%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL429-2 : 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 : n026.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 07:54:34 AM UTC 2026
% Result : Unsatisfiable 14.34s 2.61s
% Output : CNFRefutation 14.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 15 unt; 0 nHn; 13 RR)
% Number of literals : 41 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 71 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_PropLog_ODiff__weaken__left_0,axiom,
( 'c$uin'(X0,'c$uPropLog$uOthms'('c$uminus'(X4,X2,'tc$uset'('tc$uPropLog$uOpl'(X3))),X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$ulessequals'(X1,X4,'tc$uset'('tc$uPropLog$uOpl'(X3)))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uminus'(X1,X2,'tc$uset'('tc$uPropLog$uOpl'(X3))),X3),'tc$uPropLog$uOpl'(X3)) ) ).
cnf(cls_PropLog_Ohyps__Diff_0,axiom,
'c$ulessequals'('c$uPropLog$uOhyps'(X0,'c$uminus'(X1,'c$uinsert'(X2,'c$uemptyset',X3),'tc$uset'(X3)),X3),'c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOvar'(X2,X3),'c$uPropLog$uOpl$uOfalse',X3),'c$uminus'('c$uPropLog$uOhyps'(X0,X1,X3),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X2,X3),'c$uemptyset','tc$uPropLog$uOpl'(X3)),'tc$uset'('tc$uPropLog$uOpl'(X3))),'tc$uPropLog$uOpl'(X3)),'tc$uset'('tc$uPropLog$uOpl'(X3))) ).
cnf(cls_PropLog_Oinsert__Diff__same_0,axiom,
'c$ulessequals'('c$uminus'(X0,X1,'tc$uset'(X2)),'c$uinsert'(X3,'c$uminus'(X0,'c$uinsert'(X3,X1,X2),'tc$uset'(X2)),X2),'tc$uset'(X2)) ).
cnf(cls_PropLog_Oinsert__Diff__subset2_0,axiom,
'c$ulessequals'('c$uminus'('c$uinsert'(X0,'c$uminus'(X1,'c$uinsert'(X2,'c$uemptyset',X3),'tc$uset'(X3)),X3),X4,'tc$uset'(X3)),'c$uinsert'(X0,'c$uminus'(X1,'c$uinsert'(X2,X4,X3),'tc$uset'(X3)),X3),'tc$uset'(X3)) ).
cnf(cls_PropLog_Othms__excluded__middle__rule_0,axiom,
( 'c$uin'(X0,'c$uPropLog$uOthms'(X2,X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X1,'c$uPropLog$uOpl$uOfalse',X3),X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X1,X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3)) ) ).
cnf(cls_PropLog_Oweaken__left_0,axiom,
( 'c$uin'(X0,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$ulessequals'(X1,X3,'tc$uset'('tc$uPropLog$uOpl'(X2)))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)) ) ).
cnf(cls_conjecture_3,negated_conjecture,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'('v$up',X0,'t$ua'),'v$uF','tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ).
cnf(cls_conjecture_5,negated_conjecture,
~ 'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'('v$up','v$ut','t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'('v$uv','t$ua'),'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ).
cnf(c0,plain,
( 'c$uin'(X0,'c$uPropLog$uOthms'('c$uminus'(X4,X2,'tc$uset'('tc$uPropLog$uOpl'(X3))),X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$ulessequals'(X1,X4,'tc$uset'('tc$uPropLog$uOpl'(X3)))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uminus'(X1,X2,'tc$uset'('tc$uPropLog$uOpl'(X3))),X3),'tc$uPropLog$uOpl'(X3)) ),
inference(clausification,[status(esa)],[cls_PropLog_ODiff__weaken__left_0]) ).
cnf(c1,plain,
'c$ulessequals'('c$uPropLog$uOhyps'(X0,'c$uminus'(X1,'c$uinsert'(X2,'c$uemptyset',X3),'tc$uset'(X3)),X3),'c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOvar'(X2,X3),'c$uPropLog$uOpl$uOfalse',X3),'c$uminus'('c$uPropLog$uOhyps'(X0,X1,X3),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X2,X3),'c$uemptyset','tc$uPropLog$uOpl'(X3)),'tc$uset'('tc$uPropLog$uOpl'(X3))),'tc$uPropLog$uOpl'(X3)),'tc$uset'('tc$uPropLog$uOpl'(X3))),
inference(clausification,[status(esa)],[cls_PropLog_Ohyps__Diff_0]) ).
