%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL849-1 : 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 : 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 07:55:36 AM UTC 2026
% Result : Unsatisfiable 163.87s 29.96s
% Output : CNFRefutation 163.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 13 unt; 3 nHn; 10 RR)
% Number of literals : 25 ( 12 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 36 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_not__less__less__Suc__eq_0,axiom,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$unat')
| ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uSuc'(X1),'tc$unat')
| X0 = X1 ) ).
cnf(cls_gr0__conv__Suc_1,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'c$uSuc'(X0),'tc$unat') ).
cnf(cls_nat__less__le_1,axiom,
~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X0,'tc$unat') ).
cnf(cls_foldl__Nil_0,axiom,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1 ).
cnf(cls_foldl__Cons_0,axiom,
'c$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_conjecture_0,negated_conjecture,
'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uOCons'(hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB') != hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))) ).
cnf(c47,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$unat')
| X1 = X0
| ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uSuc'(X1),'tc$unat') ),
inference(clausification,[status(esa)],[cls_not__less__less__Suc__eq_0]) ).
cnf(c136,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'c$uSuc'(X0),'tc$unat'),
inference(clausification,[status(esa)],[cls_gr0__conv__Suc_1]) ).
cnf(c494,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X0,'tc$unat'),
inference(clausification,[status(esa)],[cls_nat__less__le_1]) ).
cnf(c649,plain,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1,
inference(clausification,[status(esa)],[cls_foldl__Nil_0]) ).
cnf(c652,plain,
'c$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(c660,plain,
hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))) != 'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uOCons'(hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uOCons'(X2,'c$uList$uOlist$uONil'(X3),X3),X4,X3) = hAPP(hAPP(X0,X1),X2),
inference(superposition,[status(thm)],[c652,c649]) ).
cnf(d1,plain,
( 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),X0,'tc$unat')
| X0 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(resolution,[status(thm)],[c136,c47]) ).
cnf(d2,plain,
( 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),X0,'tc$unat')
| hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))) != 'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X0),'c$uList$uOlist$uOCons'(hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB') ),
inference(superposition,[status(thm)],[d1,c660]) ).
cnf(d3,plain,
( 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),X0,'tc$unat')
| hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))),hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))) != hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X0)),hAPP(hAPP('c$uLambda$uOlift','v$uta'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'))) ),
inference(demodulation,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat'),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c494,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL849-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 23:43:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 163.87/29.96 % SZS status Unsatisfiable for theBenchmark.p
% 163.87/29.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------