TSTP Solution File: SWW245+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : Tue Apr 30 20:49:54 EDT 2024
% Result : Theorem 1.14s 0.64s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n022.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 23:11:43 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % Drodi V3.6.0
% 1.14/0.64 % Refutation found
% 1.14/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.14/0.64 % SZS output start CNFRefutation for theBenchmark
% 1.14/0.64 fof(f2,axiom,(
% 1.14/0.64 ( class_Rings_Oidom(t_a)=> ~ (! [B_z] :( B_z != c_Groups_Ozero__class_Ozero(t_a)=> hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z) = c_Groups_Ozero__class_Ozero(t_a) ) )) ),
% 1.14/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.64 fof(f3,axiom,(
% 1.14/0.64 ( class_Rings_Oidom(t_a)=> ~ (! [B_z] :( B_z != c_Groups_Ozero__class_Ozero(t_a)=> hAPP(c_Polynomial_Opoly(t_a,v_p),B_z) = c_Groups_Ozero__class_Ozero(t_a) ) )) ),
% 1.14/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.64 fof(f4,axiom,(
% 1.14/0.64 ( class_Rings_Oidom(t_a)=> ( v_c____ != c_Groups_Ozero__class_Ozero(t_a)=> (? [B_k,B_a] :( B_a != c_Groups_Ozero__class_Ozero(t_a)& (? [B_q] :( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )& (! [B_z] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z)) )) )) )) ) ),
% 1.14/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.64 fof(f5,axiom,(
% 1.14/0.64 ( class_Rings_Oidom(t_a)=> ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)=> (? [B_k,B_a] :( B_a != c_Groups_Ozero__class_Ozero(t_a)& (? [B_q] :( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )& (! [B_z] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z)) )) )) )) ) ),
% 1.14/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.64 fof(f22,axiom,(
% 1.14/0.64 (! [V_q_2,V_pa_2,T_b] :( ( class_Int_Oring__char__0(T_b)& class_Rings_Oidom(T_b) )=> ( c_Polynomial_Opoly(T_b,V_pa_2) = c_Polynomial_Opoly(T_b,V_q_2)<=> V_pa_2 = V_q_2 ) ) )),
% 1.14/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.64 fof(f29,axiom,(
% 1.14/0.64 (! [V_n_2,V_m_2] :( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )| ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)& V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) )),
% 1.14/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.64 fof(f61,axiom,(
% 1.14/0.64 (! [V_n_2,V_m_2,V_k_2] :( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<=> ( V_m_2 = V_n_2| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f62,axiom,(
% 1.14/0.65 (! [V_n_2,V_k_2,V_m_2] :( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)<=> ( V_m_2 = V_n_2| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f70,axiom,(
% 1.14/0.65 (! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f91,axiom,(
% 1.14/0.65 (! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f97,axiom,(
% 1.14/0.65 (! [V_n_2,V_m_2] :( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f98,axiom,(
% 1.14/0.65 (! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f99,axiom,(
% 1.14/0.65 (! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f100,axiom,(
% 1.14/0.65 (! [V_n_2,V_m_2] :( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f101,axiom,(
% 1.14/0.65 (! [V_n,V_m] :( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f102,axiom,(
% 1.14/0.65 (! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f187,axiom,(
% 1.14/0.65 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f188,axiom,(
% 1.14/0.65 (! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f189,axiom,(
% 1.14/0.65 (! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f1067,axiom,(
% 1.14/0.65 class_Int_Oring__char__0(tc_Int_Oint) ),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f1075,axiom,(
% 1.14/0.65 class_Rings_Oidom(tc_Int_Oint) ),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f1160,conjecture,(
% 1.14/0.65 (? [B_k,B_a] :( B_a != c_Groups_Ozero__class_Ozero(t_a)& (? [B_q] :( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )& (! [B_z] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z)) )) )) )),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f1161,negated_conjecture,(
% 1.14/0.65 ~((? [B_k,B_a] :( B_a != c_Groups_Ozero__class_Ozero(t_a)& (? [B_q] :( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )& (! [B_z] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z)) )) )) ))),
% 1.14/0.65 inference(negated_conjecture,[status(cth)],[f1160])).
% 1.14/0.65 fof(f1162,hypothesis,(
% 1.14/0.65 class_Rings_Oidom(t_a) ),
% 1.14/0.65 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.14/0.65 fof(f1166,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(?[B_z]: (~B_z=c_Groups_Ozero__class_Ozero(t_a)&~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=c_Groups_Ozero__class_Ozero(t_a)))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 1.14/0.65 fof(f1167,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(~sk0_1=c_Groups_Ozero__class_Ozero(t_a)&~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_1)=c_Groups_Ozero__class_Ozero(t_a))),
% 1.14/0.65 inference(skolemization,[status(esa)],[f1166])).
% 1.14/0.65 fof(f1168,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~sk0_1=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1167])).
% 1.14/0.65 fof(f1169,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_1)=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1167])).
% 1.14/0.65 fof(f1170,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(?[B_z]: (~B_z=c_Groups_Ozero__class_Ozero(t_a)&~hAPP(c_Polynomial_Opoly(t_a,v_p),B_z)=c_Groups_Ozero__class_Ozero(t_a)))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 1.14/0.65 fof(f1171,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(~sk0_2=c_Groups_Ozero__class_Ozero(t_a)&~hAPP(c_Polynomial_Opoly(t_a,v_p),sk0_2)=c_Groups_Ozero__class_Ozero(t_a))),
% 1.14/0.65 inference(skolemization,[status(esa)],[f1170])).
