%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Mon Sep 7 12:14:32 PM UTC 2026
% Result : Unsatisfiable 60.36s 8.08s
% Output : CNFRefutation 60.36s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named cls_conjecture_1ERROR: Could not build tree for root finalERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(800,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(cnf,[status(esa)],[cls_conjecture_1]) ).
cnf(l0,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(instantiation,[status(thm)],[800]) ).
cnf(767,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X0,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X0),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf,[status(esa)],[cls_Beta_0]) ).
cnf(l6,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_s))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(instantiation,[status(thm)],[767]) ).
cnf(803,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf,[status(esa)],[cls_conjecture_4]) ).
cnf(l11,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(instantiation,[status(thm)],[803]) ).
cnf(801,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(cnf,[status(esa)],[cls_conjecture_2]) ).
cnf(l12,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(instantiation,[status(thm)],[801]) ).
cnf(736,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(cnf,[status(esa)],[cls_app__last_0]) ).
cnf(l10,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(instantiation,[status(thm)],[736]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l6,l11,l12,l10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 04:59:23 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.15/0.40 % launching worker at depth: 1
% 0.15/0.40 % launching worker at depth: 3
% 0.15/0.40 % launching worker at depth: 2
% 0.15/0.40 % launching worker at depth: 7
% 0.15/0.40 % launching worker at depth: 5
% 0.15/0.40 % launching worker at depth: 6
% 0.15/0.40 % launching worker at depth: 4
% 0.15/0.40 % launching worker at depth: 8
% 0.15/0.40 % launching worker at depth: 9
% 0.15/0.47 % launching worker at depth: 10
% 60.36/8.08 % SZS status Theorem for theBenchmark
% 60.36/8.08 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------