TSTP Solution File: SWW288+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW288+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 20:49:58 EDT 2024
% Result : Theorem 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW288+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 23:17:26 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % Drodi V3.6.0
% 0.20/0.48 % Refutation found
% 0.20/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.48 fof(f5,axiom,(
% 0.20/0.48 (! [V_p,V_a,T_a] :( class_Rings_Oidom(T_a)=> ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)=> c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )& ( V_a != c_Groups_Ozero__class_Ozero(T_a)=> c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)) = c_Polynomial_Odegree(T_a,V_p) ) ) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f7,axiom,(
% 0.20/0.48 (! [V_x] :( ( class_Int_Oring__char__0(t_a)& class_Rings_Oidom(t_a) )=> hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f8,axiom,(
% 0.20/0.48 (! [V_n,V_a,T_a] :( class_Groups_Ozero(T_a)=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)=> c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)) = V_n ) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f14,axiom,(
% 0.20/0.48 ( ( class_Int_Oring__char__0(t_a)& class_Rings_Oidom(t_a) )=> v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ) ),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f17,axiom,(
% 0.20/0.48 (! [V_a,T_a] :( class_Groups_Ozero(T_a)=> c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f27,axiom,(
% 0.20/0.48 (! [V_pa_2,V_a_2,T_b] :( class_Rings_Oidom(T_b)=> ( c_Polynomial_Osmult(T_b,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) ) ) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f30,axiom,(
% 0.20/0.48 (! [V_n_2,V_a_2,T_b] :( class_Groups_Ozero(T_b)=> ( c_Polynomial_Omonom(T_b,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f1012,axiom,(
% 0.20/0.48 (! [T] :( class_Int_Oring__char__0(T)=> class_Groups_Ozero(T) ) )),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f1216,conjecture,(
% 0.20/0.48 c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f1217,negated_conjecture,(
% 0.20/0.48 ~(c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )),
% 0.20/0.48 inference(negated_conjecture,[status(cth)],[f1216])).
% 0.20/0.48 fof(f1218,hypothesis,(
% 0.20/0.48 class_Int_Oring__char__0(t_a) ),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f1219,hypothesis,(
% 0.20/0.48 class_Rings_Oidom(t_a) ),
% 0.20/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.48 fof(f1233,plain,(
% 0.20/0.48 ![V_p,V_a,T_a]: (~class_Rings_Oidom(T_a)|((~V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Polynomial_Odegree(T_a,V_p))))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.20/0.48 fof(f1234,plain,(
% 0.20/0.48 ![T_a]: (~class_Rings_Oidom(T_a)|((![V_a]: (~V_a=c_Groups_Ozero__class_Ozero(T_a)|(![V_p]: c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(![V_a]: (V_a=c_Groups_Ozero__class_Ozero(T_a)|(![V_p]: c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Polynomial_Odegree(T_a,V_p))))))),
% 0.20/0.48 inference(miniscoping,[status(esa)],[f1233])).
% 0.20/0.48 fof(f1235,plain,(
% 0.20/0.48 ![X0,X1,X2]: (~class_Rings_Oidom(X0)|~X1=c_Groups_Ozero__class_Ozero(X0)|c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1234])).
% 0.20/0.48 fof(f1239,plain,(
% 0.20/0.48 ![V_x]: ((~class_Int_Oring__char__0(t_a)|~class_Rings_Oidom(t_a))|hAPP(c_Polynomial_Opoly(t_a,v_p),V_x)=hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.20/0.48 fof(f1240,plain,(
% 0.20/0.48 (~class_Int_Oring__char__0(t_a)|~class_Rings_Oidom(t_a))|(![V_x]: hAPP(c_Polynomial_Opoly(t_a,v_p),V_x)=hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)))),
% 0.20/0.48 inference(miniscoping,[status(esa)],[f1239])).
% 0.20/0.48 fof(f1241,plain,(
% 0.20/0.48 ![X0]: (~class_Int_Oring__char__0(t_a)|~class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1240])).
