%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL836-1 : 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 : n006.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 01:11:14 PM UTC 2026
% Result : Unsatisfiable 82.01s 26.15s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/15.66 % Computer : n006.cluster.edu
% 0.17/15.66 % Model : x86_64 x86_64
% 0.17/15.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.66 % Memory : 8046.5625MB
% 0.17/15.66 % OS : Linux 6.8.0-71-generic
% 0.17/15.66 % CPULimit : 300
% 0.17/15.66 % WCLimit : 300
% 0.17/15.66 % DateTime : Mon Sep 21 01:07:14 UTC 2026
% 0.17/15.67 % CPUTime :
% 0.22/15.73 % Drodi V4.1.1
% 82.01/26.15 % Refutation found
% 82.01/26.15 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 82.01/26.15 % SZS output start CNFRefutation for theBenchmark
% 82.01/26.15 fof(f462,axiom,(
% 82.01/26.15 c_Type_Otyping(v_e____,v_u____,v_T____) ),
% 82.01/26.15 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 82.01/26.15 fof(f569,axiom,(
% 82.01/26.15 (![V_t,V_s]: (c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ))),
% 82.01/26.15 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 82.01/26.15 fof(f582,axiom,(
% 82.01/26.15 (![V_u,V_i,V_e,V_T_H]: (( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)))| ~ c_Type_Otyping(V_e,V_u,v_T____)| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))| ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H) ) ))),
% 82.01/26.15 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 82.01/26.15 fof(f590,axiom,(
% 82.01/26.15 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
% 82.01/26.15 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 82.01/26.15 fof(f593,axiom,(
% 82.01/26.15 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
% 82.01/26.15 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 82.01/26.15 fof(f594,negated_conjecture,(
% 82.01/26.15 ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
% 82.01/26.15 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 82.01/26.15 fof(f1382,plain,(
% 82.01/26.15 c_Type_Otyping(v_e____,v_u____,v_T____)),
% 82.01/26.15 inference(cnf_transformation,[status(thm)],[f462])).
% 82.01/26.15 fof(f1528,plain,(
% 82.01/26.15 ![X0,X1]: (c_Lambda_Osubstn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
% 82.01/26.15 inference(cnf_transformation,[status(thm)],[f569])).
% 82.01/26.15 fof(f1551,plain,(
% 82.01/26.15 ![V_i,V_e]: ((![V_u]: ((hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)))|~c_Type_Otyping(V_e,V_u,v_T____))|~hBOOL(hAPP(c_InductTermi_OIT,V_u))))|(![V_T_H]: ~c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H)))),
% 82.01/26.15 inference(miniscoping,[status(thm)],[f582])).
% 82.01/26.15 fof(f1552,plain,(
% 82.01/26.15 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1)))|~c_Type_Otyping(X2,X0,v_T____)|~hBOOL(hAPP(c_InductTermi_OIT,X0))|~c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3))),
% 82.01/26.15 inference(cnf_transformation,[status(thm)],[f1551])).
% 82.01/26.15 fof(f1563,plain,(
% 82.01/26.15 hBOOL(hAPP(c_InductTermi_OIT,v_u____))),
% 82.01/26.15 inference(cnf_transformation,[status(thm)],[f590])).
% 82.01/26.15 fof(f1566,plain,(
% 82.01/26.15 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)),
% 82.01/26.15 inference(cnf_transformation,[status(thm)],[f593])).
% 82.01/26.15 fof(f1567,plain,(
% 82.01/26.15 ~hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))),
% 82.01/26.15 inference(cnf_transformation,[status(thm)],[f594])).
% 82.01/26.15 fof(f1625,plain,(
% 82.01/26.15 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1)))|~c_Type_Otyping(X2,X0,v_T____)|~hBOOL(hAPP(c_InductTermi_OIT,X0))|~c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3))),
% 82.01/26.15 inference(forward_demodulation,[status(thm)],[f1528,f1552])).
