%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:54:35 AM UTC 2026
% Result : Unsatisfiable 10.14s 2.75s
% Output : CNFRefutation 10.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 7 RR)
% Number of literals : 14 ( 2 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$uPropLog$uOsat'('c$uemptyset','v$up','t$ua') ).
cnf(cls_conjecture_1,negated_conjecture,
~ 'c$uin'('v$up','c$uPropLog$uOthms'('c$uemptyset','t$ua'),'tc$uPropLog$uOpl'('t$ua')) ).
cnf(cls_PropLog_Ocompleteness__0__lemma__dest_0,axiom,
( 'c$uin'(X0,'c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'(X0,X2,X1),'c$uPropLog$uOhyps'(X0,X3,X1),'tc$uset'('tc$uPropLog$uOpl'(X1))),X1),'tc$uPropLog$uOpl'(X1))
| ~ 'c$uPropLog$uOsat'('c$uemptyset',X0,X1) ) ).
cnf(cls_Set_ODiff__cancel_0,axiom,
'c$uminus'(X0,X0,'tc$uset'(X1)) = 'c$uemptyset' ).
cnf(c0,plain,
'c$uPropLog$uOsat'('c$uemptyset','v$up','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
~ 'c$uin'('v$up','c$uPropLog$uOthms'('c$uemptyset','t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'c$uin'(X0,'c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'(X0,X2,X1),'c$uPropLog$uOhyps'(X0,X3,X1),'tc$uset'('tc$uPropLog$uOpl'(X1))),X1),'tc$uPropLog$uOpl'(X1))
| ~ 'c$uPropLog$uOsat'('c$uemptyset',X0,X1) ),
inference(clausification,[status(esa)],[cls_PropLog_Ocompleteness__0__lemma__dest_0]) ).
cnf(c3,plain,
'c$uminus'(X0,X0,'tc$uset'(X1)) = 'c$uemptyset',
inference(clausification,[status(esa)],[cls_Set_ODiff__cancel_0]) ).
cnf(d0,plain,
( ~ 'c$uPropLog$uOsat'('c$uemptyset',X0,X2)
| 'c$uin'(X0,'c$uPropLog$uOthms'('c$uemptyset',X2),'tc$uPropLog$uOpl'(X2)) ),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d1,plain,
~ 'c$uPropLog$uOsat'('c$uemptyset','v$up','t$ua'),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c0,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 22:32:31 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.14/2.75 % SZS status Unsatisfiable for theBenchmark.p
% 10.14/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------