% 1.14/0.65 fof(f1172,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~sk0_2=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1171])).
% 1.14/0.65 fof(f1173,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~hAPP(c_Polynomial_Opoly(t_a,v_p),sk0_2)=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1171])).
% 1.14/0.65 fof(f1174,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(v_c____=c_Groups_Ozero__class_Ozero(t_a)|(?[B_k,B_a]: (~B_a=c_Groups_Ozero__class_Ozero(t_a)&(?[B_q]: (((~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))&(![B_z]: hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 1.14/0.65 fof(f1175,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(v_c____=c_Groups_Ozero__class_Ozero(t_a)|(?[B_a]: (~B_a=c_Groups_Ozero__class_Ozero(t_a)&(?[B_k,B_q]: (((~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))&(![B_z]: hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1174])).
% 1.14/0.65 fof(f1176,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(v_c____=c_Groups_Ozero__class_Ozero(t_a)|(~sk0_3=c_Groups_Ozero__class_Ozero(t_a)&(((~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))&(![B_z]: hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),sk0_4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_3,sk0_5)),B_z))))))),
% 1.14/0.65 inference(skolemization,[status(esa)],[f1175])).
% 1.14/0.65 fof(f1177,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|v_c____=c_Groups_Ozero__class_Ozero(t_a)|~sk0_3=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1176])).
% 1.14/0.65 fof(f1178,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|v_c____=c_Groups_Ozero__class_Ozero(t_a)|~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1176])).
% 1.14/0.65 fof(f1179,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|v_c____=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1176])).
% 1.14/0.65 fof(f1180,plain,(
% 1.14/0.65 ![X0]: (~class_Rings_Oidom(t_a)|v_c____=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sk0_4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_3,sk0_5)),X0)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1176])).
% 1.14/0.65 fof(f1181,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(~v_c____=c_Groups_Ozero__class_Ozero(t_a)|(?[B_k,B_a]: (~B_a=c_Groups_Ozero__class_Ozero(t_a)&(?[B_q]: (((~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))&(![B_z]: hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 1.14/0.65 fof(f1182,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(~v_c____=c_Groups_Ozero__class_Ozero(t_a)|(?[B_a]: (~B_a=c_Groups_Ozero__class_Ozero(t_a)&(?[B_k,B_q]: (((~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))&(![B_z]: hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1181])).
% 1.14/0.65 fof(f1183,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|(~v_c____=c_Groups_Ozero__class_Ozero(t_a)|(~sk0_6=c_Groups_Ozero__class_Ozero(t_a)&(((~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))&(![B_z]: hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),sk0_7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_6,sk0_8)),B_z))))))),
% 1.14/0.65 inference(skolemization,[status(esa)],[f1182])).
% 1.14/0.65 fof(f1184,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~v_c____=c_Groups_Ozero__class_Ozero(t_a)|~sk0_6=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1183])).
% 1.14/0.65 fof(f1185,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~v_c____=c_Groups_Ozero__class_Ozero(t_a)|~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1183])).
% 1.14/0.65 fof(f1186,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|~v_c____=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1183])).
% 1.14/0.65 fof(f1187,plain,(
% 1.14/0.65 ![X0]: (~class_Rings_Oidom(t_a)|~v_c____=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sk0_7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_6,sk0_8)),X0)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1183])).
% 1.14/0.65 fof(f1246,plain,(
% 1.14/0.65 ![V_q_2,V_pa_2,T_b]: ((~class_Int_Oring__char__0(T_b)|~class_Rings_Oidom(T_b))|(c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)<=>V_pa_2=V_q_2))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f22])).
% 1.14/0.65 fof(f1247,plain,(
% 1.14/0.65 ![V_q_2,V_pa_2,T_b]: ((~class_Int_Oring__char__0(T_b)|~class_Rings_Oidom(T_b))|((~c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)|V_pa_2=V_q_2)&(c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)|~V_pa_2=V_q_2)))),
% 1.14/0.65 inference(NNF_transformation,[status(esa)],[f1246])).
% 1.14/0.65 fof(f1248,plain,(
% 1.14/0.65 ![T_b]: ((~class_Int_Oring__char__0(T_b)|~class_Rings_Oidom(T_b))|((![V_q_2,V_pa_2]: (~c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)|V_pa_2=V_q_2))&(![V_q_2,V_pa_2]: (c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)|~V_pa_2=V_q_2))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1247])).
% 1.14/0.65 fof(f1249,plain,(
% 1.14/0.65 ![X0,X1,X2]: (~class_Int_Oring__char__0(X0)|~class_Rings_Oidom(X0)|~c_Polynomial_Opoly(X0,X1)=c_Polynomial_Opoly(X0,X2)|X1=X2)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1248])).
% 1.14/0.65 fof(f1273,plain,(
% 1.14/0.65 ![V_n_2,V_m_2]: ((~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|((V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|((~V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(~V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 1.14/0.65 inference(NNF_transformation,[status(esa)],[f29])).
% 1.14/0.65 fof(f1274,plain,(
% 1.14/0.65 (![V_n_2,V_m_2]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|((V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&(![V_n_2,V_m_2]: (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|((~V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(~V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1273])).
% 1.14/0.65 fof(f1275,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X0=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1274])).
% 1.14/0.65 fof(f1276,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X0=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1274])).
% 1.14/0.65 fof(f1277,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1274])).