% 82.01/26.15 fof(f1626,plain,(
% 82.01/26.15 ![X0,X1,X2,X3]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X0),X1)))|~c_Type_Otyping(X2,X0,v_T____)|~hBOOL(hAPP(c_InductTermi_OIT,X0))|~c_Type_Otyping(c_Type_Oshift(X2,X1,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3))),
% 82.01/26.15 inference(forward_demodulation,[status(thm)],[f1528,f1625])).
% 82.01/26.15 fof(f1629,plain,(
% 82.01/26.15 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)),
% 82.01/26.15 inference(forward_demodulation,[status(thm)],[f1528,f1566])).
% 82.01/26.15 fof(f1630,plain,(
% 82.01/26.15 ~hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))),
% 82.01/26.15 inference(forward_demodulation,[status(thm)],[f1528,f1567])).
% 82.01/26.15 fof(f3260,plain,(
% 82.01/26.15 ![X0,X1]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0)))|~hBOOL(hAPP(c_InductTermi_OIT,v_u____))|~c_Type_Otyping(c_Type_Oshift(v_e____,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1))),
% 82.01/26.15 inference(resolution,[status(thm)],[f1382,f1626])).
% 82.01/26.15 fof(f3261,definition,(
% 82.01/26.15 ![X0,X1]: (sQ132_spl <=> (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0)))|~c_Type_Otyping(c_Type_Oshift(v_e____,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1)))),
% 82.01/26.15 introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition])).
% 82.01/26.15 fof(f3262,plain,(
% 82.01/26.15 ![X0,X1]: (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),X0)))|~c_Type_Otyping(c_Type_Oshift(v_e____,X0,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1)|~sQ132_spl)),
% 82.01/26.15 inference(component_clause,[status(thm)],[f3261])).
% 82.01/26.15 fof(f3264,definition,(
% 82.01/26.15 sQ133_spl <=> (hBOOL(hAPP(c_InductTermi_OIT,v_u____)))),
% 82.01/26.15 introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition])).
% 82.01/26.15 fof(f3266,plain,(
% 82.01/26.15 ~hBOOL(hAPP(c_InductTermi_OIT,v_u____))|sQ133_spl),
% 82.01/26.15 inference(component_clause,[status(thm)],[f3264])).
% 82.01/26.15 fof(f3267,plain,(
% 82.01/26.15 sQ132_spl|~sQ133_spl),
% 82.01/26.15 inference(split_clause,[status(thm)],[f3260,f3261,f3264])).
% 82.01/26.15 fof(f3268,plain,(
% 82.01/26.15 $false|sQ133_spl),
% 82.01/26.15 inference(forward_subsumption_resolution,[status(thm)],[f3266,f1563])).
% 82.01/26.15 fof(f3269,plain,(
% 82.01/26.15 sQ133_spl),
% 82.01/26.15 inference(contradiction_clause,[status(thm)],[f3268])).
% 39.26/26.23 fof(f20734,plain,(
% 39.26/26.23 hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))|~sQ132_spl),
% 39.26/26.23 inference(resolution,[status(thm)],[f1629,f3262])).
% 39.26/26.23 fof(f20745,plain,(
% 39.26/26.23 $false|~sQ132_spl),
% 39.26/26.23 inference(forward_subsumption_resolution,[status(thm)],[f20734,f1630])).
% 39.26/26.23 fof(f20746,plain,(
% 39.26/26.23 ~sQ132_spl),
% 39.26/26.23 inference(contradiction_clause,[status(thm)],[f20745])).
% 39.26/26.23 fof(f20747,plain,(
% 39.26/26.23 $false),
% 39.26/26.23 inference(sat_refutation,[status(thm)],[f3267,f3269,f20746])).
% 39.26/26.23 % SZS output end CNFRefutation for theBenchmark.p
% 39.26/26.26 % Elapsed time: 10.576110 seconds
% 39.26/26.26 % CPU time: 82.985536 seconds
% 39.26/26.26 % Total memory used: 658.343 MB
% 39.26/26.26 % Net memory used: 631.458 MB
%------------------------------------------------------------------------------