%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL784-1 : 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 : n018.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 07:55:25 AM UTC 2026
% Result : Unsatisfiable 25.56s 3.69s
% Output : CNFRefutation 25.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 12 RR)
% Number of literals : 17 ( 9 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 15 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uLambda$uOdB$uOVar'(X0)),X1),X0) = X1 ).
cnf(cls_foldl__Nil_0,axiom,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1 ).
cnf(cls_True_0,axiom,
'v$un' = 'v$ui' ).
cnf(cls_Nil_0,axiom,
'v$urs' = 'c$uList$uOlist$uONil'('tc$uLambda$uOdB') ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('v$un'),'v$urs','tc$uLambda$uOdB','tc$uLambda$uOdB')),'v$uu'),'v$ui'))) ).
cnf(c220,plain,
hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uLambda$uOdB$uOVar'(X0)),X1),X0) = X1,
inference(clausification,[status(esa)],[cls_subst__eq_0]) ).
cnf(c244,plain,
'c$uList$uOfoldl'(X0,X1,'c$uList$uOlist$uONil'(X2),X3,X2) = X1,
inference(clausification,[status(esa)],[cls_foldl__Nil_0]) ).
cnf(c247,plain,
'v$un' = 'v$ui',
inference(clausification,[status(esa)],[cls_True_0]) ).
cnf(c273,plain,
'v$urs' = 'c$uList$uOlist$uONil'('tc$uLambda$uOdB'),
inference(clausification,[status(esa)],[cls_Nil_0]) ).
cnf(c282,plain,
hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')),
inference(clausification,[status(esa)],[cls_uIT_0]) ).
cnf(c296,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOdB$uOVar'('v$un'),'v$urs','tc$uLambda$uOdB','tc$uLambda$uOdB')),'v$uu'),'v$ui'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
'c$uList$uOfoldl'(X0,X1,'v$urs',X2,'tc$uLambda$uOdB') = X1,
inference(superposition,[status(thm)],[c273,c244]) ).
cnf(d1,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uLambda$uOdB$uOVar'('v$un')),'v$uu'),'v$ui'))),
inference(demodulation,[status(thm)],[c296,d0]) ).
cnf(d2,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP(hAPP('c$uLambda$uOsubst','c$uLambda$uOdB$uOVar'('v$un')),'v$uu'),'v$un'))),
inference(demodulation,[status(thm)],[d1,c247]) ).
cnf(d3,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT','v$uu')),
inference(demodulation,[status(thm)],[d2,c220]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c282,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 23:35:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.56/3.69 % SZS status Unsatisfiable for theBenchmark.p
% 25.56/3.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------