TSTP Solution File: SWW186+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:44:27 EDT 2023
% Result : Theorem 0.20s 0.46s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 10:57:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.44 % Drodi V3.5.1
% 0.20/0.46 % Refutation found
% 0.20/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.46 fof(f3,axiom,(
% 0.20/0.46 (! [V_h,V_a,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f4,axiom,(
% 0.20/0.46 (! [V_h,V_p,V_a,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) )),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f5,axiom,(
% 0.20/0.46 (! [V_a,V_p,V_c,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))=> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f12,axiom,(
% 0.20/0.46 (! [V_pa_2,V_a_2,T_b] :( class_Groups_Ozero(T_b)=> ( c_Polynomial_OpCons(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)) ) ) ) )),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f1003,axiom,(
% 0.20/0.46 (! [T] :( class_Rings_Ocomm__semiring__0(T)=> class_Groups_Ozero(T) ) )),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f1179,hypothesis,(
% 0.20/0.46 ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f1180,hypothesis,(
% 0.20/0.46 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f1181,conjecture,(
% 0.20/0.46 ( v_a = c_Groups_Ozero__class_Ozero(t_a)& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f1182,negated_conjecture,(
% 0.20/0.46 ~(( v_a = c_Groups_Ozero__class_Ozero(t_a)& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )),
% 0.20/0.46 inference(negated_conjecture,[status(cth)],[f1181])).
% 0.20/0.46 fof(f1183,hypothesis,(
% 0.20/0.46 class_Rings_Ocomm__semiring__0(t_a) ),
% 0.20/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.46 fof(f1190,plain,(
% 0.20/0.46 ![V_h,V_a,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.20/0.46 fof(f1191,plain,(
% 0.20/0.46 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_h,V_a]: c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.20/0.46 inference(miniscoping,[status(esa)],[f1190])).
% 0.20/0.46 fof(f1192,plain,(
% 0.20/0.46 ![X0,X1,X2]: (~class_Rings_Ocomm__semiring__0(X0)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2)=c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f1191])).
% 0.20/0.46 fof(f1193,plain,(
% 0.20/0.46 ![V_h,V_p,V_a,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.20/0.46 fof(f1194,plain,(
% 0.20/0.46 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_h,V_p,V_a]: c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))))),
% 0.20/0.46 inference(miniscoping,[status(esa)],[f1193])).
% 0.20/0.46 fof(f1195,plain,(
% 0.20/0.46 ![X0,X1,X2,X3]: (~class_Rings_Ocomm__semiring__0(X0)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,X2),X3)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X3)),c_Polynomial_OpCons(X0,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X3))))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f1194])).
% 0.20/0.46 fof(f1196,plain,(
% 0.20/0.46 ![V_a,V_p,V_c,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.20/0.46 fof(f1197,plain,(
% 0.20/0.46 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_p]: ((![V_a,V_c]: ~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.20/0.46 inference(miniscoping,[status(esa)],[f1196])).
% 0.20/0.46 fof(f1198,plain,(
% 0.20/0.46 ![X0,X1,X2,X3]: (~class_Rings_Ocomm__semiring__0(X0)|~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X2))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))|X2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f1197])).
% 0.20/0.46 fof(f1219,plain,(
% 0.20/0.46 ![V_pa_2,V_a_2,T_b]: (~class_Groups_Ozero(T_b)|(c_Polynomial_OpCons(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)))))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.20/0.46 fof(f1220,plain,(
% 0.20/0.46 ![V_pa_2,V_a_2,T_b]: (~class_Groups_Ozero(T_b)|((~c_Polynomial_OpCons(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_OpCons(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))))))),
% 0.20/0.46 inference(NNF_transformation,[status(esa)],[f1219])).
% 0.20/0.46 fof(f1221,plain,(
% 0.20/0.46 ![T_b]: (~class_Groups_Ozero(T_b)|((![V_pa_2,V_a_2]: (~c_Polynomial_OpCons(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_OpCons(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)))))))),
% 0.20/0.46 inference(miniscoping,[status(esa)],[f1220])).
% 0.20/0.46 fof(f1222,plain,(
% 0.20/0.46 ![X0,X1,X2]: (~class_Groups_Ozero(X0)|~c_Polynomial_OpCons(X0,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))|X1=c_Groups_Ozero__class_Ozero(X0))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f1221])).