% 1.14/0.65 fof(f1380,plain,(
% 1.14/0.65 ![V_n_2,V_m_2,V_k_2]: ((~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|(V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|(~V_m_2=V_n_2&~V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 1.14/0.65 inference(NNF_transformation,[status(esa)],[f61])).
% 1.14/0.65 fof(f1381,plain,(
% 1.14/0.65 (![V_n_2,V_m_2,V_k_2]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|(V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(![V_n_2,V_m_2,V_k_2]: (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|(~V_m_2=V_n_2&~V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1380])).
% 1.14/0.65 fof(f1382,plain,(
% 1.14/0.65 ![X0,X1,X2]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)|X1=X2|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1381])).
% 1.14/0.65 fof(f1385,plain,(
% 1.14/0.65 ![V_n_2,V_k_2,V_m_2]: ((~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|(V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|(~V_m_2=V_n_2&~V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 1.14/0.65 inference(NNF_transformation,[status(esa)],[f62])).
% 1.14/0.65 fof(f1386,plain,(
% 1.14/0.65 (![V_n_2,V_k_2,V_m_2]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|(V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(![V_n_2,V_k_2,V_m_2]: (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|(~V_m_2=V_n_2&~V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1385])).
% 1.14/0.65 fof(f1389,plain,(
% 1.14/0.65 ![X0,X1,X2]: (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)|~X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1386])).
% 1.14/0.65 fof(f1408,plain,(
% 1.14/0.65 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f70])).
% 1.14/0.65 fof(f1471,plain,(
% 1.14/0.65 ![X0]: (~c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(X0))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f91])).
% 1.14/0.65 fof(f1477,plain,(
% 1.14/0.65 ![V_n_2,V_m_2]: ((~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(~V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 1.14/0.65 inference(NNF_transformation,[status(esa)],[f97])).
% 1.14/0.65 fof(f1478,plain,(
% 1.14/0.65 (![V_n_2,V_m_2]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(![V_n_2,V_m_2]: (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(~V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1477])).
% 1.14/0.65 fof(f1480,plain,(
% 1.14/0.65 ![X0,X1]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1478])).
% 1.14/0.65 fof(f1482,plain,(
% 1.14/0.65 ![X0]: (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)=X0)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f98])).
% 1.14/0.65 fof(f1483,plain,(
% 1.14/0.65 ![X0]: (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X0)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f99])).
% 1.14/0.65 fof(f1484,plain,(
% 1.14/0.65 ![V_n_2,V_m_2]: ((~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 1.14/0.65 inference(NNF_transformation,[status(esa)],[f100])).
% 1.14/0.65 fof(f1485,plain,(
% 1.14/0.65 (![V_n_2,V_m_2]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(![V_n_2,V_m_2]: (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1484])).
% 1.14/0.65 fof(f1486,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1485])).
% 1.14/0.65 fof(f1489,plain,(
% 1.14/0.65 ![V_n,V_m]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f101])).
% 1.14/0.65 fof(f1490,plain,(
% 1.14/0.65 ![V_n]: ((![V_m]: ~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f1489])).
% 1.14/0.65 fof(f1491,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=X0|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1490])).
% 1.14/0.65 fof(f1492,plain,(
% 1.14/0.65 ![X0,X1]: (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Nat_OSuc(X1))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f102])).
% 1.14/0.65 fof(f1753,plain,(
% 1.14/0.65 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f187])).
% 1.14/0.65 fof(f1754,plain,(
% 1.14/0.65 ![X0]: (c_Nat_OSuc(X0)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f188])).
% 1.14/0.65 fof(f1755,plain,(
% 1.14/0.65 ![X0]: (c_Nat_OSuc(X0)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f189])).
% 1.14/0.65 fof(f4470,plain,(
% 1.14/0.65 class_Int_Oring__char__0(tc_Int_Oint)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1067])).
% 1.14/0.65 fof(f4478,plain,(
% 1.14/0.65 class_Rings_Oidom(tc_Int_Oint)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1075])).
% 1.14/0.65 fof(f4612,plain,(
% 1.14/0.65 (![B_k,B_a]: (B_a=c_Groups_Ozero__class_Ozero(t_a)|(![B_q]: (((c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))|(?[B_z]: ~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z)))))))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f1161])).
% 1.14/0.65 fof(f4613,plain,(
% 1.14/0.65 ![B_k,B_q]: (pd0_6(B_q,B_k)=>(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 introduced(predicate_definition,[f4612])).
% 1.14/0.65 fof(f4614,plain,(
% 1.14/0.65 ![B_k,B_a]: (B_a=c_Groups_Ozero__class_Ozero(t_a)|(![B_q]: ((pd0_6(B_q,B_k)|(~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))|(?[B_z]: ~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))),
% 1.14/0.65 inference(formula_renaming,[status(thm)],[f4612,f4613])).
% 1.14/0.65 fof(f4615,plain,(
% 1.14/0.65 ![B_a]: (B_a=c_Groups_Ozero__class_Ozero(t_a)|(![B_k,B_q]: ((pd0_6(B_q,B_k)|(~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))|(?[B_z]: ~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))),
% 1.14/0.65 inference(miniscoping,[status(esa)],[f4614])).
% 1.14/0.65 fof(f4616,plain,(
% 1.14/0.65 ![B_a]: (B_a=c_Groups_Ozero__class_Ozero(t_a)|(![B_k,B_q]: ((pd0_6(B_q,B_k)|(~c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))))|~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_31(B_q,B_k,B_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sk0_31(B_q,B_k,B_a)),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),sk0_31(B_q,B_k,B_a))))))),
% 1.14/0.65 inference(skolemization,[status(esa)],[f4615])).
