%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL778-1 : 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 : 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 07:55:24 AM UTC 2026
% Result : Unsatisfiable 30.50s 4.14s
% Output : CNFRefutation 30.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 2 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-5 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_conjecture_1,negated_conjecture,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$us'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$us'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))) ).
cnf(c482,plain,
'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')),
inference(clausification,[status(esa)],[cls_substn__subst__0_0]) ).
cnf(c516,plain,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$us'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c519,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp',hAPP(hAPP(hAPP('c$uLambda$uOsubst','v$ur'),'v$us'),'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(d0,plain,
~ hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))),
inference(demodulation,[status(thm)],[c519,c482]) ).
cnf(d1,plain,
hBOOL(hAPP('c$uInductTermi$uOIT',hAPP(hAPP('c$uLambda$uOdB$uOApp','c$uList$uOfoldl'('c$uLambda$uOdB$uOApp','c$uLambda$uOsubstn'('v$ur','v$us','c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'v$uss','tc$uLambda$uOdB','tc$uLambda$uOdB')),'c$uLambda$uOdB$uOVar'('v$ui')))),
inference(demodulation,[status(thm)],[c516,c482]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[d1,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 23:32:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.50/4.14 % SZS status Unsatisfiable for theBenchmark.p
% 30.50/4.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------