TSTP Solution File: LCL837-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:28:15 EDT 2024
% Result : Unsatisfiable 7.13s 1.30s
% Output : CNFRefutation 7.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n015.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 20:49:47 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.36 % Drodi V3.6.0
% 7.13/1.30 % Refutation found
% 7.13/1.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.13/1.30 % SZS output start CNFRefutation for theBenchmark
% 7.13/1.30 fof(f13,axiom,(
% 7.13/1.30 (![V_m,V_n]: (( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f74,axiom,(
% 7.13/1.30 (![V_n]: (c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f87,axiom,(
% 7.13/1.30 (![V_i,V_m]: (c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f214,axiom,(
% 7.13/1.30 (![T_a]: (( ~ class_Ring__and__Field_Ozero__neq__one(T_a)| c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f235,axiom,(
% 7.13/1.30 (![V_m,V_n]: (c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f236,axiom,(
% 7.13/1.30 (![V_m,V_n]: (c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f371,axiom,(
% 7.13/1.30 (![V_n,V_m]: (( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f375,axiom,(
% 7.13/1.30 (![V_m,V_n]: (( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f378,axiom,(
% 7.13/1.30 (![V_x]: (c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f380,axiom,(
% 7.13/1.30 (![V_n,V_m]: (( V_n = V_m| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f384,axiom,(
% 7.13/1.30 (![V_m,V_n]: (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f387,axiom,(
% 7.13/1.30 (![V_m,V_n]: (( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)| c_Suc(V_m) = V_n| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f389,axiom,(
% 7.13/1.30 (![V_m,V_n]: (( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f390,axiom,(
% 7.13/1.30 (![V_n,V_m]: (( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f392,axiom,(
% 7.13/1.30 (![V_m,V_n]: (( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f521,axiom,(
% 7.13/1.30 (![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) ) ))),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.30 fof(f541,axiom,(
% 7.13/1.30 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
% 7.13/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f570,axiom,(
% 7.13/1.31 (![V_n]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ))),
% 7.13/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f610,axiom,(
% 7.13/1.31 (![V_nat,V_nat_H]: (( c_Suc(V_nat) != c_Suc(V_nat_H)| V_nat = V_nat_H ) ))),
% 7.13/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f613,axiom,(
% 7.13/1.31 (![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) ))),
% 7.13/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f620,axiom,(
% 7.13/1.31 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____))) ),
% 7.13/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f621,negated_conjecture,(
% 7.13/1.31 ~ 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))) ),
% 7.13/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f639,axiom,(
% 7.13/1.31 class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
% 7.13/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.13/1.31 fof(f679,plain,(
% 7.13/1.31 ![V_m]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)|(![V_n]: ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)))),
% 7.13/1.31 inference(miniscoping,[status(esa)],[f13])).
% 7.13/1.31 fof(f680,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f679])).
% 7.13/1.31 fof(f787,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)=X0)),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f74])).
% 7.13/1.31 fof(f810,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)),tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f87])).
% 7.13/1.31 fof(f1035,plain,(
% 7.13/1.31 ![X0]: (~class_Ring__and__Field_Ozero__neq__one(X0)|~c_HOL_Oone__class_Oone(X0)=c_HOL_Ozero__class_Ozero(X0))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f214])).
% 7.13/1.31 fof(f1068,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f235])).
% 7.13/1.31 fof(f1069,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f236])).
% 7.13/1.31 fof(f1286,plain,(
% 7.13/1.31 ![V_n]: ((![V_m]: (c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)))|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat))),
% 7.13/1.31 inference(miniscoping,[status(esa)],[f371])).
% 7.13/1.31 fof(f1287,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f1286])).
% 7.13/1.31 fof(f1293,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f375])).
% 7.13/1.31 fof(f1297,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f378])).
% 7.13/1.31 fof(f1299,plain,(
% 7.13/1.31 ![X0,X1]: (X0=X1|~c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|c_HOL_Oord__class_Oless(X0,X1,tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f380])).
% 7.13/1.31 fof(f1303,plain,(
% 7.13/1.31 ![X0,X1]: (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Suc(X1))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f384])).
% 7.13/1.31 fof(f1306,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)|c_Suc(X0)=X1|~c_HOL_Oord__class_Oless(X0,X1,tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f387])).
% 7.13/1.31 fof(f1308,plain,(
% 7.13/1.31 ![X0,X1]: (~c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f389])).
% 7.13/1.31 fof(f1309,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|c_HOL_Oord__class_Oless(X1,X0,tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f390])).
% 7.13/1.31 fof(f1311,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f392])).