% 0.20/0.48 fof(f1242,plain,(
% 0.20/0.48 ![V_n,V_a,T_a]: (~class_Groups_Ozero(T_a)|(V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n))=V_n))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.20/0.48 fof(f1243,plain,(
% 0.20/0.48 ![T_a]: (~class_Groups_Ozero(T_a)|(![V_a]: (V_a=c_Groups_Ozero__class_Ozero(T_a)|(![V_n]: c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n))=V_n))))),
% 0.20/0.48 inference(miniscoping,[status(esa)],[f1242])).
% 0.20/0.48 fof(f1244,plain,(
% 0.20/0.48 ![X0,X1,X2]: (~class_Groups_Ozero(X0)|X1=c_Groups_Ozero__class_Ozero(X0)|c_Polynomial_Odegree(X0,c_Polynomial_Omonom(X0,X1,X2))=X2)),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1243])).
% 0.20/0.48 fof(f1251,plain,(
% 0.20/0.48 (~class_Int_Oring__char__0(t_a)|~class_Rings_Oidom(t_a))|v_p=c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.20/0.48 fof(f1252,plain,(
% 0.20/0.48 ~class_Int_Oring__char__0(t_a)|~class_Rings_Oidom(t_a)|v_p=c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1251])).
% 0.20/0.48 fof(f1259,plain,(
% 0.20/0.48 ![V_a,T_a]: (~class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.20/0.48 fof(f1260,plain,(
% 0.20/0.48 ![T_a]: (~class_Groups_Ozero(T_a)|(![V_a]: c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.20/0.48 inference(miniscoping,[status(esa)],[f1259])).
% 0.20/0.48 fof(f1261,plain,(
% 0.20/0.48 ![X0,X1]: (~class_Groups_Ozero(X0)|c_Polynomial_Omonom(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1260])).
% 0.20/0.48 fof(f1302,plain,(
% 0.20/0.48 ![V_pa_2,V_a_2,T_b]: (~class_Rings_Oidom(T_b)|(c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<=>(V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 0.20/0.48 fof(f1303,plain,(
% 0.20/0.48 ![V_pa_2,V_a_2,T_b]: (~class_Rings_Oidom(T_b)|((~c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|(V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))&(c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|(~V_a_2=c_Groups_Ozero__class_Ozero(T_b)&~V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))))),
% 0.20/0.48 inference(NNF_transformation,[status(esa)],[f1302])).
% 0.20/0.48 fof(f1304,plain,(
% 0.20/0.48 ![T_b]: (~class_Rings_Oidom(T_b)|((![V_pa_2,V_a_2]: (~c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|(V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))&(![V_pa_2,V_a_2]: (c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|(~V_a_2=c_Groups_Ozero__class_Ozero(T_b)&~V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))))),
% 0.20/0.48 inference(miniscoping,[status(esa)],[f1303])).
% 0.20/0.48 fof(f1306,plain,(
% 0.20/0.48 ![X0,X1,X2]: (~class_Rings_Oidom(X0)|c_Polynomial_Osmult(X0,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))|~X1=c_Groups_Ozero__class_Ozero(X0))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1304])).
% 0.20/0.48 fof(f1314,plain,(
% 0.20/0.48 ![V_n_2,V_a_2,T_b]: (~class_Groups_Ozero(T_b)|(c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<=>V_a_2=c_Groups_Ozero__class_Ozero(T_b)))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 0.20/0.48 fof(f1315,plain,(
% 0.20/0.48 ![V_n_2,V_a_2,T_b]: (~class_Groups_Ozero(T_b)|((~c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b))&(c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|~V_a_2=c_Groups_Ozero__class_Ozero(T_b))))),
% 0.20/0.48 inference(NNF_transformation,[status(esa)],[f1314])).
% 0.20/0.48 fof(f1316,plain,(
% 0.20/0.48 ![T_b]: (~class_Groups_Ozero(T_b)|((![V_a_2]: ((![V_n_2]: ~c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)))&(![V_a_2]: ((![V_n_2]: c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))|~V_a_2=c_Groups_Ozero__class_Ozero(T_b)))))),
% 0.20/0.48 inference(miniscoping,[status(esa)],[f1315])).