cnf(c2,plain,
'c$ulessequals'('c$uminus'(X0,X1,'tc$uset'(X2)),'c$uinsert'(X3,'c$uminus'(X0,'c$uinsert'(X3,X1,X2),'tc$uset'(X2)),X2),'tc$uset'(X2)),
inference(clausification,[status(esa)],[cls_PropLog_Oinsert__Diff__same_0]) ).
cnf(c3,plain,
'c$ulessequals'('c$uminus'('c$uinsert'(X0,'c$uminus'(X1,'c$uinsert'(X2,'c$uemptyset',X3),'tc$uset'(X3)),X3),X4,'tc$uset'(X3)),'c$uinsert'(X0,'c$uminus'(X1,'c$uinsert'(X2,X4,X3),'tc$uset'(X3)),X3),'tc$uset'(X3)),
inference(clausification,[status(esa)],[cls_PropLog_Oinsert__Diff__subset2_0]) ).
cnf(c4,plain,
( 'c$uin'(X0,'c$uPropLog$uOthms'(X2,X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X1,'c$uPropLog$uOpl$uOfalse',X3),X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X1,X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3)) ),
inference(clausification,[status(esa)],[cls_PropLog_Othms__excluded__middle__rule_0]) ).
cnf(c5,plain,
( 'c$uin'(X0,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$ulessequals'(X1,X3,'tc$uset'('tc$uPropLog$uOpl'(X2)))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)) ),
inference(clausification,[status(esa)],[cls_PropLog_Oweaken__left_0]) ).
cnf(c6,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'('v$up',X0,'t$ua'),'v$uF','tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c7,plain,
~ 'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'('v$up','v$ut','t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'('v$uv','t$ua'),'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(d0,plain,
( ~ 'c$ulessequals'('c$uPropLog$uOhyps'('v$up',X1,'t$ua'),X0,'tc$uset'('tc$uPropLog$uOpl'('t$ua')))
| 'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'(X0,'v$uF','tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ),
inference(resolution,[status(thm)],[c0,c6]) ).
cnf(d1,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOvar'(X0,'t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uminus'('c$uPropLog$uOhyps'('v$up',X1,'t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X0,'t$ua'),'c$uemptyset','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'tc$uPropLog$uOpl'('t$ua')),'v$uF','tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('c$uminus'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOvar'(X1,'t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uminus'('c$uPropLog$uOhyps'('v$up',X2,'t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X1,'t$ua'),'c$uemptyset','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'tc$uPropLog$uOpl'('t$ua')),'v$uF','tc$uset'('tc$uPropLog$uOpl'('t$ua'))),X0,'tc$uset'('tc$uPropLog$uOpl'('t$ua')))
| 'c$uin'('v$up','c$uPropLog$uOthms'(X0,'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOvar'(X0,'t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uminus'('c$uPropLog$uOhyps'('v$up',X1,'t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X0,'t$ua'),'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ 'c$uin'('v$up','c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOvar'(X1,'t$ua'),'c$uminus'('c$uPropLog$uOhyps'('v$up',X0,'t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X1,'t$ua'),'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua'))
| 'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'('v$up',X0,'t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X1,'t$ua'),'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( ~ 'c$ulessequals'('c$uminus'('c$uPropLog$uOhyps'('v$up',X1,'t$ua'),'v$uF','tc$uset'('tc$uPropLog$uOpl'('t$ua'))),X0,'tc$uset'('tc$uPropLog$uOpl'('t$ua')))
| 'c$uin'('v$up','c$uPropLog$uOthms'(X0,'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ),
inference(resolution,[status(thm)],[c5,c6]) ).
cnf(d6,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uinsert'(X0,'c$uminus'('c$uPropLog$uOhyps'('v$up',X1,'t$ua'),'c$uinsert'(X0,'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uminus'('c$uPropLog$uOhyps'('v$up',X0,'t$ua'),'c$uinsert'('c$uPropLog$uOpl$uOvar'(X1,'t$ua'),'v$uF','tc$uPropLog$uOpl'('t$ua')),'tc$uset'('tc$uPropLog$uOpl'('t$ua'))),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n026.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Fri Sep 25 22:34:55 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.34/2.61 % SZS status Unsatisfiable for theBenchmark.p
% 14.34/2.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------