% 7.13/1.31 fof(f1524,plain,(
% 7.13/1.31 ![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))),
% 7.13/1.31 inference(miniscoping,[status(esa)],[f521])).
% 7.13/1.31 fof(f1525,plain,(
% 7.13/1.31 ![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))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f1524])).
% 7.13/1.31 fof(f1555,plain,(
% 7.13/1.31 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f541])).
% 7.13/1.31 fof(f1598,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f570])).
% 7.13/1.31 fof(f1657,plain,(
% 7.13/1.31 ![X0,X1]: (~c_Suc(X0)=c_Suc(X1)|X0=X1)),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f610])).
% 7.13/1.31 fof(f1660,plain,(
% 7.13/1.31 ![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))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f613])).
% 7.13/1.31 fof(f1668,plain,(
% 7.13/1.31 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____)))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f620])).
% 7.13/1.31 fof(f1669,plain,(
% 7.13/1.31 ~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)))),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f621])).
% 7.13/1.31 fof(f1689,plain,(
% 7.13/1.31 class_Ring__and__Field_Ozero__neq__one(tc_nat)),
% 7.13/1.31 inference(cnf_transformation,[status(esa)],[f639])).
% 7.13/1.31 fof(f1741,plain,(
% 7.13/1.31 ![X0]: (~c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f1308,f1598])).
% 7.13/1.31 fof(f1745,plain,(
% 7.13/1.31 ![X0]: (~c_HOL_Oord__class_Oless(X0,X0,tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f1308,f1297])).
% 7.13/1.31 fof(f1759,plain,(
% 7.13/1.31 ![X0,X1]: (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X0,tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f810,f1308])).
% 7.13/1.31 fof(f1784,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)|c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f1309,f1293])).
% 7.13/1.31 fof(f1839,plain,(
% 7.13/1.31 ![X0,X1]: (X0=X1|c_HOL_Oord__class_Oless(X0,X1,tc_nat)|c_HOL_Oord__class_Oless(X1,X0,tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f1299,f1309])).
% 7.13/1.31 fof(f1981,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X1)),tc_nat)|c_HOL_Oord__class_Oless(X1,X0,tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f1784,f1311])).
% 7.13/1.31 fof(f2113,plain,(
% 7.13/1.31 ![X0,X1]: (~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat))),
% 7.13/1.31 inference(paramodulation,[status(thm)],[f1068,f1759])).
% 7.13/1.31 fof(f2123,plain,(
% 7.13/1.31 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(X0)),c_Suc(X1),tc_nat),tc_nat))),
% 7.13/1.31 inference(resolution,[status(thm)],[f2113,f1981])).
% 7.13/1.31 fof(f2755,plain,(
% 7.13/1.31 ~c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 7.13/1.31 inference(resolution,[status(thm)],[f1035,f1689])).
% 7.13/1.31 fof(f2773,plain,(
% 7.13/1.31 spl0_16 <=> c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),
% 7.13/1.31 introduced(split_symbol_definition)).
% 7.13/1.31 fof(f2775,plain,(
% 7.13/1.31 ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)|spl0_16),
% 7.13/1.31 inference(component_clause,[status(thm)],[f2773])).
% 7.13/1.31 fof(f2778,plain,(
% 7.13/1.31 spl0_17 <=> c_HOL_Oord__class_Oless(X0,X0,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)),
% 7.13/1.31 introduced(split_symbol_definition)).
% 7.13/1.31 fof(f2779,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(X0,X0,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~spl0_17)),
% 7.13/1.31 inference(component_clause,[status(thm)],[f2778])).
% 7.13/1.31 fof(f2781,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(X0,X0,tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat))),
% 7.13/1.31 inference(paramodulation,[status(thm)],[f787,f1287])).
% 7.13/1.31 fof(f2782,plain,(
% 7.13/1.31 spl0_17|~spl0_16),
% 7.13/1.31 inference(split_clause,[status(thm)],[f2781,f2778,f2773])).
% 7.13/1.31 fof(f2794,plain,(
% 7.13/1.31 spl0_20 <=> c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 7.13/1.31 introduced(split_symbol_definition)).
% 7.13/1.31 fof(f2795,plain,(
% 7.13/1.31 c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~spl0_20),
% 7.13/1.31 inference(component_clause,[status(thm)],[f2794])).
% 7.13/1.31 fof(f2921,plain,(
% 7.13/1.31 spl0_32 <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat)),
% 7.13/1.31 introduced(split_symbol_definition)).
% 7.13/1.31 fof(f2922,plain,(
% 7.13/1.31 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat)|~spl0_32),
% 7.13/1.31 inference(component_clause,[status(thm)],[f2921])).