% 0.20/0.48 fof(f1318,plain,(
% 0.20/0.48 ![X0,X1,X2]: (~class_Groups_Ozero(X0)|c_Polynomial_Omonom(X0,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))|~X1=c_Groups_Ozero__class_Ozero(X0))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1316])).
% 0.20/0.48 fof(f4522,plain,(
% 0.20/0.48 ![T]: (~class_Int_Oring__char__0(T)|class_Groups_Ozero(T))),
% 0.20/0.48 inference(pre_NNF_transformation,[status(esa)],[f1012])).
% 0.20/0.48 fof(f4523,plain,(
% 0.20/0.48 ![X0]: (~class_Int_Oring__char__0(X0)|class_Groups_Ozero(X0))),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f4522])).
% 0.20/0.48 fof(f4831,plain,(
% 0.20/0.48 ~c_Polynomial_Odegree(t_a,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1217])).
% 0.20/0.48 fof(f4832,plain,(
% 0.20/0.48 class_Int_Oring__char__0(t_a)),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1218])).
% 0.20/0.48 fof(f4833,plain,(
% 0.20/0.48 class_Rings_Oidom(t_a)),
% 0.20/0.48 inference(cnf_transformation,[status(esa)],[f1219])).
% 0.20/0.48 fof(f4880,plain,(
% 0.20/0.48 spl0_0 <=> class_Int_Oring__char__0(t_a)),
% 0.20/0.48 introduced(split_symbol_definition)).
% 0.20/0.48 fof(f4881,plain,(
% 0.20/0.48 class_Int_Oring__char__0(t_a)|~spl0_0),
% 0.20/0.48 inference(component_clause,[status(thm)],[f4880])).
% 0.20/0.48 fof(f4882,plain,(
% 0.20/0.48 ~class_Int_Oring__char__0(t_a)|spl0_0),
% 0.20/0.48 inference(component_clause,[status(thm)],[f4880])).
% 0.20/0.48 fof(f4883,plain,(
% 0.20/0.48 spl0_1 <=> class_Rings_Oidom(t_a)),
% 0.20/0.48 introduced(split_symbol_definition)).
% 0.20/0.48 fof(f4885,plain,(
% 0.20/0.48 ~class_Rings_Oidom(t_a)|spl0_1),
% 0.20/0.48 inference(component_clause,[status(thm)],[f4883])).
% 0.20/0.48 fof(f4894,plain,(
% 0.20/0.48 spl0_4 <=> hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a))),
% 0.20/0.48 introduced(split_symbol_definition)).
% 0.20/0.48 fof(f4895,plain,(
% 0.20/0.48 ![X0]: (hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a))|~spl0_4)),
% 0.20/0.48 inference(component_clause,[status(thm)],[f4894])).
% 0.20/0.48 fof(f4897,plain,(
% 0.20/0.48 ~spl0_0|~spl0_1|spl0_4),
% 0.20/0.48 inference(split_clause,[status(thm)],[f1241,f4880,f4883,f4894])).
% 0.20/0.48 fof(f4902,plain,(
% 0.20/0.48 spl0_6 <=> v_p=c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 0.20/0.48 introduced(split_symbol_definition)).
% 0.20/0.48 fof(f4903,plain,(
% 0.20/0.48 v_p=c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))|~spl0_6),
% 0.20/0.48 inference(component_clause,[status(thm)],[f4902])).
% 0.20/0.48 fof(f4905,plain,(
% 0.20/0.48 ~spl0_0|~spl0_1|spl0_6),
% 0.20/0.48 inference(split_clause,[status(thm)],[f1252,f4880,f4883,f4902])).
% 0.20/0.48 fof(f4906,plain,(
% 0.20/0.48 ![X0,X1]: (~class_Rings_Oidom(X0)|c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.20/0.48 inference(destructive_equality_resolution,[status(esa)],[f1235])).
