%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 01:11:05 PM UTC 2026
% Result : Unsatisfiable 0.70s 0.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:06:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.42 % Drodi V4.1.1
% 0.70/0.72 % Refutation found
% 0.70/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.70/0.72 % SZS output start CNFRefutation for theBenchmark
% 0.70/0.72 fof(f737,axiom,(
% 0.70/0.72 (![V_t,V_ts,V_u]: (hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ))),
% 0.70/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.70/0.72 fof(f768,axiom,(
% 0.70/0.72 (![V_r,V_s,V_ss]: (( 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),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| ~ 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)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ))),
% 0.70/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.70/0.72 fof(f801,negated_conjecture,(
% 0.70/0.72 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)))) ),
% 0.70/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.70/0.72 fof(f802,negated_conjecture,(
% 0.70/0.72 hBOOL(hAPP(c_InductTermi_OIT,v_s)) ),
% 0.70/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.70/0.72 fof(f804,negated_conjecture,(
% 0.70/0.72 ~ 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))) ),
% 0.70/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.70/0.72 fof(f1971,plain,(
% 0.70/0.72 ![X0,X1,X2]: (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))),
% 0.70/0.72 inference(cnf_transformation,[status(thm)],[f737])).
% 0.70/0.72 fof(f2022,plain,(
% 0.70/0.72 ![X0,X1,X2]: (hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))|~hBOOL(hAPP(c_InductTermi_OIT,X1))|~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))))),
% 0.70/0.72 inference(cnf_transformation,[status(thm)],[f768])).
% 0.70/0.72 fof(f2061,plain,(
% 0.70/0.72 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))))),
% 0.70/0.72 inference(cnf_transformation,[status(thm)],[f801])).
% 0.70/0.72 fof(f2062,plain,(
% 0.70/0.72 hBOOL(hAPP(c_InductTermi_OIT,v_s))),
% 0.70/0.72 inference(cnf_transformation,[status(thm)],[f802])).
% 0.70/0.72 fof(f2064,plain,(
% 0.70/0.72 ~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)))),
% 0.70/0.72 inference(cnf_transformation,[status(thm)],[f804])).
% 0.70/0.72 fof(f2188,plain,(
% 0.70/0.72 ~hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i))))),
% 0.70/0.72 inference(backward_demodulation,[status(thm)],[f1971,f2064])).
% 0.70/0.72 fof(f2325,plain,(
% 0.70/0.72 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))|~hBOOL(hAPP(c_InductTermi_OIT,X1))|~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))))),
% 0.70/0.73 inference(paramodulation,[status(thm)],[f1971,f2022])).
% 0.70/0.73 fof(f2327,plain,(
% 0.70/0.73 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)))|~hBOOL(hAPP(c_InductTermi_OIT,X1))|~hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))))),
% 0.70/0.73 inference(forward_demodulation,[status(thm)],[f1971,f2325])).
% 0.70/0.73 fof(f3579,plain,(
% 0.70/0.73 ![X0,X1,X2]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),v_s),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)))|~hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2))))),
% 0.70/0.73 inference(resolution,[status(thm)],[f2327,f2062])).
% 0.70/0.73 fof(f3608,plain,(
% 0.70/0.73 ~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))))),
% 0.70/0.73 inference(resolution,[status(thm)],[f3579,f2188])).
% 0.70/0.73 fof(f3616,plain,(
% 0.70/0.73 $false),
% 0.70/0.73 inference(forward_subsumption_resolution,[status(thm)],[f3608,f2061])).
% 0.70/0.73 % SZS output end CNFRefutation for theBenchmark.p
% 0.70/0.74 % Elapsed time: 0.382150 seconds
% 0.70/0.74 % CPU time: 2.382100 seconds
% 0.70/0.74 % Total memory used: 185.335 MB
% 0.70/0.74 % Net memory used: 183.460 MB
%------------------------------------------------------------------------------