% 1.14/0.65 fof(f4618,plain,(
% 1.14/0.65 ![X0,X1,X2]: (X0=c_Groups_Ozero__class_Ozero(t_a)|pd0_6(X1,X2)|~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X1))),X2))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_31(X1,X2,X0))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sk0_31(X1,X2,X0)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X0,X1)),sk0_31(X1,X2,X0))))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f4616])).
% 1.14/0.65 fof(f4619,plain,(
% 1.14/0.65 class_Rings_Oidom(t_a)),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f1162])).
% 1.14/0.65 fof(f4650,plain,(
% 1.14/0.65 ![B_k,B_q]: (~pd0_6(B_q,B_k)|(c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))&~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(pre_NNF_transformation,[status(esa)],[f4613])).
% 1.14/0.65 fof(f4651,plain,(
% 1.14/0.65 ![X0,X1]: (~pd0_6(X0,X1)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
% 1.14/0.65 inference(cnf_transformation,[status(esa)],[f4650])).
% 1.14/0.65 fof(f4653,plain,(
% 1.14/0.65 spl0_0 <=> class_Rings_Oidom(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4655,plain,(
% 1.14/0.65 ~class_Rings_Oidom(t_a)|spl0_0),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4653])).
% 1.14/0.65 fof(f4656,plain,(
% 1.14/0.65 spl0_1 <=> sk0_1=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4659,plain,(
% 1.14/0.65 ~spl0_0|~spl0_1),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1168,f4653,f4656])).
% 1.14/0.65 fof(f4660,plain,(
% 1.14/0.65 spl0_2 <=> hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_1)=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4663,plain,(
% 1.14/0.65 ~spl0_0|~spl0_2),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1169,f4653,f4660])).
% 1.14/0.65 fof(f4664,plain,(
% 1.14/0.65 spl0_3 <=> sk0_2=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4667,plain,(
% 1.14/0.65 ~spl0_0|~spl0_3),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1172,f4653,f4664])).
% 1.14/0.65 fof(f4668,plain,(
% 1.14/0.65 spl0_4 <=> hAPP(c_Polynomial_Opoly(t_a,v_p),sk0_2)=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4671,plain,(
% 1.14/0.65 ~spl0_0|~spl0_4),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1173,f4653,f4668])).
% 1.14/0.65 fof(f4672,plain,(
% 1.14/0.65 spl0_5 <=> v_c____=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4673,plain,(
% 1.14/0.65 v_c____=c_Groups_Ozero__class_Ozero(t_a)|~spl0_5),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4672])).
% 1.14/0.65 fof(f4675,plain,(
% 1.14/0.65 spl0_6 <=> sk0_3=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4678,plain,(
% 1.14/0.65 ~spl0_0|spl0_5|~spl0_6),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1177,f4653,f4672,f4675])).
% 1.14/0.65 fof(f4679,plain,(
% 1.14/0.65 spl0_7 <=> c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4682,plain,(
% 1.14/0.65 spl0_8 <=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4683,plain,(
% 1.14/0.65 c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_8),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4682])).
% 1.14/0.65 fof(f4685,plain,(
% 1.14/0.65 ~spl0_0|spl0_5|~spl0_7|spl0_8),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1178,f4653,f4672,f4679,f4682])).
% 1.14/0.65 fof(f4686,plain,(
% 1.14/0.65 spl0_9 <=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4687,plain,(
% 1.14/0.65 c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_9),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4686])).
% 1.14/0.65 fof(f4689,plain,(
% 1.14/0.65 ~spl0_0|spl0_5|spl0_7|spl0_9),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1179,f4653,f4672,f4679,f4686])).
% 1.14/0.65 fof(f4690,plain,(
% 1.14/0.65 spl0_10 <=> hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sk0_4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_3,sk0_5)),X0))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4691,plain,(
% 1.14/0.65 ![X0]: (hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sk0_4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_3,sk0_5)),X0))|~spl0_10)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4690])).
% 1.14/0.65 fof(f4693,plain,(
% 1.14/0.65 ~spl0_0|spl0_5|spl0_10),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1180,f4653,f4672,f4690])).
% 1.14/0.65 fof(f4694,plain,(
% 1.14/0.65 spl0_11 <=> sk0_6=c_Groups_Ozero__class_Ozero(t_a)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4696,plain,(
% 1.14/0.65 ~sk0_6=c_Groups_Ozero__class_Ozero(t_a)|spl0_11),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4694])).
% 1.14/0.65 fof(f4697,plain,(
% 1.14/0.65 ~spl0_0|~spl0_5|~spl0_11),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1184,f4653,f4672,f4694])).
% 1.14/0.65 fof(f4698,plain,(
% 1.14/0.65 spl0_12 <=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4699,plain,(
% 1.14/0.65 c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_12),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4698])).
% 1.14/0.65 fof(f4701,plain,(
% 1.14/0.65 ~spl0_0|~spl0_5|~spl0_7|spl0_12),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1185,f4653,f4672,f4679,f4698])).
% 1.14/0.65 fof(f4702,plain,(
% 1.14/0.65 spl0_13 <=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4703,plain,(
% 1.14/0.65 c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_13),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4702])).
