TSTP Solution File: SWV822-1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV822-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 : Wed May 31 12:44:04 EDT 2023
% Result : Unsatisfiable 11.18s 1.86s
% Output : CNFRefutation 11.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SWV822-1 : TPTP v8.1.2. Released v4.1.0.
% 0.02/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n022.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue May 30 11:39:57 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.14/0.32 % Drodi V3.5.1
% 11.18/1.86 % Refutation found
% 11.18/1.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 11.18/1.86 % SZS output start CNFRefutation for theBenchmark
% 11.18/1.86 fof(f16,axiom,(
% 11.18/1.86 (![V_m,V_n]: (( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f73,axiom,(
% 11.18/1.86 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f93,axiom,(
% 11.18/1.86 (![V_m,V_n]: (( c_lessequals(V_m,V_n,tc_nat)| ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f172,axiom,(
% 11.18/1.86 (![V_m,V_n]: (( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f173,axiom,(
% 11.18/1.86 (![V_m,V_n]: (( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)| V_m = c_HOL_Ozero__class_Ozero(tc_nat)| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f190,axiom,(
% 11.18/1.86 (![V_m,V_n]: (c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f191,axiom,(
% 11.18/1.86 (![V_m,V_n]: (c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f209,axiom,(
% 11.18/1.86 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f288,axiom,(
% 11.18/1.86 (![V_n]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f645,axiom,(
% 11.18/1.86 (![V_m]: (c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f654,axiom,(
% 11.18/1.86 (![V_nat,V_nat_H]: (( c_Suc(V_nat) != c_Suc(V_nat_H)| V_nat = V_nat_H ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f656,axiom,(
% 11.18/1.86 (![V_P,V_s,V_n,V_s1]: (( c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(V_P),tc_Com_Ocom),V_s,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1),V_s1)| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f669,axiom,(
% 11.18/1.86 (![V_m,V_n]: (c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f673,axiom,(
% 11.18/1.86 (![V_pn,V_s0,V_n,V_s1]: (( c_Natural_Oevaln(c_Com_Ocom_OBODY(V_pn),V_s0,c_Suc(V_n),V_s1)| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(V_pn),tc_Com_Ocom),V_s0,V_n,V_s1) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f679,axiom,(
% 11.18/1.86 (![V_n,V_P,V_s,V_s1]: (( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1))| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f691,negated_conjecture,(
% 11.18/1.86 ( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ) ),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f695,negated_conjecture,(
% 11.18/1.86 ( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)| c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb) ) ),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f699,negated_conjecture,(
% 11.18/1.86 ( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)) ) ),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f700,negated_conjecture,(
% 11.18/1.86 (![V_Za,V_s_Ha,V_sa,V_Z,V_s_H,V_s]: (( hBOOL(hAPP(hAPP(v_Q,V_Za),V_s_Ha))| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),V_sa,v_n,V_s_Ha)| ~ hBOOL(hAPP(hAPP(v_P,V_Za),V_sa))| hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),V_s,c_Suc(v_n),V_s_H)| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) ) ))),
% 11.18/1.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 11.18/1.86 fof(f755,plain,(
% 11.18/1.86 ![V_n]: ((![V_m]: ~c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)=V_m)|V_n=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(miniscoping,[status(esa)],[f16])).
% 11.18/1.86 fof(f756,plain,(
% 11.18/1.86 ![X0,X1]: (~c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)=X0|X1=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f755])).
% 11.18/1.86 fof(f851,plain,(
% 11.18/1.86 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f73])).
% 11.18/1.86 fof(f884,plain,(
% 11.18/1.86 ![X0,X1]: (c_lessequals(X0,X1,tc_nat)|~c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f93])).
% 11.18/1.86 fof(f1005,plain,(
% 11.18/1.86 ![V_m]: ((![V_n]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 11.18/1.86 inference(miniscoping,[status(esa)],[f172])).
% 11.18/1.86 fof(f1006,plain,(
% 11.18/1.86 ![X0,X1]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)|X1=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|X0=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f1005])).
% 11.18/1.86 fof(f1007,plain,(
% 11.18/1.86 ![V_n]: ((![V_m]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)))|V_n=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(miniscoping,[status(esa)],[f173])).
% 11.18/1.86 fof(f1008,plain,(
% 11.18/1.86 ![X0,X1]: (~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)|X0=c_HOL_Ozero__class_Ozero(tc_nat)|X1=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f1007])).
% 11.18/1.86 fof(f1036,plain,(
% 11.18/1.86 ![X0,X1]: (c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f190])).
% 11.18/1.86 fof(f1037,plain,(
% 11.18/1.86 ![X0,X1]: (c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)=c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f191])).
