%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET814+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 : n010.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 08:33:16 AM UTC 2026
% Result : Theorem 29.47s 4.17s
% Output : CNFRefutation 29.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 3 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 41 ( 15 ~; 16 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(sum,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ) ).
fof(ordinal_number,axiom,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& 'strict$uwell$uorder'('member$upredicate',X0)
& set(X0) ) ) ).
fof(thV14,conjecture,
! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
inference(negate_conjecture,[status(cth)],[thV14]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c3,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c24,plain,
( member(sK28(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(clausification,[status(esa)],[sum]) ).
cnf(c25,plain,
( member(X0,sK28(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(clausification,[status(esa)],[sum]) ).
cnf(c31,plain,
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(clausification,[status(esa)],[ordinal_number]) ).
cnf(c65,plain,
member(sK73,on),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
~ subset(sum(sK73),sK73),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,sK73)
| subset(X0,sK73) ),
inference(resolution,[status(thm)],[c31,c65]) ).
cnf(d1,plain,
( ~ member(X0,sum(sK73))
| subset(sK28(X0,sK73),sK73) ),
inference(resolution,[status(thm)],[d0,c24]) ).
cnf(d2,plain,
( member(X0,X2)
| ~ subset(sK28(X0,X1),X2)
| ~ member(X0,sum(X1)) ),
inference(resolution,[status(thm)],[c25,c1]) ).
cnf(d3,plain,
( ~ member(X0,sum(sK73))
| ~ member(X0,sum(sK73))
| member(X0,sK73) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( subset(sum(sK73),X0)
| member(sK6(sum(sK73),X0),sK73) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( subset(sum(sK73),sK73)
| subset(sum(sK73),sK73) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c66,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:18:29 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.47/4.17 % SZS status Theorem for theBenchmark.p
% 29.47/4.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------