% 0.20/0.46 fof(f4394,plain,(
% 0.20/0.46 ![T]: (~class_Rings_Ocomm__semiring__0(T)|class_Groups_Ozero(T))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f1003])).
% 0.20/0.46 fof(f4395,plain,(
% 0.20/0.46 ![X0]: (~class_Rings_Ocomm__semiring__0(X0)|class_Groups_Ozero(X0))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f4394])).
% 0.20/0.46 fof(f4644,plain,(
% 0.20/0.46 ~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f1179])).
% 0.20/0.46 fof(f4645,plain,(
% 0.20/0.46 ~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f4644])).
% 0.20/0.46 fof(f4646,plain,(
% 0.20/0.46 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f1180])).
% 0.20/0.46 fof(f4647,plain,(
% 0.20/0.46 (~v_a=c_Groups_Ozero__class_Ozero(t_a)|~v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 0.20/0.46 inference(pre_NNF_transformation,[status(esa)],[f1182])).
% 0.20/0.46 fof(f4648,plain,(
% 0.20/0.46 ~v_a=c_Groups_Ozero__class_Ozero(t_a)|~v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f4647])).
% 0.20/0.46 fof(f4649,plain,(
% 0.20/0.46 class_Rings_Ocomm__semiring__0(t_a)),
% 0.20/0.46 inference(cnf_transformation,[status(esa)],[f1183])).
% 0.20/0.46 fof(f4664,plain,(
% 0.20/0.46 spl0_0 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4665,plain,(
% 0.20/0.46 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_0),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4664])).
% 0.20/0.46 fof(f4667,plain,(
% 0.20/0.46 spl0_1 <=> v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4668,plain,(
% 0.20/0.46 v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_1),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4667])).
% 0.20/0.46 fof(f4670,plain,(
% 0.20/0.46 ~spl0_0|spl0_1),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4645,f4664,f4667])).
% 0.20/0.46 fof(f4671,plain,(
% 0.20/0.46 spl0_2 <=> v_a=c_Groups_Ozero__class_Ozero(t_a)),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4674,plain,(
% 0.20/0.46 ~spl0_2|~spl0_1),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4648,f4671,f4667])).
% 0.20/0.46 fof(f4813,plain,(
% 0.20/0.46 spl0_3 <=> class_Rings_Ocomm__semiring__0(t_a)),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4815,plain,(
% 0.20/0.46 ~class_Rings_Ocomm__semiring__0(t_a)|spl0_3),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4813])).
% 0.20/0.46 fof(f4816,plain,(
% 0.20/0.46 spl0_4 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4817,plain,(
% 0.20/0.46 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_4),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4816])).
% 0.20/0.46 fof(f4819,plain,(
% 0.20/0.46 ~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f4646,f1195])).
% 0.20/0.46 fof(f4820,plain,(
% 0.20/0.46 ~spl0_3|spl0_4),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4819,f4813,f4816])).
% 0.20/0.46 fof(f4821,plain,(
% 0.20/0.46 $false|spl0_3),
% 0.20/0.46 inference(forward_subsumption_resolution,[status(thm)],[f4815,f4649])).
% 0.20/0.46 fof(f4822,plain,(
% 0.20/0.46 spl0_3),
% 0.20/0.46 inference(contradiction_clause,[status(thm)],[f4821])).
% 0.20/0.46 fof(f4823,plain,(
% 0.20/0.46 ~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.46 inference(resolution,[status(thm)],[f1198,f4646])).
% 0.20/0.46 fof(f4824,plain,(
% 0.20/0.46 ~spl0_3|spl0_0),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4823,f4813,f4664])).
% 0.20/0.46 fof(f4830,plain,(
% 0.20/0.46 spl0_6 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4831,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_6)),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4830])).
% 0.20/0.46 fof(f4833,plain,(
% 0.20/0.46 ![X0]: (~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_4)),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f4817,f1195])).
% 0.20/0.46 fof(f4834,plain,(
% 0.20/0.46 ~spl0_3|spl0_6|~spl0_4),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4833,f4813,f4830,f4816])).
% 0.20/0.46 fof(f4840,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_4|~spl0_6)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4817,f4831])).
