%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 07:55:34 AM UTC 2026
% Result : Unsatisfiable 6.98s 24.69s
% Output : CNFRefutation 6.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 14 unt; 0 nHn; 18 RR)
% Number of literals : 35 ( 2 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-5 aty)
% Number of variables : 21 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_uT_0,axiom,
'c$uType$uOtyping'('v$ue','v$uu','v$uT') ).
cnf(cls_substn__subst__0_0,axiom,
'c$uLambda$uOsubstn'(X0,X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')) = hAPP(hAPP(hAPP('c$uLambda$uOsubst',X0),X1),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')) ).
cnf(cls_SI1_0,axiom,
( ~ 'c$uType$uOtyping'('c$uType$uOshift'(X2,X1,'v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),X3)
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0))
| ~ 'c$uType$uOtyping'(X2,X0,'v$uT')
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),X0),X1))) ) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')) ).
cnf(cls_CHAINED_0_02,axiom,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),'v$uT$uH') ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),'v$uu'),'v$ui'))) ).
cnf(c461,plain,
'c$uType$uOtyping'('v$ue','v$uu','v$uT'),
inference(clausification,[status(esa)],[cls_uT_0]) ).
cnf(c568,plain,
'c$uLambda$uOsubstn'(X0,X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')) = hAPP(hAPP(hAPP('c$uLambda$uOsubst',X0),X1),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),
inference(clausification,[status(esa)],[cls_substn__subst__0_0]) ).
cnf(c581,plain,
( ~ 'c$uType$uOtyping'('c$uType$uOshift'(X2,X1,'v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),X3)
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0))
| ~ 'c$uType$uOtyping'(X2,X0,'v$uT')
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),X0),X1))) ),
inference(clausification,[status(esa)],[cls_SI1_0]) ).
cnf(c589,plain,
hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')),
inference(clausification,[status(esa)],[cls_uIT_0]) ).
cnf(c592,plain,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),'v$uT$uH'),
inference(clausification,[status(esa)],[cls_CHAINED_0_02]) ).
cnf(c593,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),'v$uu'),'v$ui'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$ua','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),'v$uu'),'v$ui'))),
inference(demodulation,[status(thm)],[c593,c568]) ).
cnf(d1,plain,
( ~ 'c$uType$uOtyping'('c$uType$uOshift'(X2,X1,'v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$ua'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),X3)
| ~ 'c$uType$uOtyping'(X2,X0,'v$uT')
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$ua','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),X0),X1)))
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0)) ),
inference(demodulation,[status(thm)],[c581,c568]) ).
cnf(d2,plain,
( ~ 'c$uType$uOtyping'('c$uType$uOshift'(X2,X1,'v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$ua','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),X3)
| ~ 'c$uType$uOtyping'(X2,X0,'v$uT')
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$ua','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),X0),X1)))
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0)) ),
inference(demodulation,[status(thm)],[d1,c568]) ).
cnf(d3,plain,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$ua','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB'),'v$uT$uH'),
inference(demodulation,[status(thm)],[c592,c568]) ).
cnf(d4,plain,
( ~ 'c$uType$uOtyping'('v$ue',X0,'v$uT')
| hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$ua','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),X0),'v$ui')))
| ~ hBOOL(hAPP('c$uInductTermi$uOIT',X0)) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'c$uType$uOtyping'('v$ue','v$uu','v$uT')
| ~ hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')),
inference(resolution,[status(thm)],[c461,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c589,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 23:42:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.98/24.69 % SZS status Unsatisfiable for theBenchmark.p
% 6.98/24.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------