%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL837-1 : 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 01:11:14 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL837-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 01:07:39 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.07/0.32 % Drodi V4.1.1
% 0.07/0.50 % Refutation found
% 0.07/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.50 % SZS output start CNFRefutation for theBenchmark
% 0.07/0.50 fof(f61,axiom,(
% 0.07/0.50 (![V_n]: (c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)) ))),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f521,axiom,(
% 0.07/0.50 (![V_t,V_v,V_i,V_j,V_u]: (( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j)| ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ))),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f570,axiom,(
% 0.07/0.50 (![V_n]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ))),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f580,axiom,(
% 0.07/0.50 (![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)) ))),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f613,axiom,(
% 0.07/0.50 (![V_t,V_ts,V_u,V_i]: (hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ))),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f620,axiom,(
% 0.07/0.50 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____))) ),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f621,negated_conjecture,(
% 0.07/0.50 ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
% 0.07/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.50 fof(f764,plain,(
% 0.07/0.50 ![X0]: (c_Suc(X0)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f61])).
% 0.07/0.50 fof(f1524,plain,(
% 0.07/0.50 ![V_i,V_j]: ((![V_t,V_v,V_u]: hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j))|~c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat))),
% 0.07/0.50 inference(miniscoping,[status(thm)],[f521])).
% 0.07/0.50 fof(f1525,plain,(
% 0.07/0.50 ![X0,X1,X2,X3,X4]: (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X1),X3)),X2)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X4),X2)),X1),X3)|~c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f1524])).
% 0.07/0.50 fof(f1598,plain,(
% 0.07/0.50 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f570])).
% 0.07/0.50 fof(f1611,plain,(
% 0.07/0.50 ![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)))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f580])).
% 0.07/0.50 fof(f1660,plain,(
% 0.07/0.50 ![X0,X1,X2,X3]: (hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X2),X3),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f613])).
% 0.07/0.50 fof(f1668,plain,(
% 0.07/0.50 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____)))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f620])).
% 0.07/0.50 fof(f1669,plain,(
% 0.07/0.50 ~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))),
% 0.07/0.50 inference(cnf_transformation,[status(thm)],[f621])).
% 0.07/0.50 fof(f1737,plain,(
% 0.07/0.50 ![X0,X1,X2,X3,X4]: (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X1),X3)),X2)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X4),X2)),X1),X3)|~c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat))),
% 0.07/0.50 inference(forward_demodulation,[status(thm)],[f764,f1525])).
% 0.07/0.50 fof(f1784,plain,(
% 0.07/0.50 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____)))),
% 0.07/0.50 inference(forward_demodulation,[status(thm)],[f1611,f1668])).
% 0.07/0.50 fof(f1785,plain,(
% 0.07/0.50 ~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____)),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))),
% 0.07/0.50 inference(forward_demodulation,[status(thm)],[f1611,f1669])).
% 0.07/0.50 fof(f2220,plain,(
% 0.07/0.50 ![X0,X1,X2,X3]: (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(c_Lambda_Olift,X1),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X2)),c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X3),c_HOL_Ozero__class_Ozero(tc_nat))),X1),X2))),
% 0.07/0.50 inference(resolution,[status(thm)],[f1737,f1598])).
% 0.07/0.50 fof(f2233,plain,(
% 0.07/0.50 ![X0,X1,X2,X3]: (c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(c_Lambda_Olift,X1),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X2),c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X3),c_HOL_Ozero__class_Ozero(tc_nat))),X1),X2))),
% 0.07/0.50 inference(forward_demodulation,[status(thm)],[f1611,f2220])).
% 0.07/0.50 fof(f2234,plain,(
% 0.07/0.50 ~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat))),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))),
% 0.07/0.50 inference(backward_demodulation,[status(thm)],[f2235,f1785])).
% 0.59/0.51 fof(f2235,plain,(
% 0.59/0.51 ![X0,X1,X2,X3]: (c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),hAPP(hAPP(c_Lambda_Olift,X1),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X2),c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osubstn(X0,X3,c_HOL_Ozero__class_Ozero(tc_nat))),X1),X2))),
% 0.59/0.51 inference(forward_demodulation,[status(thm)],[f1611,f2233])).
% 0.59/0.51 fof(f2236,plain,(
% 0.59/0.51 ~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____)))),
% 0.59/0.51 inference(forward_demodulation,[status(thm)],[f1660,f2234])).
% 0.59/0.51 fof(f2237,plain,(
% 0.59/0.51 $false),
% 0.59/0.51 inference(forward_subsumption_resolution,[status(thm)],[f2236,f1784])).
% 0.59/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.59/0.51 % Elapsed time: 0.203404 seconds
% 0.59/0.51 % CPU time: 1.226393 seconds
% 0.59/0.51 % Total memory used: 160.688 MB
% 0.59/0.51 % Net memory used: 159.099 MB
%------------------------------------------------------------------------------