% 0.20/0.46 fof(f4847,plain,(
% 0.20/0.46 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_0),
% 0.20/0.46 inference(backward_demodulation,[status(thm)],[f4665,f4646])).
% 0.20/0.46 fof(f4848,plain,(
% 0.20/0.46 c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_0),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4665,f4847])).
% 0.20/0.46 fof(f4849,plain,(
% 0.20/0.46 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_4|~spl0_6|~spl0_0),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4840,f4848])).
% 0.20/0.46 fof(f4852,plain,(
% 0.20/0.46 spl0_9 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4853,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_9)),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4852])).
% 0.20/0.46 fof(f4855,plain,(
% 0.20/0.46 ![X0]: (~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_0)),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f4665,f1195])).
% 0.20/0.46 fof(f4856,plain,(
% 0.20/0.46 ~spl0_3|spl0_9|~spl0_0),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4855,f4813,f4852,f4664])).
% 0.20/0.46 fof(f4862,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_0|~spl0_9)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4665,f4853])).
% 0.20/0.46 fof(f4863,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)|~spl0_4|~spl0_6|~spl0_0|~spl0_9)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4840,f4862])).
% 0.20/0.46 fof(f4866,plain,(
% 0.20/0.46 spl0_11 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4867,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_11)),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4866])).
% 0.20/0.46 fof(f4869,plain,(
% 0.20/0.46 ![X0]: (~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_4|~spl0_6|~spl0_0)),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f4849,f1195])).
% 0.20/0.46 fof(f4870,plain,(
% 0.20/0.46 ~spl0_3|spl0_11|~spl0_4|~spl0_6|~spl0_0),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4869,f4813,f4866,f4816,f4830,f4664])).
% 0.20/0.46 fof(f4876,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))|~spl0_4|~spl0_6|~spl0_0|~spl0_11)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4849,f4867])).
% 0.20/0.46 fof(f4877,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,v_p)),v_h)|~spl0_4|~spl0_6|~spl0_0|~spl0_11)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4840,f4876])).
% 0.20/0.46 fof(f4899,plain,(
% 0.20/0.46 ![X0]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4863,f4877])).
% 0.20/0.46 fof(f4905,plain,(
% 0.20/0.46 spl0_17 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4906,plain,(
% 0.20/0.46 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)))|~spl0_17)),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4905])).
% 0.20/0.46 fof(f4908,plain,(
% 0.20/0.46 ![X0,X1]: (~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)))|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11)),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f4899,f1195])).
% 0.20/0.46 fof(f4909,plain,(
% 0.20/0.46 ~spl0_3|spl0_17|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11),
% 0.20/0.46 inference(split_clause,[status(thm)],[f4908,f4813,f4905,f4852,f4816,f4830,f4664,f4866])).
% 0.20/0.46 fof(f4911,plain,(
% 0.20/0.46 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,c_Polynomial_OpCons(t_a,v_a,v_p)))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)))|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17)),
% 0.20/0.46 inference(forward_demodulation,[status(thm)],[f4899,f4906])).
% 0.20/0.46 fof(f4981,plain,(
% 0.20/0.46 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)=v_p|~spl0_1|~spl0_4),
% 0.20/0.46 inference(backward_demodulation,[status(thm)],[f4668,f4817])).
% 0.20/0.46 fof(f4982,plain,(
% 0.20/0.46 spl0_26 <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1)=c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 0.20/0.46 introduced(split_symbol_definition)).
% 0.20/0.46 fof(f4983,plain,(
% 0.20/0.46 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1)=c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))|~spl0_26)),
% 0.20/0.46 inference(component_clause,[status(thm)],[f4982])).
% 0.20/0.46 fof(f4985,plain,(
% 0.20/0.46 ![X0,X1]: (~class_Rings_Ocomm__semiring__0(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1)=c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))|~spl0_1)),
% 0.20/0.47 inference(paramodulation,[status(thm)],[f4668,f1192])).
% 0.20/0.47 fof(f4986,plain,(
% 0.20/0.47 ~spl0_3|spl0_26|~spl0_1),
% 0.20/0.47 inference(split_clause,[status(thm)],[f4985,f4813,f4982,f4667])).
