%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL445-2 : 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 : 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 07:54:38 AM UTC 2026
% Result : Unsatisfiable 9.24s 6.59s
% Output : CNFRefutation 9.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 12 unt; 0 nHn; 17 RR)
% Number of literals : 29 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$uin'('v$uq','c$uPropLog$uOthms'('c$uinsert'('v$up','v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('v$uq','c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','c$uPropLog$uOpl$uOfalse','t$ua'),'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$uin'('v$uq','c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) ).
cnf(cls_PropLog_Odeduction_0,axiom,
( 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X1,X0,X3),'c$uPropLog$uOthms'(X2,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_Othms_OMP_0,axiom,
( 'c$uin'(X3,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X3,X2),'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)) ) ).
cnf(cls_PropLog_Othms__excluded__middle_0,axiom,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),'c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,'c$uPropLog$uOpl$uOfalse',X2),X1,X2),X1,X2),X2),'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)) ).
cnf(c0,plain,
'c$uin'('v$uq','c$uPropLog$uOthms'('c$uinsert'('v$up','v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'c$uin'('v$uq','c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','c$uPropLog$uOpl$uOfalse','t$ua'),'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
~ 'c$uin'('v$uq','c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
( 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X1,X0,X3),'c$uPropLog$uOthms'(X2,X3),'tc$uPropLog$uOpl'(X3))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X1,X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3)) ),
inference(clausification,[status(esa)],[cls_PropLog_Odeduction_0]) ).
cnf(c4,plain,
( 'c$uin'(X3,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X3,X2),'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)) ),
inference(clausification,[status(esa)],[cls_PropLog_Othms_OMP_0]) ).
cnf(c5,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),'c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,'c$uPropLog$uOpl$uOfalse',X2),X1,X2),X1,X2),X2),'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),
inference(clausification,[status(esa)],[cls_PropLog_Othms__excluded__middle_0]) ).
cnf(d0,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','c$uPropLog$uOpl$uOfalse','t$ua'),'v$uq','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
( ~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X2,X1),'c$uPropLog$uOthms'(X3,X1),'tc$uPropLog$uOpl'(X1))
| 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,'c$uPropLog$uOpl$uOfalse',X1),X2,X1),X2,X1),'c$uPropLog$uOthms'(X3,X1),'tc$uPropLog$uOpl'(X1)) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d2,plain,
( ~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,'c$uPropLog$uOpl$uOfalse',X2),X1,X2),'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2))
| 'c$uin'(X1,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2))
| ~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( ~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua'))
| 'c$uin'('v$uq','c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
~ 'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n002.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 22:37:11 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.24/6.59 % SZS status Unsatisfiable for theBenchmark.p
% 9.24/6.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------