% 11.18/1.86 fof(f1068,plain,(
% 11.18/1.86 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f209])).
% 11.18/1.86 fof(f1196,plain,(
% 11.18/1.86 ![X0]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f288])).
% 11.18/1.86 fof(f1779,plain,(
% 11.18/1.86 ![X0]: (~c_Suc(X0)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f645])).
% 11.18/1.86 fof(f1788,plain,(
% 11.18/1.86 ![X0,X1]: (~c_Suc(X0)=c_Suc(X1)|X0=X1)),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f654])).
% 11.18/1.86 fof(f1790,plain,(
% 11.18/1.86 ![X0,X1,X2,X3]: (c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X0),tc_Com_Ocom),X1,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X0,X2,X1,X3),X3)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,X2,X3))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f656])).
% 11.18/1.86 fof(f1806,plain,(
% 11.18/1.86 ![X0,X1]: (c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)=c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f669])).
% 11.18/1.86 fof(f1810,plain,(
% 11.18/1.86 ![X0,X1,X2,X3]: (c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,c_Suc(X2),X3)|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X0),tc_Com_Ocom),X1,X2,X3))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f673])).
% 11.18/1.86 fof(f1816,plain,(
% 11.18/1.86 ![X0,X1,X2,X3]: (X0=c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X1,X0,X2,X3))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,X0,X3))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f679])).
% 11.18/1.86 fof(f1831,plain,(
% 11.18/1.86 hBOOL(hAPP(hAPP(v_P,v_x),v_xa))|hBOOL(hAPP(hAPP(v_P,v_x),v_xa))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f691])).
% 11.18/1.86 fof(f1835,plain,(
% 11.18/1.86 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)|c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f695])).
% 11.18/1.86 fof(f1839,plain,(
% 11.18/1.86 ~hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|~hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f699])).
% 11.18/1.86 fof(f1840,plain,(
% 11.18/1.86 ![V_Z,V_s]: ((![V_s_H]: (((![V_Za,V_sa]: ((![V_s_Ha]: (hBOOL(hAPP(hAPP(v_Q,V_Za),V_s_Ha))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),V_sa,v_n,V_s_Ha)))|~hBOOL(hAPP(hAPP(v_P,V_Za),V_sa))))|hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H)))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),V_s,c_Suc(v_n),V_s_H)))|~hBOOL(hAPP(hAPP(v_P,V_Z),V_s)))),
% 11.18/1.86 inference(miniscoping,[status(esa)],[f700])).
% 11.18/1.86 fof(f1841,plain,(
% 11.18/1.86 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X2,v_n,X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))|hBOOL(hAPP(hAPP(v_Q,X3),X4))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X5,c_Suc(v_n),X4)|~hBOOL(hAPP(hAPP(v_P,X3),X5)))),
% 11.18/1.86 inference(cnf_transformation,[status(esa)],[f1840])).
% 11.18/1.86 fof(f1869,plain,(
% 11.18/1.86 spl0_0 <=> hBOOL(hAPP(hAPP(v_P,v_x),v_xa))),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f1870,plain,(
% 11.18/1.86 hBOOL(hAPP(hAPP(v_P,v_x),v_xa))|~spl0_0),
% 11.18/1.86 inference(component_clause,[status(thm)],[f1869])).
% 11.18/1.86 fof(f1872,plain,(
% 11.18/1.86 spl0_0),
% 11.18/1.86 inference(split_clause,[status(thm)],[f1831,f1869])).
% 11.18/1.86 fof(f1873,plain,(
% 11.18/1.86 spl0_1 <=> c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f1874,plain,(
% 11.18/1.86 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)|~spl0_1),
% 11.18/1.86 inference(component_clause,[status(thm)],[f1873])).
% 11.18/1.86 fof(f1877,plain,(
% 11.18/1.86 spl0_2 <=> hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f1879,plain,(
% 11.18/1.86 ~hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|spl0_2),
% 11.18/1.86 inference(component_clause,[status(thm)],[f1877])).
% 11.18/1.86 fof(f1881,plain,(
% 11.18/1.86 spl0_3 <=> c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f1882,plain,(
% 11.18/1.86 c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)|~spl0_3),
% 11.18/1.86 inference(component_clause,[status(thm)],[f1881])).
% 11.18/1.86 fof(f1885,plain,(
% 11.18/1.86 spl0_1|spl0_3),
% 11.18/1.86 inference(split_clause,[status(thm)],[f1835,f1873,f1881])).
% 11.18/1.86 fof(f1889,plain,(
% 11.18/1.86 ~spl0_2),
% 11.18/1.86 inference(split_clause,[status(thm)],[f1839,f1877])).