% 0.20/0.47 fof(f4992,plain,(
% 0.20/0.47 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1)=c_Polynomial_OpCons(t_a,X0,v_p)|~spl0_1|~spl0_26)),
% 0.20/0.47 inference(forward_demodulation,[status(thm)],[f4668,f4983])).
% 0.20/0.47 fof(f5026,plain,(
% 0.20/0.47 c_Polynomial_OpCons(t_a,v_a,v_p)=v_p|~spl0_26|~spl0_1|~spl0_4),
% 0.20/0.47 inference(backward_demodulation,[status(thm)],[f4992,f4981])).
% 0.20/0.47 fof(f5065,plain,(
% 0.20/0.47 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,c_Polynomial_OpCons(t_a,v_a,v_p))),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)))|~spl0_26|~spl0_1|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17)),
% 0.20/0.47 inference(forward_demodulation,[status(thm)],[f5026,f4911])).
% 0.20/0.47 fof(f5066,plain,(
% 0.20/0.47 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)))|~spl0_26|~spl0_1|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17)),
% 0.20/0.47 inference(forward_demodulation,[status(thm)],[f5026,f5065])).
% 0.20/0.47 fof(f5067,plain,(
% 0.20/0.47 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Polynomial_OpCons(t_a,X1,v_p)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,v_p),v_h)))|~spl0_26|~spl0_1|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17)),
% 0.20/0.47 inference(forward_demodulation,[status(thm)],[f4992,f5066])).
% 0.20/0.47 fof(f5068,plain,(
% 0.20/0.47 ![X0,X1]: (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Polynomial_OpCons(t_a,X1,v_p)),c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)))|~spl0_26|~spl0_1|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17)),
% 0.20/0.47 inference(forward_demodulation,[status(thm)],[f4992,f5067])).
% 0.20/0.47 fof(f5077,plain,(
% 0.20/0.47 spl0_36 <=> ~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Polynomial_OpCons(t_a,X1,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 0.20/0.47 introduced(split_symbol_definition)).
% 0.20/0.47 fof(f5078,plain,(
% 0.20/0.47 ![X0,X1]: (~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Polynomial_OpCons(t_a,X1,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_36)),
% 0.20/0.47 inference(component_clause,[status(thm)],[f5077])).
% 0.20/0.47 fof(f5080,plain,(
% 0.20/0.47 ![X0,X1]: (~class_Rings_Ocomm__semiring__0(t_a)|~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Polynomial_OpCons(t_a,X1,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_26|~spl0_1|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17)),
% 0.63/0.70 inference(paramodulation,[status(thm)],[f5068,f1198])).
% 0.63/0.70 fof(f5081,plain,(
% 0.63/0.70 ~spl0_3|spl0_36|~spl0_26|~spl0_1|~spl0_9|~spl0_4|~spl0_6|~spl0_0|~spl0_11|~spl0_17),
% 0.63/0.70 inference(split_clause,[status(thm)],[f5080,f4813,f5077,f4982,f4667,f4852,f4816,f4830,f4664,f4866,f4905])).
% 0.63/0.70 fof(f5082,plain,(
% 0.63/0.70 ![X0,X1]: (~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=v_p|c_Polynomial_OpCons(t_a,X1,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|~spl0_1|~spl0_36)),
% 0.63/0.70 inference(forward_demodulation,[status(thm)],[f4668,f5078])).
% 0.63/0.70 fof(f5083,plain,(
% 0.63/0.70 ![X0,X1]: (~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Polynomial_OpCons(t_a,X1,v_p)),v_h)=v_p|c_Polynomial_OpCons(t_a,X1,v_p)=v_p|~spl0_1|~spl0_36)),
% 0.63/0.70 inference(forward_demodulation,[status(thm)],[f4668,f5082])).
% 0.63/0.70 fof(f5133,plain,(
% 0.63/0.70 spl0_46 <=> ~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=v_p),
% 0.63/0.70 introduced(split_symbol_definition)).
% 0.63/0.70 fof(f5134,plain,(
% 0.63/0.70 ![X0]: (~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=v_p|~spl0_46)),
% 0.63/0.70 inference(component_clause,[status(thm)],[f5133])).
