%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 01:11:16 PM UTC 2026
% Result : Unsatisfiable 4.35s 1.03s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 01:08:22 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 4.35/1.03 % Refutation found
% 4.35/1.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.35/1.03 % SZS output start CNFRefutation for theBenchmark
% 4.35/1.03 fof(f270,axiom,(
% 4.35/1.03 (![V_t,V_k]: (c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f290,axiom,(
% 4.35/1.03 (![V_n]: (~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f321,axiom,(
% 4.35/1.03 (![V_x,V_s]: (( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)| c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x) = c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) ) ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f324,axiom,(
% 4.35/1.03 (![V_t,V_k,V_s]: (c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f327,axiom,(
% 4.35/1.03 (![V_t,V_s,V_n]: (c_Lambda_Osubstn(V_t,V_s,V_n) = c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n) ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f337,axiom,(
% 4.35/1.03 (![V_t,V_s]: (c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f359,axiom,(
% 4.35/1.03 (![V_t,V_u,V_s,V_k]: (c_Lambda_Osubstn(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubstn(V_t,V_s,V_k),c_Lambda_Osubstn(V_u,V_s,V_k)) ))),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f361,axiom,(
% 4.35/1.03 c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) ),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f362,negated_conjecture,(
% 4.35/1.03 ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)) ),
% 4.35/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.35/1.03 fof(f832,plain,(
% 4.35/1.03 ![X0,X1]: (c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1)=X0)),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f270])).
% 4.35/1.03 fof(f860,plain,(
% 4.35/1.03 ![X0]: (~c_HOL_Oord__class_Oless(X0,X0,tc_nat))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f290])).
% 4.35/1.03 fof(f894,plain,(
% 4.35/1.03 ![V_x]: (c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|(![V_s]: c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x)=c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat))))),
% 4.35/1.03 inference(miniscoping,[status(thm)],[f321])).
% 4.35/1.03 fof(f895,plain,(
% 4.35/1.03 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,X0,tc_nat)|c_Lambda_Osubstn(c_Lambda_OdB_OVar(X0),X1,X0)=c_Lambda_Oliftn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f894])).
% 4.35/1.03 fof(f899,plain,(
% 4.35/1.03 ![X0,X1,X2]: (c_Lambda_Osubst(c_Lambda_Olift(X0,X1),X2,X1)=X0)),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f324])).
% 4.35/1.03 fof(f904,plain,(
% 4.35/1.03 ![X0,X1,X2]: (c_Lambda_Osubstn(X0,X1,X2)=c_Lambda_Osubst(X0,c_Lambda_Oliftn(X2,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f327])).
% 4.35/1.03 fof(f917,plain,(
% 4.35/1.03 ![X0,X1]: (c_Lambda_Osubstn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f337])).
% 4.35/1.03 fof(f947,plain,(
% 4.35/1.03 ![X0,X1,X2,X3]: (c_Lambda_Osubstn(c_Lambda_OdB_OApp(X0,X1),X2,X3)=c_Lambda_OdB_OApp(c_Lambda_Osubstn(X0,X2,X3),c_Lambda_Osubstn(X1,X2,X3)))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f359])).
% 4.35/1.03 fof(f949,plain,(
% 4.35/1.03 c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f361])).
% 4.35/1.03 fof(f950,plain,(
% 4.35/1.03 ~c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____))),
% 4.35/1.03 inference(cnf_transformation,[status(thm)],[f362])).
% 4.35/1.03 fof(f988,plain,(
% 4.35/1.03 ![X0,X1]: (c_Lambda_Osubstn(c_Lambda_OdB_OVar(X0),X1,X0)=c_Lambda_Oliftn(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)))),
% 4.35/1.03 inference(forward_subsumption_resolution,[status(thm)],[f895,f860])).
% 4.35/1.03 fof(f991,plain,(
% 4.35/1.05 c_InductTermi_OIT(c_Lambda_Osubstn(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))),
% 4.35/1.05 inference(forward_demodulation,[status(thm)],[f917,f949])).
% 4.35/1.05 fof(f9366,plain,(
% 4.35/1.05 ![X0,X1,X2]: (c_Lambda_Osubstn(c_Lambda_Olift(X0,X1),X2,X1)=X0)),
% 4.35/1.05 inference(paramodulation,[status(thm)],[f899,f904])).
% 4.35/1.05 fof(f9714,plain,(
% 4.35/1.05 ![X0,X1,X2,X3]: (c_Lambda_Osubstn(c_Lambda_OdB_OApp(X0,c_Lambda_Olift(X1,X2)),X3,X2)=c_Lambda_OdB_OApp(c_Lambda_Osubstn(X0,X3,X2),X1))),
% 4.35/1.05 inference(paramodulation,[status(thm)],[f9366,f947])).
% 4.35/1.05 fof(f9783,plain,(
% 4.35/1.05 c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Osubstn(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)),v_ta____))),
% 4.35/1.05 inference(backward_demodulation,[status(thm)],[f9714,f991])).
% 4.35/1.05 fof(f10082,plain,(
% 4.35/1.05 c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)),v_ta____))),
% 4.35/1.05 inference(forward_demodulation,[status(thm)],[f988,f9783])).
% 4.35/1.05 fof(f10083,plain,(
% 4.35/1.05 c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____))),
% 4.35/1.05 inference(forward_demodulation,[status(thm)],[f832,f10082])).
% 4.35/1.05 fof(f10084,plain,(
% 4.35/1.05 $false),
% 4.35/1.05 inference(forward_subsumption_resolution,[status(thm)],[f10083,f950])).
% 4.35/1.05 % SZS output end CNFRefutation for theBenchmark.p
% 4.35/1.05 % Elapsed time: 0.751699 seconds
% 4.35/1.05 % CPU time: 5.658277 seconds
% 4.35/1.05 % Total memory used: 265.530 MB
% 4.35/1.05 % Net memory used: 256.118 MB
%------------------------------------------------------------------------------