% 11.18/1.86 fof(f1890,plain,(
% 11.18/1.86 spl0_4 <=> hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X2,v_n,X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f1891,plain,(
% 11.18/1.86 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),X2,v_n,X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))|~spl0_4)),
% 11.18/1.86 inference(component_clause,[status(thm)],[f1890])).
% 11.18/1.86 fof(f1893,plain,(
% 11.18/1.86 spl0_5 <=> hBOOL(hAPP(hAPP(v_Q,X3),X4))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X5,c_Suc(v_n),X4)|~hBOOL(hAPP(hAPP(v_P,X3),X5))),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f1894,plain,(
% 11.18/1.86 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(v_Q,X0),X1))|~c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X2,c_Suc(v_n),X1)|~hBOOL(hAPP(hAPP(v_P,X0),X2))|~spl0_5)),
% 11.18/1.86 inference(component_clause,[status(thm)],[f1893])).
% 11.18/1.86 fof(f1896,plain,(
% 11.18/1.86 spl0_4|spl0_5),
% 11.18/1.86 inference(split_clause,[status(thm)],[f1841,f1890,f1893])).
% 11.18/1.86 fof(f1966,plain,(
% 11.18/1.86 ![X0]: (c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),
% 11.18/1.86 inference(resolution,[status(thm)],[f884,f1196])).
% 11.18/1.86 fof(f3336,plain,(
% 11.18/1.86 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(forward_demodulation,[status(thm)],[f1806,f851])).
% 11.18/1.86 fof(f3543,plain,(
% 11.18/1.86 spl0_22 <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f3544,plain,(
% 11.18/1.86 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|~spl0_22),
% 11.18/1.86 inference(component_clause,[status(thm)],[f3543])).
% 11.18/1.86 fof(f5368,plain,(
% 11.18/1.86 spl0_31 <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f5371,plain,(
% 11.18/1.86 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(resolution,[status(thm)],[f1006,f3336])).
% 11.18/1.86 fof(f5372,plain,(
% 11.18/1.86 spl0_31|spl0_22),
% 11.18/1.86 inference(split_clause,[status(thm)],[f5371,f5368,f3543])).
% 11.18/1.86 fof(f5380,plain,(
% 11.18/1.86 spl0_32 <=> c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f5385,plain,(
% 11.18/1.86 ~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(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))=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 inference(paramodulation,[status(thm)],[f3336,f1008])).
% 11.18/1.86 fof(f5386,plain,(
% 11.18/1.86 ~spl0_31|spl0_32|spl0_22),
% 11.18/1.86 inference(split_clause,[status(thm)],[f5385,f5368,f5380,f3543])).
% 11.18/1.86 fof(f5395,plain,(
% 11.18/1.86 $false|~spl0_22),
% 11.18/1.86 inference(forward_subsumption_resolution,[status(thm)],[f3544,f1779])).
% 11.18/1.86 fof(f5396,plain,(
% 11.18/1.86 ~spl0_22),
% 11.18/1.86 inference(contradiction_clause,[status(thm)],[f5395])).
% 11.18/1.86 fof(f5415,plain,(
% 11.18/1.86 ![X0,X1]: (~c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)=X0|c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(paramodulation,[status(thm)],[f1036,f756])).
% 11.18/1.86 fof(f5442,plain,(
% 11.18/1.86 ![X0,X1]: (~c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat)=X1|c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat))),
% 11.18/1.86 inference(paramodulation,[status(thm)],[f1037,f756])).
% 11.18/1.86 fof(f5464,plain,(
% 11.18/1.86 spl0_39 <=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f5466,plain,(
% 11.18/1.86 ~c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)|spl0_39),
% 11.18/1.86 inference(component_clause,[status(thm)],[f5464])).
% 11.18/1.86 fof(f6104,plain,(
% 11.18/1.86 c_Suc(v_n)=c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb))|~spl0_1),
% 11.18/1.86 inference(resolution,[status(thm)],[f1816,f1874])).
% 11.18/1.86 fof(f6511,plain,(
% 11.18/1.86 spl0_200 <=> c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f6514,plain,(
% 11.18/1.86 ~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 inference(paramodulation,[status(thm)],[f1068,f5415])).
% 11.18/1.86 fof(f6515,plain,(
% 11.18/1.86 ~spl0_31|spl0_200),
% 11.18/1.86 inference(split_clause,[status(thm)],[f6514,f5368,f6511])).
% 11.18/1.86 fof(f6520,plain,(
% 11.18/1.86 spl0_201 <=> c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 introduced(split_symbol_definition)).
