%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 92.99s 30.29s
% Output : CNFRefutation 92.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 14 unt; 0 nHn; 5 RR)
% Number of literals : 18 ( 4 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-5 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_foldl__Cons_0,axiom,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uOCons'(X2,X3,X4),X5,X4) = 'c$uList$uOfoldl'(X0,hAPP(hAPP(X0,X1),X2),X3,X5,X4) ).
cnf(cls_substn__subst__0_0,axiom,
'c$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$unat')) ).
cnf(cls_beta_0,axiom,
hBOOL(hAPP(hAPP('c$uLambda$uObeta',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'(X0)),X1)),hAPP(hAPP(hAPP('c$uLambda$uOsubst',X0),X1),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))) ).
cnf(cls_apps__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP('c$uLambda$uObeta',X0),X2))
| hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X0,X1,'tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X2,X1,'tc$uLambda$uOdB','tc$uLambda$uOdB'))) ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'('v$ur')),'v$ua'),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$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$uOdB'))) ).
cnf(c379,plain,
'c$uList$uOfoldl'(X0,hAPP(hAPP(X0,X1),X2),X3,X4,X5) = 'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uOCons'(X2,X3,X5),X4,X5),
inference(clausification,[status(esa)],[cls_foldl__Cons_0]) ).
cnf(c402,plain,
hAPP(hAPP(hAPP('c$uLambda$uOsubst',X0),X1),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')) = 'c$uLambda$uOsubstn'(X0,X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),
inference(clausification,[status(esa)],[cls_substn__subst__0_0]) ).
cnf(c434,plain,
hBOOL(hAPP(hAPP('c$uLambda$uObeta',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'(X0)),X1)),hAPP(hAPP(hAPP('c$uLambda$uOsubst',X0),X1),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))),
inference(clausification,[status(esa)],[cls_beta_0]) ).
cnf(c435,plain,
( ~ hBOOL(hAPP(hAPP('c$uLambda$uObeta',X0),X2))
| hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X0,X1,'tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',X2,X1,'tc$uLambda$uOdB','tc$uLambda$uOdB'))) ),
inference(clausification,[status(esa)],[cls_apps__preserves__beta_0]) ).
cnf(c443,plain,
~ hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'('v$ur')),'v$ua'),'v$uas','tc$uLambda$uOdB','tc$uLambda$uOdB')),'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'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
~ hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'('v$ur'),'c$uList$uOlist$uOCons'('v$ua','v$uas','tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB')),'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'))),
inference(demodulation,[status(thm)],[c443,c379]) ).
cnf(d1,plain,
~ hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'('v$ur'),'c$uList$uOlist$uOCons'('v$ua','v$uas','tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB')),'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'))),
inference(demodulation,[status(thm)],[d0,c402]) ).
cnf(d2,plain,
hBOOL(hAPP(hAPP('c$uLambda$uObeta',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'(X0)),X1)),'c$uLambda$uOsubstn'(X0,X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')))),
inference(demodulation,[status(thm)],[c434,c402]) ).
cnf(d3,plain,
hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'(X0)),X1),X2,'tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'(X0,X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),X2,'tc$uLambda$uOdB','tc$uLambda$uOdB'))),
inference(resolution,[status(thm)],[c435,d2]) ).
cnf(d4,plain,
hBOOL(hAPP(hAPP('c$uLambda$uObeta','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOAbs'(X0),'c$uList$uOlist$uOCons'(X1,X2,'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'(X0,X1,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),X2,'tc$uLambda$uOdB','tc$uLambda$uOdB'))),
inference(demodulation,[status(thm)],[d3,c379]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n009.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 23:41:29 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.99/30.29 % SZS status Unsatisfiable for theBenchmark.p
% 92.99/30.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------