% 7.13/1.31 fof(f2927,plain,(
% 7.13/1.31 spl0_33 <=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),
% 7.13/1.31 introduced(split_symbol_definition)).
% 7.13/1.31 fof(f2928,plain,(
% 7.13/1.31 c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|~spl0_33),
% 7.13/1.31 inference(component_clause,[status(thm)],[f2927])).
% 7.13/1.31 fof(f2930,plain,(
% 7.13/1.31 c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|spl0_16),
% 7.13/1.31 inference(resolution,[status(thm)],[f2775,f1839])).
% 7.13/1.31 fof(f2931,plain,(
% 7.13/1.31 spl0_32|spl0_33|spl0_16),
% 7.13/1.31 inference(split_clause,[status(thm)],[f2930,f2921,f2927,f2773])).
% 7.13/1.31 fof(f2941,plain,(
% 7.13/1.31 ![X0]: (~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)|~spl0_17)),
% 7.13/1.31 inference(forward_subsumption_resolution,[status(thm)],[f2779,f1745])).
% 7.13/1.31 fof(f3036,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Oone__class_Oone(tc_nat),tc_nat)|~spl0_32)),
% 7.13/1.31 inference(paramodulation,[status(thm)],[f2922,f1311])).
% 7.13/1.31 fof(f3037,plain,(
% 7.13/1.31 ![X0]: (~c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Oone__class_Oone(tc_nat),tc_nat)|~spl0_32)),
% 7.13/1.31 inference(forward_subsumption_resolution,[status(thm)],[f3036,f1741])).
% 7.13/1.31 fof(f3053,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|~spl0_32)),
% 7.13/1.31 inference(paramodulation,[status(thm)],[f2922,f1309])).
% 7.13/1.31 fof(f3069,plain,(
% 7.13/1.31 ![X0]: (~c_Suc(X0)=c_HOL_Oone__class_Oone(tc_nat)|X0=c_HOL_Ozero__class_Ozero(tc_nat)|~spl0_32)),
% 7.13/1.31 inference(paramodulation,[status(thm)],[f2922,f1657])).
% 7.13/1.31 fof(f3084,plain,(
% 7.13/1.31 $false|~spl0_17),
% 7.13/1.31 inference(resolution,[status(thm)],[f2941,f2123])).
% 7.13/1.31 fof(f3085,plain,(
% 7.13/1.31 ~spl0_17),
% 7.13/1.31 inference(contradiction_clause,[status(thm)],[f3084])).
% 7.13/1.31 fof(f3124,plain,(
% 7.13/1.31 spl0_38 <=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
% 7.13/1.31 introduced(split_symbol_definition)).
% 7.13/1.31 fof(f3125,plain,(
% 7.13/1.31 c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~spl0_38),
% 7.13/1.31 inference(component_clause,[status(thm)],[f3124])).
% 7.13/1.31 fof(f3127,plain,(
% 7.13/1.31 c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~spl0_33),
% 7.13/1.31 inference(resolution,[status(thm)],[f2928,f1299])).
% 7.13/1.31 fof(f3128,plain,(
% 7.13/1.31 spl0_20|spl0_38|~spl0_33),
% 7.13/1.31 inference(split_clause,[status(thm)],[f3127,f2794,f3124,f2927])).
% 7.13/1.31 fof(f3132,plain,(
% 7.13/1.31 $false|~spl0_20),
% 7.13/1.31 inference(forward_subsumption_resolution,[status(thm)],[f2795,f2755])).
% 7.13/1.31 fof(f3133,plain,(
% 7.13/1.31 ~spl0_20),
% 7.13/1.31 inference(contradiction_clause,[status(thm)],[f3132])).
% 7.13/1.31 fof(f3134,plain,(
% 7.13/1.31 $false|~spl0_38),
% 7.13/1.31 inference(forward_subsumption_resolution,[status(thm)],[f3125,f1741])).
% 7.13/1.31 fof(f3135,plain,(
% 7.13/1.31 ~spl0_38),
% 7.13/1.31 inference(contradiction_clause,[status(thm)],[f3134])).
% 7.13/1.31 fof(f3260,plain,(
% 7.13/1.31 ![X0]: (c_Suc(X0)=c_HOL_Oone__class_Oone(tc_nat)|~c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)|~spl0_32)),
% 7.13/1.31 inference(resolution,[status(thm)],[f3037,f1306])).
% 7.13/1.31 fof(f3595,plain,(
% 7.13/1.31 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|c_Suc(X0)=c_HOL_Oone__class_Oone(tc_nat)|~spl0_32)),
% 7.13/1.31 inference(resolution,[status(thm)],[f3053,f3260])).