% 11.18/1.86 fof(f6523,plain,(
% 11.18/1.86 ~c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)),
% 11.18/1.86 inference(paramodulation,[status(thm)],[f1068,f5442])).
% 11.18/1.86 fof(f6524,plain,(
% 11.18/1.86 ~spl0_31|spl0_201),
% 11.18/1.86 inference(split_clause,[status(thm)],[f6523,f5368,f6520])).
% 11.18/1.86 fof(f6911,plain,(
% 11.18/1.86 $false|spl0_39),
% 11.18/1.86 inference(forward_subsumption_resolution,[status(thm)],[f5466,f1966])).
% 11.18/1.86 fof(f6912,plain,(
% 11.18/1.86 spl0_39),
% 11.18/1.86 inference(contradiction_clause,[status(thm)],[f6911])).
% 11.18/1.86 fof(f6978,plain,(
% 11.18/1.86 v_n=c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb)|~spl0_1),
% 11.18/1.86 inference(resolution,[status(thm)],[f6104,f1788])).
% 11.18/1.86 fof(f9064,plain,(
% 11.18/1.86 c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb),v_xb)|~spl0_1),
% 11.18/1.86 inference(resolution,[status(thm)],[f1790,f1874])).
% 11.18/1.88 fof(f9065,plain,(
% 11.18/1.88 c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)|~spl0_1),
% 11.18/1.88 inference(forward_demodulation,[status(thm)],[f6978,f9064])).
% 11.18/1.88 fof(f9689,plain,(
% 11.18/1.88 ![X0]: (hBOOL(hAPP(hAPP(v_Q,X0),v_xb))|~hBOOL(hAPP(hAPP(v_P,X0),v_xa))|~spl0_1|~spl0_4)),
% 11.18/1.88 inference(resolution,[status(thm)],[f9065,f1891])).
% 11.18/1.88 fof(f9796,plain,(
% 11.18/1.88 hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|~spl0_1|~spl0_4|~spl0_0),
% 11.18/1.88 inference(resolution,[status(thm)],[f9689,f1870])).
% 11.18/1.88 fof(f9797,plain,(
% 11.18/1.88 $false|spl0_2|~spl0_1|~spl0_4|~spl0_0),
% 11.18/1.88 inference(forward_subsumption_resolution,[status(thm)],[f9796,f1879])).
% 11.18/1.88 fof(f9798,plain,(
% 11.18/1.88 spl0_2|~spl0_1|~spl0_4|~spl0_0),
% 11.18/1.88 inference(contradiction_clause,[status(thm)],[f9797])).
% 11.18/1.88 fof(f9799,plain,(
% 11.18/1.88 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)|~spl0_3),
% 11.18/1.88 inference(resolution,[status(thm)],[f1882,f1810])).
% 11.18/1.88 fof(f9800,plain,(
% 11.18/1.88 spl0_1|~spl0_3),
% 11.18/1.88 inference(split_clause,[status(thm)],[f9799,f1873,f1881])).
% 11.18/1.88 fof(f9868,plain,(
% 11.18/1.88 ![X0]: (hBOOL(hAPP(hAPP(v_Q,X0),v_xb))|~hBOOL(hAPP(hAPP(v_P,X0),v_xa))|~spl0_5|~spl0_1)),
% 11.18/1.88 inference(resolution,[status(thm)],[f1894,f1874])).
% 11.18/1.88 fof(f9898,plain,(
% 11.18/1.88 hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))|~spl0_5|~spl0_1|~spl0_0),
% 11.18/1.88 inference(resolution,[status(thm)],[f9868,f1870])).
% 11.18/1.88 fof(f9899,plain,(
% 11.18/1.88 $false|spl0_2|~spl0_5|~spl0_1|~spl0_0),
% 11.18/1.88 inference(forward_subsumption_resolution,[status(thm)],[f9898,f1879])).
% 11.18/1.88 fof(f9900,plain,(
% 11.18/1.88 spl0_2|~spl0_5|~spl0_1|~spl0_0),
% 11.18/1.88 inference(contradiction_clause,[status(thm)],[f9899])).
% 11.18/1.88 fof(f9901,plain,(
% 11.18/1.88 $false),
% 11.18/1.88 inference(sat_refutation,[status(thm)],[f1872,f1885,f1889,f1896,f5372,f5386,f5396,f6515,f6524,f6912,f9798,f9800,f9900])).
% 11.18/1.88 % SZS output end CNFRefutation for theBenchmark.p
% 11.18/1.90 % Elapsed time: 1.611285 seconds
% 11.18/1.90 % CPU time: 11.600612 seconds
% 11.18/1.90 % Memory used: 190.314 MB
%------------------------------------------------------------------------------