% 1.14/0.65 fof(f4705,plain,(
% 1.14/0.65 ~spl0_0|~spl0_5|spl0_7|spl0_13),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1186,f4653,f4672,f4679,f4702])).
% 1.14/0.65 fof(f4706,plain,(
% 1.14/0.65 spl0_14 <=> hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sk0_7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_6,sk0_8)),X0))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4707,plain,(
% 1.14/0.65 ![X0]: (hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sk0_7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sk0_6,sk0_8)),X0))|~spl0_14)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4706])).
% 1.14/0.65 fof(f4709,plain,(
% 1.14/0.65 ~spl0_0|~spl0_5|spl0_14),
% 1.14/0.65 inference(split_clause,[status(thm)],[f1187,f4653,f4672,f4706])).
% 1.14/0.65 fof(f4720,plain,(
% 1.14/0.65 spl0_18 <=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_11))),sk0_10))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4721,plain,(
% 1.14/0.65 c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_11))),sk0_10))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_18),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4720])).
% 1.14/0.65 fof(f4736,plain,(
% 1.14/0.65 spl0_22 <=> ~pd0_6(X0,X1)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4737,plain,(
% 1.14/0.65 ![X0,X1]: (~pd0_6(X0,X1)|~spl0_22)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4736])).
% 1.14/0.65 fof(f4739,plain,(
% 1.14/0.65 spl0_22|spl0_7),
% 1.14/0.65 inference(split_clause,[status(thm)],[f4651,f4736,f4679])).
% 1.14/0.65 fof(f4756,plain,(
% 1.14/0.65 ![X0,X1]: (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(destructive_equality_resolution,[status(esa)],[f1389])).
% 1.14/0.65 fof(f4900,plain,(
% 1.14/0.65 ![X0,X1,X2]: (X0=c_Groups_Ozero__class_Ozero(t_a)|~c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X1))),X2))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_31(X1,X2,X0))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sk0_31(X1,X2,X0)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X0,X1)),sk0_31(X1,X2,X0)))|~spl0_22)),
% 1.14/0.65 inference(backward_subsumption_resolution,[status(thm)],[f4618,f4737])).
% 1.14/0.65 fof(f4902,plain,(
% 1.14/0.65 spl0_23 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4903,plain,(
% 1.14/0.65 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_23),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4902])).
% 1.14/0.65 fof(f4905,plain,(
% 1.14/0.65 spl0_24 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4908,plain,(
% 1.14/0.65 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 inference(resolution,[status(thm)],[f1482,f1275])).
% 1.14/0.65 fof(f4909,plain,(
% 1.14/0.65 spl0_23|spl0_24),
% 1.14/0.65 inference(split_clause,[status(thm)],[f4908,f4902,f4905])).
% 1.14/0.65 fof(f4910,plain,(
% 1.14/0.65 spl0_25 <=> ~X0=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4911,plain,(
% 1.14/0.65 ![X0]: (~X0=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_25)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4910])).
% 1.14/0.65 fof(f4915,plain,(
% 1.14/0.65 $false|~spl0_23),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f4903,f1471])).
% 1.14/0.65 fof(f4916,plain,(
% 1.14/0.65 ~spl0_23),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f4915])).
% 1.14/0.65 fof(f4917,plain,(
% 1.14/0.65 spl0_26 <=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4920,plain,(
% 1.14/0.65 c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 inference(resolution,[status(thm)],[f1483,f1275])).
% 1.14/0.65 fof(f4921,plain,(
% 1.14/0.65 spl0_26|spl0_23),
% 1.14/0.65 inference(split_clause,[status(thm)],[f4920,f4917,f4902])).
% 1.14/0.65 fof(f4927,plain,(
% 1.14/0.65 ~c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1753,f1471])).
% 1.14/0.65 fof(f4929,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f1276])).
% 1.14/0.65 fof(f4930,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f4929])).
% 1.14/0.65 fof(f4931,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f4930])).
% 1.14/0.65 fof(f4932,plain,(
% 1.14/0.65 spl0_27 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4933,plain,(
% 1.14/0.65 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~spl0_27),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4932])).
% 1.14/0.65 fof(f4935,plain,(
% 1.14/0.65 spl0_28 <=> c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4938,plain,(
% 1.14/0.65 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 inference(resolution,[status(thm)],[f4931,f1482])).
% 1.14/0.65 fof(f4939,plain,(
% 1.14/0.65 spl0_27|spl0_28),
% 1.14/0.65 inference(split_clause,[status(thm)],[f4938,f4932,f4935])).
% 1.14/0.65 fof(f4942,plain,(
% 1.14/0.65 spl0_29 <=> ~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4945,plain,(
% 1.14/0.65 ![X0]: (~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1482,f4931])).
% 1.14/0.65 fof(f4946,plain,(
% 1.14/0.65 spl0_29|spl0_27),
% 1.14/0.65 inference(split_clause,[status(thm)],[f4945,f4942,f4932])).
% 1.14/0.65 fof(f4949,plain,(
% 1.14/0.65 $false|~spl0_27),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f4933,f4927])).
% 1.14/0.65 fof(f4950,plain,(
% 1.14/0.65 ~spl0_27),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f4949])).
% 1.14/0.65 fof(f4951,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f1277])).
% 1.14/0.65 fof(f4956,plain,(
% 1.14/0.65 spl0_30 <=> ~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4957,plain,(
% 1.14/0.65 ![X0]: (~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_30)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4956])).