% 7.13/1.31 fof(f3629,plain,(
% 7.13/1.31 ![X0,X1]: (c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat))=c_HOL_Oone__class_Oone(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)|~spl0_32)),
% 7.13/1.31 inference(resolution,[status(thm)],[f3595,f680])).
% 7.13/1.31 fof(f4269,plain,(
% 7.13/1.31 c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 7.13/1.31 inference(forward_demodulation,[status(thm)],[f1303,f1555])).
% 7.13/1.31 fof(f4270,plain,(
% 7.13/1.31 c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))=c_HOL_Oone__class_Oone(tc_nat)|~spl0_32),
% 7.13/1.31 inference(forward_demodulation,[status(thm)],[f2922,f4269])).
% 7.13/1.31 fof(f4345,plain,(
% 7.13/1.31 ![X0]: (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))))|~spl0_32)),
% 7.13/1.31 inference(paramodulation,[status(thm)],[f4270,f1303])).
% 7.13/1.31 fof(f5843,plain,(
% 7.13/1.31 ![X0]: (c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))=c_HOL_Oone__class_Oone(tc_nat)|~spl0_32)),
% 7.13/1.33 inference(resolution,[status(thm)],[f3629,f1741])).
% 7.13/1.33 fof(f5854,plain,(
% 7.13/1.33 ![X0]: (c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|~spl0_32)),
% 7.13/1.33 inference(resolution,[status(thm)],[f5843,f3069])).
% 7.13/1.33 fof(f6122,plain,(
% 7.13/1.33 ![X0]: (c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat))|~spl0_32)),
% 7.13/1.33 inference(paramodulation,[status(thm)],[f5854,f1069])).
% 7.13/1.33 fof(f6123,plain,(
% 7.13/1.33 ![X0]: (c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat))|~spl0_32)),
% 7.13/1.33 inference(forward_demodulation,[status(thm)],[f2922,f6122])).
% 7.13/1.33 fof(f6124,plain,(
% 7.13/1.33 ![X0]: (X0=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat))|~spl0_32)),
% 7.13/1.33 inference(forward_demodulation,[status(thm)],[f787,f6123])).
% 7.13/1.33 fof(f6348,plain,(
% 7.13/1.33 ![X0]: (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)))|~spl0_32)),
% 7.13/1.33 inference(forward_demodulation,[status(thm)],[f6124,f4345])).
% 7.13/1.33 fof(f6349,plain,(
% 7.13/1.33 ![X0]: (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))=c_Suc(X0)|~spl0_32)),
% 7.13/1.33 inference(forward_demodulation,[status(thm)],[f6124,f6348])).
% 7.13/1.33 fof(f6352,plain,(
% 7.13/1.33 ![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)|~spl0_32)),
% 7.13/1.33 inference(backward_demodulation,[status(thm)],[f6349,f1525])).
% 7.13/1.33 fof(f6673,plain,(
% 7.13/1.33 ![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)|~spl0_32)),
% 7.13/1.33 inference(resolution,[status(thm)],[f6352,f1598])).
% 7.13/1.33 fof(f11622,plain,(
% 7.13/1.33 ~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____),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)))|~spl0_32),
% 7.13/1.33 inference(backward_demodulation,[status(thm)],[f6673,f1669])).
% 7.13/1.33 fof(f11623,plain,(
% 7.13/1.33 ~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____)))|~spl0_32),
% 7.13/1.33 inference(forward_demodulation,[status(thm)],[f1660,f11622])).
% 7.13/1.33 fof(f11624,plain,(
% 7.13/1.33 $false|~spl0_32),
% 7.13/1.33 inference(forward_subsumption_resolution,[status(thm)],[f11623,f1668])).
% 7.13/1.33 fof(f11625,plain,(
% 7.13/1.33 ~spl0_32),
% 7.13/1.33 inference(contradiction_clause,[status(thm)],[f11624])).
% 7.13/1.33 fof(f11626,plain,(
% 7.13/1.33 $false),
% 7.13/1.33 inference(sat_refutation,[status(thm)],[f2782,f2931,f3085,f3128,f3133,f3135,f11625])).
% 7.13/1.33 % SZS output end CNFRefutation for theBenchmark.p
% 7.13/1.33 % Elapsed time: 1.011759 seconds
% 7.13/1.33 % CPU time: 7.607060 seconds
% 7.13/1.33 % Total memory used: 182.072 MB
% 7.13/1.33 % Net memory used: 179.117 MB
%------------------------------------------------------------------------------