% 0.20/0.48 fof(f4909,plain,(
% 0.20/0.48 ![X0,X1]: (~class_Rings_Oidom(X0)|c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 0.20/0.48 inference(destructive_equality_resolution,[status(esa)],[f1306])).
% 0.20/0.48 fof(f4911,plain,(
% 0.20/0.48 ![X0,X1]: (~class_Groups_Ozero(X0)|c_Polynomial_Omonom(X0,c_Groups_Ozero__class_Ozero(X0),X1)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 0.20/0.48 inference(destructive_equality_resolution,[status(esa)],[f1318])).
% 0.20/0.48 fof(f5068,plain,(
% 0.20/0.48 ![X0]: (c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),X0))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.20/0.48 inference(resolution,[status(thm)],[f4906,f4833])).
% 0.20/0.48 fof(f5070,plain,(
% 0.20/0.48 $false|spl0_1),
% 0.20/0.48 inference(forward_subsumption_resolution,[status(thm)],[f4885,f4833])).
% 0.20/0.48 fof(f5071,plain,(
% 0.20/0.48 spl0_1),
% 0.20/0.48 inference(contradiction_clause,[status(thm)],[f5070])).
% 0.20/0.48 fof(f5146,plain,(
% 0.20/0.48 $false|spl0_0),
% 0.20/0.48 inference(forward_subsumption_resolution,[status(thm)],[f4832,f4882])).
% 0.20/0.48 fof(f5147,plain,(
% 0.20/0.48 spl0_0),
% 0.20/0.48 inference(contradiction_clause,[status(thm)],[f5146])).
% 0.20/0.48 fof(f5148,plain,(
% 0.20/0.48 ![X0,X1]: (hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=hAPP(c_Polynomial_Opoly(t_a,v_p),X1)|~spl0_4)),
% 0.20/0.48 inference(paramodulation,[status(thm)],[f4895,f4895])).
% 0.20/0.48 fof(f5167,plain,(
% 0.20/0.48 ![X0]: (v_p=c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))|~spl0_6|~spl0_4)),
% 0.20/0.48 inference(paramodulation,[status(thm)],[f5148,f4903])).
% 0.20/0.48 fof(f5237,plain,(
% 0.20/0.48 ![X0]: (c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),X0)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 0.20/0.48 inference(resolution,[status(thm)],[f4909,f4833])).
% 0.20/0.48 fof(f5238,plain,(
% 0.20/0.48 c_Polynomial_Odegree(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.20/0.48 inference(backward_demodulation,[status(thm)],[f5237,f5068])).
% 0.20/0.48 fof(f5260,plain,(
% 0.20/0.48 class_Groups_Ozero(t_a)|~spl0_0),
% 0.20/0.48 inference(resolution,[status(thm)],[f4523,f4881])).
% 0.20/0.48 fof(f5322,plain,(
% 0.20/0.48 ![X0]: (c_Polynomial_Omonom(t_a,c_Groups_Ozero__class_Ozero(t_a),X0)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_0)),
% 0.20/0.48 inference(resolution,[status(thm)],[f5260,f4911])).
% 0.20/0.48 fof(f5330,plain,(
% 0.20/0.48 ![X0]: (c_Polynomial_Omonom(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))|~spl0_0)),
% 0.20/0.48 inference(resolution,[status(thm)],[f5260,f1261])).
% 0.20/0.48 fof(f5331,plain,(
% 0.20/0.48 ![X0,X1]: (X0=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_Odegree(t_a,c_Polynomial_Omonom(t_a,X0,X1))=X1|~spl0_0)),
% 0.20/0.48 inference(resolution,[status(thm)],[f5260,f1244])).
% 0.20/0.48 fof(f5356,plain,(
% 0.20/0.48 spl0_27 <=> hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=c_Groups_Ozero__class_Ozero(t_a)),
% 0.20/0.48 introduced(split_symbol_definition)).