% 1.14/0.65 fof(f4985,plain,(
% 1.14/0.65 spl0_31 <=> ~X0=X0),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f4986,plain,(
% 1.14/0.65 ![X0]: (~X0=X0|~spl0_31)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f4985])).
% 1.14/0.65 fof(f5001,plain,(
% 1.14/0.65 spl0_32 <=> ~c_Nat_OSuc(X0)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5004,plain,(
% 1.14/0.65 ![X0]: (~c_Nat_OSuc(X0)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1754,f4951])).
% 1.14/0.65 fof(f5005,plain,(
% 1.14/0.65 spl0_32|spl0_27),
% 1.14/0.65 inference(split_clause,[status(thm)],[f5004,f5001,f4932])).
% 1.14/0.65 fof(f5019,plain,(
% 1.14/0.65 spl0_34 <=> ~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5020,plain,(
% 1.14/0.65 ![X0]: (~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~spl0_34)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f5019])).
% 1.14/0.65 fof(f5037,plain,(
% 1.14/0.65 spl0_36 <=> ~c_Nat_OSuc(X0)=X0),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5040,plain,(
% 1.14/0.65 ![X0]: (~c_Nat_OSuc(X0)=X0|c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1755,f1491])).
% 1.14/0.65 fof(f5041,plain,(
% 1.14/0.65 spl0_36|spl0_27),
% 1.14/0.65 inference(split_clause,[status(thm)],[f5040,f5037,f4932])).
% 1.14/0.65 fof(f5190,plain,(
% 1.14/0.65 spl0_37 <=> ~c_Nat_OSuc(X0)=c_Nat_OSuc(X0)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5191,plain,(
% 1.14/0.65 ![X0]: (~c_Nat_OSuc(X0)=c_Nat_OSuc(X0)|~spl0_37)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f5190])).
% 1.14/0.65 fof(f5223,plain,(
% 1.14/0.65 spl0_38 <=> X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5224,plain,(
% 1.14/0.65 ![X0]: (X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_38)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f5223])).
% 1.14/0.65 fof(f5253,plain,(
% 1.14/0.65 spl0_40 <=> ~c_Nat_OSuc(X0)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5256,plain,(
% 1.14/0.65 ![X0]: (~c_Nat_OSuc(X0)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1754,f1486])).
% 1.14/0.65 fof(f5257,plain,(
% 1.14/0.65 spl0_40|spl0_27),
% 1.14/0.65 inference(split_clause,[status(thm)],[f5256,f5253,f4932])).
% 1.14/0.65 fof(f5258,plain,(
% 1.14/0.65 spl0_41 <=> ~X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5259,plain,(
% 1.14/0.65 ![X0]: (~X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_41)),
% 1.14/0.65 inference(component_clause,[status(thm)],[f5258])).
% 1.14/0.65 fof(f5429,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Nat_OSuc(X1)))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1492,f1471])).
% 1.14/0.65 fof(f5453,plain,(
% 1.14/0.65 ![X0,X1]: (~c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X0),X1))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f1408,f5429])).
% 1.14/0.65 fof(f5585,plain,(
% 1.14/0.65 spl0_43 <=> X0=X0),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f5588,plain,(
% 1.14/0.65 ![X0,X1]: (X0=X0|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 1.14/0.65 inference(equality_resolution,[status(esa)],[f1382])).
% 1.14/0.65 fof(f5589,plain,(
% 1.14/0.65 spl0_43|spl0_38),
% 1.14/0.65 inference(split_clause,[status(thm)],[f5588,f5585,f5223])).
% 1.14/0.65 fof(f5599,plain,(
% 1.14/0.65 $false|~spl0_38),
% 1.14/0.65 inference(backward_subsumption_resolution,[status(thm)],[f5453,f5224])).
% 1.14/0.65 fof(f5600,plain,(
% 1.14/0.65 ~spl0_38),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f5599])).
% 1.14/0.65 fof(f6655,plain,(
% 1.14/0.65 $false|spl0_0),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f4619,f4655])).
% 1.14/0.65 fof(f6656,plain,(
% 1.14/0.65 spl0_0),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6655])).
% 1.14/0.65 fof(f6659,plain,(
% 1.14/0.65 $false|~spl0_41),
% 1.14/0.65 inference(destructive_equality_resolution,[status(esa)],[f5259])).
% 1.14/0.65 fof(f6660,plain,(
% 1.14/0.65 ~spl0_41),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6659])).
% 1.14/0.65 fof(f6661,plain,(
% 1.14/0.65 $false|~spl0_37),
% 1.14/0.65 inference(trivial_equality_resolution,[status(esa)],[f5191])).
% 1.14/0.65 fof(f6662,plain,(
% 1.14/0.65 ~spl0_37),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6661])).
% 1.14/0.65 fof(f6663,plain,(
% 1.14/0.65 $false|~spl0_34),
% 1.14/0.65 inference(destructive_equality_resolution,[status(esa)],[f5020])).
% 1.14/0.65 fof(f6664,plain,(
% 1.14/0.65 ~spl0_34),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6663])).
% 1.14/0.65 fof(f6665,plain,(
% 1.14/0.65 $false|~spl0_31),
% 1.14/0.65 inference(trivial_equality_resolution,[status(esa)],[f4986])).
% 1.14/0.65 fof(f6666,plain,(
% 1.14/0.65 ~spl0_31),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6665])).
% 1.14/0.65 fof(f6667,plain,(
% 1.14/0.65 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_30),
% 1.14/0.65 inference(destructive_equality_resolution,[status(esa)],[f4957])).