% 0.63/0.70 fof(f5136,plain,(
% 0.63/0.70 spl0_47 <=> c_Polynomial_OpCons(t_a,v_a,v_p)=v_p),
% 0.63/0.70 introduced(split_symbol_definition)).
% 0.63/0.70 fof(f5137,plain,(
% 0.63/0.70 c_Polynomial_OpCons(t_a,v_a,v_p)=v_p|~spl0_47),
% 0.63/0.70 inference(component_clause,[status(thm)],[f5136])).
% 0.63/0.70 fof(f5139,plain,(
% 0.63/0.70 ![X0]: (~c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),v_h)=v_p|c_Polynomial_OpCons(t_a,v_a,v_p)=v_p|~spl0_36|~spl0_26|~spl0_1|~spl0_4)),
% 0.63/0.70 inference(paramodulation,[status(thm)],[f5026,f5083])).
% 0.63/0.70 fof(f5140,plain,(
% 0.63/0.70 spl0_46|spl0_47|~spl0_36|~spl0_26|~spl0_1|~spl0_4),
% 0.63/0.70 inference(split_clause,[status(thm)],[f5139,f5133,f5136,f5077,f4982,f4667,f4816])).
% 0.63/0.70 fof(f5141,plain,(
% 0.63/0.70 ![X0]: (~c_Polynomial_OpCons(t_a,X0,v_p)=v_p|~spl0_1|~spl0_26|~spl0_46)),
% 0.63/0.70 inference(forward_demodulation,[status(thm)],[f4992,f5134])).
% 0.63/0.70 fof(f5143,plain,(
% 0.63/0.70 $false|~spl0_46|~spl0_26|~spl0_1|~spl0_4),
% 0.63/0.70 inference(backward_subsumption_resolution,[status(thm)],[f5026,f5141])).
% 0.63/0.70 fof(f5144,plain,(
% 0.63/0.70 ~spl0_46|~spl0_26|~spl0_1|~spl0_4),
% 0.63/0.70 inference(contradiction_clause,[status(thm)],[f5143])).
% 0.63/0.70 fof(f5208,plain,(
% 0.63/0.70 spl0_53 <=> class_Groups_Ozero(t_a)),
% 0.63/0.70 introduced(split_symbol_definition)).
% 0.63/0.70 fof(f5210,plain,(
% 0.63/0.70 ~class_Groups_Ozero(t_a)|spl0_53),
% 0.63/0.70 inference(component_clause,[status(thm)],[f5208])).
% 0.63/0.70 fof(f5216,plain,(
% 0.63/0.70 ~class_Groups_Ozero(t_a)|~v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|v_a=c_Groups_Ozero__class_Ozero(t_a)|~spl0_47),
% 0.63/0.70 inference(paramodulation,[status(thm)],[f5137,f1222])).
% 0.63/0.70 fof(f5217,plain,(
% 0.63/0.70 ~spl0_53|~spl0_1|spl0_2|~spl0_47),
% 0.63/0.70 inference(split_clause,[status(thm)],[f5216,f5208,f4667,f4671,f5136])).
% 0.63/0.70 fof(f5540,plain,(
% 0.63/0.70 class_Groups_Ozero(t_a)),
% 0.63/0.70 inference(resolution,[status(thm)],[f4395,f4649])).
% 0.63/0.70 fof(f5541,plain,(
% 0.63/0.70 $false|spl0_53),
% 0.63/0.70 inference(forward_subsumption_resolution,[status(thm)],[f5540,f5210])).
% 0.63/0.70 fof(f5542,plain,(
% 0.63/0.70 spl0_53),
% 0.63/0.70 inference(contradiction_clause,[status(thm)],[f5541])).
% 0.63/0.70 fof(f5543,plain,(
% 0.63/0.70 $false),
% 0.63/0.70 inference(sat_refutation,[status(thm)],[f4670,f4674,f4820,f4822,f4824,f4834,f4856,f4870,f4909,f4986,f5081,f5140,f5144,f5217,f5542])).
% 0.63/0.70 % SZS output end CNFRefutation for theBenchmark.p
% 0.63/0.70 % Elapsed time: 0.136503 seconds
% 0.63/0.70 % CPU time: 0.290171 seconds
% 0.63/0.70 % Memory used: 50.132 MB
%------------------------------------------------------------------------------