(X0,X1,X2) ),
inference(clausification,[status(esa)],[lower_bound]) ).
cnf(c104,plain,
subset(sK103,sK104),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c105,plain,
'lower$ubound'(sK105,sK101,sK104),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c106,plain,
~ 'lower$ubound'(sK105,sK101,sK103),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( apply(sK101,sK105,X0)
| ~ member(X0,sK104) ),
inference(resolution,[status(thm)],[c60,c105]) ).
cnf(d1,plain,
( ~ member(sK64(sK101,X0,sK105),sK104)
| 'lower$ubound'(sK105,sK101,X0) ),
inference(resolution,[status(thm)],[c62,d0]) ).
cnf(d2,plain,
( member(sK64(X1,X2,X0),X3)
| ~ subset(X2,X3)
| 'lower$ubound'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c61,c0]) ).
cnf(d3,plain,
( 'lower$ubound'(sK105,sK101,X0)
| 'lower$ubound'(sK105,sK101,X0)
| ~ subset(X0,sK104) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
~ subset(sK103,sK104),
inference(resolution,[status(thm)],[d3,c106]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c104,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 08:12:18 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.88/3.68 % SZS status Theorem for theBenchmark.p
% 24.88/3.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------