% 1.14/0.65 fof(f6668,plain,(
% 1.14/0.65 $false|~spl0_30),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f6667,f4927])).
% 1.14/0.65 fof(f6669,plain,(
% 1.14/0.65 ~spl0_30),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6668])).
% 1.14/0.65 fof(f6670,plain,(
% 1.14/0.65 ![X0]: (~X0=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~spl0_25)),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f4911])).
% 1.14/0.65 fof(f6671,plain,(
% 1.14/0.65 $false|~spl0_25),
% 1.14/0.65 inference(destructive_equality_resolution,[status(esa)],[f6670])).
% 1.14/0.65 fof(f6672,plain,(
% 1.14/0.65 ~spl0_25),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6671])).
% 1.14/0.65 fof(f6674,plain,(
% 1.14/0.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_11))),c_Nat_OSuc(sk0_10))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_18),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1492,f4721])).
% 1.14/0.65 fof(f6675,plain,(
% 1.14/0.65 $false|~spl0_18),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f6674,f5429])).
% 1.14/0.65 fof(f6676,plain,(
% 1.14/0.65 ~spl0_18),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6675])).
% 1.14/0.65 fof(f6677,plain,(
% 1.14/0.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),c_Nat_OSuc(sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_13),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1492,f4703])).
% 1.14/0.65 fof(f6678,plain,(
% 1.14/0.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),c_Nat_OSuc(sk0_7))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_12),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1492,f4699])).
% 1.14/0.65 fof(f6679,plain,(
% 1.14/0.65 $false|~spl0_12),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f6678,f5429])).
% 1.14/0.65 fof(f6680,plain,(
% 1.14/0.65 ~spl0_12),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6679])).
% 1.14/0.65 fof(f6681,plain,(
% 1.14/0.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),c_Nat_OSuc(sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_9),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1492,f4687])).
% 1.14/0.65 fof(f6682,plain,(
% 1.14/0.65 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),c_Nat_OSuc(sk0_4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_8),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1492,f4683])).
% 1.14/0.65 fof(f6683,plain,(
% 1.14/0.65 $false|~spl0_8),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f6682,f5429])).
% 1.14/0.65 fof(f6684,plain,(
% 1.14/0.65 ~spl0_8),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f6683])).
% 1.14/0.65 fof(f6687,plain,(
% 1.14/0.65 ![X0,X1,X2]: (X0=c_Groups_Ozero__class_Ozero(t_a)|~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X1))),c_Nat_OSuc(X2))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_31(X1,X2,X0))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sk0_31(X1,X2,X0)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X0,X1)),sk0_31(X1,X2,X0)))|~spl0_22)),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1492,f4900])).
% 1.14/0.65 fof(f6952,plain,(
% 1.14/0.65 ![X0,X1,X2]: (X0=v_c____|~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X1))),c_Nat_OSuc(X2))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sk0_31(X1,X2,X0))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sk0_31(X1,X2,X0)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X0,X1)),sk0_31(X1,X2,X0)))|~spl0_5|~spl0_22)),
% 1.14/0.65 inference(backward_demodulation,[status(thm)],[f4673,f6687])).
% 1.14/0.65 fof(f6955,plain,(
% 1.14/0.65 ~sk0_6=v_c____|~spl0_5|spl0_11),
% 1.14/0.65 inference(backward_demodulation,[status(thm)],[f4673,f4696])).
% 1.14/0.65 fof(f7029,plain,(
% 1.14/0.65 spl0_61 <=> sk0_6=v_c____),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f7030,plain,(
% 1.14/0.65 sk0_6=v_c____|~spl0_61),
% 1.14/0.65 inference(component_clause,[status(thm)],[f7029])).
% 1.14/0.65 fof(f7032,plain,(
% 1.14/0.65 spl0_62 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),c_Nat_OSuc(sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f7034,plain,(
% 1.14/0.65 ~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),c_Nat_OSuc(sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|spl0_62),
% 1.14/0.65 inference(component_clause,[status(thm)],[f7032])).
% 1.14/0.65 fof(f7035,plain,(
% 1.14/0.65 sk0_6=v_c____|~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_8))),c_Nat_OSuc(sk0_7))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_5|~spl0_22|~spl0_14),
% 1.14/0.65 inference(resolution,[status(thm)],[f6952,f4707])).
% 1.14/0.65 fof(f7036,plain,(
% 1.14/0.65 spl0_61|~spl0_62|~spl0_5|~spl0_22|~spl0_14),
% 1.14/0.65 inference(split_clause,[status(thm)],[f7035,f7029,f7032,f4672,f4736,f4706])).
% 1.14/0.65 fof(f7042,plain,(
% 1.14/0.65 ~c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_13|spl0_62),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f6677,f7034])).
% 1.14/0.65 fof(f7043,plain,(
% 1.14/0.65 $false|~spl0_13|spl0_62),
% 1.14/0.65 inference(trivial_equality_resolution,[status(esa)],[f7042])).
% 1.14/0.65 fof(f7044,plain,(
% 1.14/0.65 ~spl0_13|spl0_62),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f7043])).
% 1.14/0.65 fof(f7045,plain,(
% 1.14/0.65 $false|~spl0_5|spl0_11|~spl0_61),
% 1.14/0.65 inference(forward_subsumption_resolution,[status(thm)],[f7030,f6955])).
