%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL763-1 : 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 : n007.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 07:55:22 AM UTC 2026
% Result : Unsatisfiable 30.33s 7.12s
% Output : CNFRefutation 30.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 4 RR)
% Number of literals : 15 ( 2 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 18 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_listsp_ONil_0,axiom,
'c$uList$uOlistsp'(X0,'c$uList$uOlist$uONil'(X1),X1) ).
cnf(cls_IT_OVar_0,axiom,
( ~ 'c$uList$uOlistsp'('c$uInductTermi$uOIT',X1,'tc$uLambda$uOdB')
| hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X0),X1,'tc$uLambda$uOdB','tc$uLambda$uOdB'))) ) ).
cnf(cls_foldl__Nil_0,axiom,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1 ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('v$un'),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'))) ).
cnf(c197,plain,
'c$uList$uOlistsp'(X0,'c$uList$uOlist$uONil'(X1),X1),
inference(clausification,[status(esa)],[cls_listsp_ONil_0]) ).
cnf(c385,plain,
( ~ 'c$uList$uOlistsp'('c$uInductTermi$uOIT',X1,'tc$uLambda$uOdB')
| hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'(X0),X1,'tc$uLambda$uOdB','tc$uLambda$uOdB'))) ),
inference(clausification,[status(esa)],[cls_IT_OVar_0]) ).
cnf(c395,plain,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1,
inference(clausification,[status(esa)],[cls_foldl__Nil_0]) ).
cnf(c400,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('v$un'),'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB','tc$uLambda$uOdB'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT','c$uLambda$uOdB$uOVar'('v$un'))),
inference(demodulation,[status(thm)],[c400,c395]) ).
cnf(d1,plain,
( ~ 'c$uList$uOlistsp'('c$uInductTermi$uOIT','c$uList$uOlist$uONil'('tc$uLambda$uOdB'),'tc$uLambda$uOdB')
| hBOOL(hAPP('c$uInductTermi$uOIT','c$uLambda$uOdB$uOVar'(X0))) ),
inference(superposition,[status(thm)],[c395,c385]) ).
cnf(d2,plain,
hBOOL(hAPP('c$uInductTermi$uOIT','c$uLambda$uOdB$uOVar'(X0))),
inference(resolution,[status(thm)],[c197,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n007.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 23:28:53 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.33/7.12 % SZS status Unsatisfiable for theBenchmark.p
% 30.33/7.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------