% 0.20/0.48 fof(f5357,plain,(
% 0.20/0.48 ![X0]: (hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=c_Groups_Ozero__class_Ozero(t_a)|~spl0_27)),
% 0.20/0.48 inference(component_clause,[status(thm)],[f5356])).
% 0.20/0.48 fof(f5386,plain,(
% 0.20/0.48 ![X0]: (v_p=c_Polynomial_Omonom(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_0|~spl0_6|~spl0_4)),
% 0.20/0.48 inference(backward_demodulation,[status(thm)],[f5330,f5167])).
% 0.20/0.48 fof(f5408,plain,(
% 0.20/0.48 spl0_32 <=> c_Polynomial_Odegree(t_a,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.20/0.48 introduced(split_symbol_definition)).
% 0.20/0.48 fof(f5409,plain,(
% 0.20/0.48 c_Polynomial_Odegree(t_a,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_32),
% 0.20/0.48 inference(component_clause,[status(thm)],[f5408])).
% 0.20/0.48 fof(f5411,plain,(
% 0.20/0.48 ![X0]: (hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_Odegree(t_a,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_0|~spl0_6|~spl0_4)),
% 0.20/0.48 inference(paramodulation,[status(thm)],[f5386,f5331])).
% 0.20/0.48 fof(f5412,plain,(
% 0.20/0.48 spl0_27|spl0_32|~spl0_0|~spl0_6|~spl0_4),
% 0.20/0.48 inference(split_clause,[status(thm)],[f5411,f5356,f5408,f4880,f4902,f4894])).
% 0.20/0.48 fof(f5421,plain,(
% 0.20/0.48 $false|~spl0_32),
% 0.20/0.48 inference(forward_subsumption_resolution,[status(thm)],[f5409,f4831])).
% 0.20/0.48 fof(f5422,plain,(
% 0.20/0.48 ~spl0_32),
% 0.20/0.48 inference(contradiction_clause,[status(thm)],[f5421])).
% 0.20/0.48 fof(f5426,plain,(
% 0.20/0.48 ![X0]: (hAPP(c_Polynomial_Opoly(t_a,v_p),X0)=c_Groups_Ozero__class_Ozero(t_a)|~spl0_27|~spl0_4)),
% 0.20/0.49 inference(backward_demodulation,[status(thm)],[f5357,f5148])).
% 0.20/0.49 fof(f5440,plain,(
% 0.20/0.49 v_p=c_Polynomial_Omonom(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_27|~spl0_0|~spl0_6|~spl0_4),
% 0.20/0.49 inference(forward_demodulation,[status(thm)],[f5426,f5386])).
% 0.20/0.49 fof(f5441,plain,(
% 0.20/0.49 v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_27|~spl0_0|~spl0_6|~spl0_4),
% 0.20/0.49 inference(forward_demodulation,[status(thm)],[f5322,f5440])).
% 0.20/0.49 fof(f5451,plain,(
% 0.20/0.49 c_Polynomial_Odegree(t_a,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_27|~spl0_0|~spl0_6|~spl0_4),
% 0.20/0.49 inference(backward_demodulation,[status(thm)],[f5441,f5238])).
% 0.20/0.49 fof(f5452,plain,(
% 0.20/0.49 spl0_32|~spl0_27|~spl0_0|~spl0_6|~spl0_4),
% 0.20/0.49 inference(split_clause,[status(thm)],[f5451,f5408,f5356,f4880,f4902,f4894])).
% 0.20/0.49 fof(f5454,plain,(
% 0.20/0.49 $false),
% 0.20/0.49 inference(sat_refutation,[status(thm)],[f4897,f4905,f5071,f5147,f5412,f5422,f5452])).
% 0.20/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.51 % Elapsed time: 0.163887 seconds
% 0.20/0.51 % CPU time: 0.773331 seconds
% 0.20/0.51 % Total memory used: 163.047 MB
% 0.20/0.51 % Net memory used: 162.343 MB
%------------------------------------------------------------------------------