% 1.14/0.65 fof(f7046,plain,(
% 1.14/0.65 ~spl0_5|spl0_11|~spl0_61),
% 1.14/0.65 inference(contradiction_clause,[status(thm)],[f7045])).
% 1.14/0.65 fof(f7332,plain,(
% 1.14/0.65 spl0_74 <=> ~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.65 fof(f7339,plain,(
% 1.14/0.65 ![X0,X1]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f1480])).
% 1.14/0.65 fof(f7340,plain,(
% 1.14/0.65 ![X0,X1]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1=c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 1.14/0.65 inference(forward_demodulation,[status(thm)],[f1753,f7339])).
% 1.14/0.65 fof(f7341,plain,(
% 1.14/0.65 ![X0]: (~hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 1.14/0.65 inference(paramodulation,[status(thm)],[f4756,f7340])).
% 1.14/0.65 fof(f7342,plain,(
% 1.14/0.65 spl0_74|spl0_27),
% 1.14/0.65 inference(split_clause,[status(thm)],[f7341,f7332,f4932])).
% 1.14/0.65 fof(f7359,plain,(
% 1.14/0.65 spl0_75 <=> class_Rings_Oidom(tc_Int_Oint)),
% 1.14/0.65 introduced(split_symbol_definition)).
% 1.14/0.66 fof(f7361,plain,(
% 1.14/0.66 ~class_Rings_Oidom(tc_Int_Oint)|spl0_75),
% 1.14/0.66 inference(component_clause,[status(thm)],[f7359])).
% 1.14/0.66 fof(f7362,plain,(
% 1.14/0.66 spl0_76 <=> ~c_Polynomial_Opoly(tc_Int_Oint,X0)=c_Polynomial_Opoly(tc_Int_Oint,X1)|X0=X1),
% 1.14/0.66 introduced(split_symbol_definition)).
% 1.14/0.66 fof(f7365,plain,(
% 1.14/0.66 ![X0,X1]: (~class_Rings_Oidom(tc_Int_Oint)|~c_Polynomial_Opoly(tc_Int_Oint,X0)=c_Polynomial_Opoly(tc_Int_Oint,X1)|X0=X1)),
% 1.14/0.66 inference(resolution,[status(thm)],[f1249,f4470])).
% 1.14/0.66 fof(f7366,plain,(
% 1.14/0.66 ~spl0_75|spl0_76),
% 1.14/0.66 inference(split_clause,[status(thm)],[f7365,f7359,f7362])).
% 1.14/0.66 fof(f7367,plain,(
% 1.14/0.66 $false|spl0_75),
% 1.14/0.66 inference(forward_subsumption_resolution,[status(thm)],[f7361,f4478])).
% 1.14/0.66 fof(f7368,plain,(
% 1.14/0.66 spl0_75),
% 1.14/0.66 inference(contradiction_clause,[status(thm)],[f7367])).
% 1.14/0.66 fof(f7530,plain,(
% 1.14/0.66 spl0_80 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),c_Nat_OSuc(sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))),
% 1.14/0.66 introduced(split_symbol_definition)).
% 1.14/0.66 fof(f7532,plain,(
% 1.14/0.66 ~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),c_Nat_OSuc(sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|spl0_80),
% 1.14/0.66 inference(component_clause,[status(thm)],[f7530])).
% 1.14/0.66 fof(f7533,plain,(
% 1.14/0.66 sk0_3=c_Groups_Ozero__class_Ozero(t_a)|~c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sk0_5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sk0_5))),c_Nat_OSuc(sk0_4))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_10|~spl0_22),
% 1.14/0.66 inference(resolution,[status(thm)],[f4691,f6687])).
% 1.14/0.66 fof(f7534,plain,(
% 1.14/0.66 spl0_6|~spl0_80|~spl0_10|~spl0_22),
% 1.14/0.66 inference(split_clause,[status(thm)],[f7533,f4675,f7530,f4690,f4736])).
% 1.14/0.66 fof(f7540,plain,(
% 1.14/0.66 ~c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|~spl0_9|spl0_80),
% 1.14/0.66 inference(forward_demodulation,[status(thm)],[f6681,f7532])).
% 1.14/0.66 fof(f7541,plain,(
% 1.14/0.66 $false|~spl0_9|spl0_80),
% 1.14/0.66 inference(trivial_equality_resolution,[status(esa)],[f7540])).
% 1.14/0.66 fof(f7542,plain,(
% 1.14/0.66 ~spl0_9|spl0_80),
% 1.14/0.66 inference(contradiction_clause,[status(thm)],[f7541])).
% 1.14/0.66 fof(f7543,plain,(
% 1.14/0.66 $false),
% 1.14/0.66 inference(sat_refutation,[status(thm)],[f4659,f4663,f4667,f4671,f4678,f4685,f4689,f4693,f4697,f4701,f4705,f4709,f4739,f4909,f4916,f4921,f4939,f4946,f4950,f5005,f5041,f5257,f5589,f5600,f6656,f6660,f6662,f6664,f6666,f6669,f6672,f6676,f6680,f6684,f7036,f7044,f7046,f7342,f7366,f7368,f7534,f7542])).
% 1.14/0.66 % SZS output end CNFRefutation for theBenchmark.p
% 1.14/0.67 % Elapsed time: 0.318025 seconds
% 1.14/0.67 % CPU time: 1.767993 seconds
% 1.14/0.67 % Total memory used: 176.745 MB
% 1.14/0.67 % Net memory used: 175.715 MB
%------------------------------------------------------------------------------