%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL788-1 : 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 : n008.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 07:55:26 AM UTC 2026
% Result : Unsatisfiable 35.79s 4.96s
% Output : CNFRefutation 35.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 20 unt; 0 nHn; 16 RR)
% Number of literals : 34 ( 17 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-5 aty)
% Number of variables : 59 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_foldl__Nil_0,axiom,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1 ).
cnf(cls_var__app__type__eq_0,axiom,
( ~ 'c$uType$uOtyping'(X2,'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X3),X4,'tc$uLambda$uOdB','tc$uLambda$uOdB'),X0)
| ~ 'c$uType$uOtyping'(X2,'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X3),X4,'tc$uLambda$uOdB','tc$uLambda$uOdB'),X1)
| X0 = X1 ) ).
cnf(cls_typing_OVar_0,axiom,
'c$uType$uOtyping'(X0,'c$uLambda$uOdB$uOVar'(X1),hAPP(X0,X1)) ).
cnf(cls_True_0,axiom,
'v$un' = 'v$ui' ).
cnf(cls_shift__eq_0,axiom,
hAPP('c$uType$uOshift'(X0,X1,X2,X3),X1) = X2 ).
cnf(cls_foldr_Osimps_I2_J_0,axiom,
'c$uList$uOfoldr'(X0,'c$uList$uOlist$uOCons'(X1,X2,X3),X4,X3,X5) = hAPP(hAPP(X0,X1),'c$uList$uOfoldr'(X0,X2,X4,X3,X5)) ).
cnf(cls_varT_0,axiom,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uLambda$uOdB$uOVar'('v$un'),hAPP(hAPP('c$uType$uOtype$uOFun','v$uT$uH$uH'),'c$uList$uOfoldr'('c$uType$uOtype$uOFun','v$uTs','v$uT$uH','tc$uType$uOtype','tc$uType$uOtype'))) ).
cnf(cls_conjecture_0,negated_conjecture,
'v$uT' != hAPP(hAPP('c$uType$uOtype$uOFun','v$uT$uH$uH'),'c$uList$uOfoldr'('c$uType$uOtype$uOFun','v$uTs','v$uT$uH','tc$uType$uOtype','tc$uType$uOtype')) ).
cnf(c86,plain,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1,
inference(clausification,[status(esa)],[cls_foldl__Nil_0]) ).
cnf(c164,plain,
( ~ 'c$uType$uOtyping'(X2,'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X3),X4,'tc$uLambda$uOdB','tc$uLambda$uOdB'),X0)
| ~ 'c$uType$uOtyping'(X2,'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X3),X4,'tc$uLambda$uOdB','tc$uLambda$uOdB'),X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[cls_var__app__type__eq_0]) ).
cnf(c183,plain,
'c$uType$uOtyping'(X0,'c$uLambda$uOdB$uOVar'(X1),hAPP(X0,X1)),
inference(clausification,[status(esa)],[cls_typing_OVar_0]) ).
cnf(c194,plain,
'v$un' = 'v$ui',
inference(clausification,[status(esa)],[cls_True_0]) ).
cnf(c195,plain,
hAPP('c$uType$uOshift'(X0,X1,X2,X3),X1) = X2,
inference(clausification,[status(esa)],[cls_shift__eq_0]) ).
cnf(c225,plain,
'c$uList$uOfoldr'(X0,'c$uList$uOlist$uOCons'(X1,X2,X3),X4,X3,X5) = hAPP(hAPP(X0,X1),'c$uList$uOfoldr'(X0,X2,X4,X3,X5)),
inference(clausification,[status(esa)],[cls_foldr_Osimps_I2_J_0]) ).
cnf(c229,plain,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uLambda$uOdB$uOVar'('v$un'),hAPP(hAPP('c$uType$uOtype$uOFun','v$uT$uH$uH'),'c$uList$uOfoldr'('c$uType$uOtype$uOFun','v$uTs','v$uT$uH','tc$uType$uOtype','tc$uType$uOtype'))),
inference(clausification,[status(esa)],[cls_varT_0]) ).
cnf(c239,plain,
'v$uT' != hAPP(hAPP('c$uType$uOtype$uOFun','v$uT$uH$uH'),'c$uList$uOfoldr'('c$uType$uOtype$uOFun','v$uTs','v$uT$uH','tc$uType$uOtype','tc$uType$uOtype')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uLambda$uOdB$uOVar'('v$ui'),hAPP(hAPP('c$uType$uOtype$uOFun','v$uT$uH$uH'),'c$uList$uOfoldr'('c$uType$uOtype$uOFun','v$uTs','v$uT$uH','tc$uType$uOtype','tc$uType$uOtype'))),
inference(demodulation,[status(thm)],[c229,c194]) ).
cnf(d1,plain,
'c$uType$uOtyping'('c$uType$uOshift'('v$ue','v$ui','v$uT','tc$uType$uOtype'),'c$uLambda$uOdB$uOVar'('v$ui'),'c$uList$uOfoldr'('c$uType$uOtype$uOFun','c$uList$uOlist$uOCons'('v$uT$uH$uH','v$uTs','tc$uType$uOtype'),'v$uT$uH','tc$uType$uOtype','tc$uType$uOtype')),
inference(demodulation,[status(thm)],[d0,c225]) ).
cnf(d2,plain,
'c$uType$uOtyping'('c$uType$uOshift'(X0,X1,X2,X3),'c$uLambda$uOdB$uOVar'(X1),X2),
inference(superposition,[status(thm)],[c195,c183]) ).
cnf(d3,plain,
( ~ 'c$uType$uOtyping'(X1,'c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X0),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'),X3)
| X2 = X3
| ~ 'c$uType$uOtyping'(X1,'c$uLambda$uOdB$uOVar'(X0),X2) ),
inference(superposition,[status(thm)],[c86,c164]) ).
cnf(d4,plain,
( ~ 'c$uType$uOtyping'(X3,'c$uLambda$uOdB$uOVar'(X0),X1)
| ~ 'c$uType$uOtyping'(X3,'c$uLambda$uOdB$uOVar'(X0),X2)
| X1 = X2 ),
inference(demodulation,[status(thm)],[d3,c86]) ).
cnf(d5,plain,
( ~ 'c$uType$uOtyping'('c$uType$uOshift'(X2,X3,X0,X4),'c$uLambda$uOdB$uOVar'(X3),X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'v$uT' = 'c$uList$uOfoldr'('c$uType$uOtype$uOFun','c$uList$uOlist$uOCons'('v$uT$uH$uH','v$uTs','tc$uType$uOtype'),'v$uT$uH','tc$uType$uOtype','tc$uType$uOtype'),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
'v$uT' != 'c$uList$uOfoldr'('c$uType$uOtype$uOFun','c$uList$uOlist$uOCons'('v$uT$uH$uH','v$uTs','tc$uType$uOtype'),'v$uT$uH','tc$uType$uOtype','tc$uType$uOtype'),
inference(demodulation,[status(thm)],[c239,c225]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL788-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 23:34:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.79/4.96 % SZS status Unsatisfiable for theBenchmark.p
% 35.79/4.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------