TSTP Solution File: SWW269+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW269+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 20:49:56 EDT 2024
% Result : Theorem 26.00s 3.67s
% Output : CNFRefutation 26.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWW269+1 : TPTP v8.1.2. Released v5.2.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.29 % Computer : n032.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Apr 29 23:14:05 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.13/0.34 % Drodi V3.6.0
% 26.00/3.67 % Refutation found
% 26.00/3.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.00/3.67 % SZS output start CNFRefutation for theBenchmark
% 26.00/3.67 fof(f1,axiom,(
% 26.00/3.67 (! [V_g_2,V_f_2] :( (! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x))=> V_f_2 = V_g_2 ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f2,axiom,(
% 26.00/3.67 v_d____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f3,axiom,(
% 26.00/3.67 (! [B_w] :( B_w != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),B_w) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f15,axiom,(
% 26.00/3.67 (! [V_q_2,V_pa_2,T_a] :( ( class_Int_Oring__char__0(T_a)& class_Rings_Oidom(T_a) )=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)<=> V_pa_2 = V_q_2 ) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f17,axiom,(
% 26.00/3.67 (! [V_x,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f22,axiom,(
% 26.00/3.67 (! [V_y] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),V_y) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f81,axiom,(
% 26.00/3.67 (! [V_r,V_q,V_c,V_p,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) = c_Polynomial_OpCons(T_a,V_r,V_q)=> ( V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)& V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c) ) ) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f86,axiom,(
% 26.00/3.67 (! [V_p,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f118,axiom,(
% 26.00/3.67 (! [V_n] : c_Nat_OSuc(V_n) != V_n )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f121,axiom,(
% 26.00/3.67 (! [V_a,T_a] :( class_Rings_Ocomm__semiring__1(T_a)=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f135,axiom,(
% 26.00/3.67 (! [V_n,V_m] :( V_m = V_n=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f506,axiom,(
% 26.00/3.67 (! [T_a] :( class_Rings_Ozero__neq__one(T_a)=> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) )),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f594,axiom,(
% 26.00/3.67 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1020,axiom,(
% 26.00/3.67 class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1028,axiom,(
% 26.00/3.67 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1031,axiom,(
% 26.00/3.67 class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1032,axiom,(
% 26.00/3.67 class_Orderings_Opreorder(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1033,axiom,(
% 26.00/3.67 class_Orderings_Olinorder(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1038,axiom,(
% 26.00/3.67 class_Orderings_Oorder(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1042,axiom,(
% 26.00/3.67 class_Groups_Ozero(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.00/3.67 fof(f1045,axiom,(
% 26.00/3.67 class_HOL_Oequal(tc_Nat_Onat) ),
% 26.00/3.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1047,axiom,(
% 26.43/3.69 class_Orderings_Opreorder(tc_HOL_Obool) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1048,axiom,(
% 26.43/3.69 class_Orderings_Oorder(tc_HOL_Obool) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1052,axiom,(
% 26.43/3.69 class_HOL_Oequal(tc_HOL_Obool) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1070,axiom,(
% 26.43/3.69 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1071,axiom,(
% 26.43/3.69 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1076,axiom,(
% 26.43/3.69 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1084,axiom,(
% 26.43/3.69 class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1092,axiom,(
% 26.43/3.69 class_Rings_Oidom(tc_Complex_Ocomplex) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1124,axiom,(
% 26.43/3.69 (! [T_1] :( class_Rings_Ocomm__semiring__1(T_1)=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) )),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1159,conjecture,(
% 26.43/3.69 c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
% 26.43/3.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.43/3.69 fof(f1160,negated_conjecture,(
% 26.43/3.69 ~(c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )),
% 26.43/3.69 inference(negated_conjecture,[status(cth)],[f1159])).
% 26.43/3.69 fof(f1161,plain,(
% 26.43/3.69 ![V_g_2,V_f_2]: ((?[B_x]: ~hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x))|V_f_2=V_g_2)),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 26.43/3.69 fof(f1162,plain,(
% 26.43/3.69 ![V_g_2,V_f_2]: (~hAPP(V_f_2,sk0_0(V_f_2,V_g_2))=hAPP(V_g_2,sk0_0(V_f_2,V_g_2))|V_f_2=V_g_2)),
% 26.43/3.69 inference(skolemization,[status(esa)],[f1161])).
% 26.43/3.69 fof(f1163,plain,(
% 26.43/3.69 ![X0,X1]: (~hAPP(X0,sk0_0(X0,X1))=hAPP(X1,sk0_0(X0,X1))|X0=X1)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1162])).
% 26.43/3.69 fof(f1164,plain,(
% 26.43/3.69 v_d____=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f2])).
% 26.43/3.69 fof(f1165,plain,(
% 26.43/3.69 ![B_w]: (B_w=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),B_w)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 26.43/3.69 fof(f1166,plain,(
% 26.43/3.69 ![X0]: (X0=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),X0)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1165])).
% 26.43/3.69 fof(f1205,plain,(
% 26.43/3.69 ![V_q_2,V_pa_2,T_a]: ((~class_Int_Oring__char__0(T_a)|~class_Rings_Oidom(T_a))|(c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)<=>V_pa_2=V_q_2))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 26.43/3.69 fof(f1206,plain,(
% 26.43/3.69 ![V_q_2,V_pa_2,T_a]: ((~class_Int_Oring__char__0(T_a)|~class_Rings_Oidom(T_a))|((~c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)|V_pa_2=V_q_2)&(c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)|~V_pa_2=V_q_2)))),
% 26.43/3.69 inference(NNF_transformation,[status(esa)],[f1205])).
% 26.43/3.69 fof(f1207,plain,(
% 26.43/3.69 ![T_a]: ((~class_Int_Oring__char__0(T_a)|~class_Rings_Oidom(T_a))|((![V_q_2,V_pa_2]: (~c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)|V_pa_2=V_q_2))&(![V_q_2,V_pa_2]: (c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)|~V_pa_2=V_q_2))))),
% 26.43/3.69 inference(miniscoping,[status(esa)],[f1206])).
% 26.43/3.69 fof(f1208,plain,(
% 26.43/3.69 ![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)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1207])).
% 26.43/3.69 fof(f1215,plain,(
% 26.43/3.69 ![V_x,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Ozero__class_Ozero(T_a))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 26.43/3.69 fof(f1216,plain,(
% 26.43/3.69 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_x]: hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Ozero__class_Ozero(T_a)))),
% 26.43/3.69 inference(miniscoping,[status(esa)],[f1215])).
% 26.43/3.69 fof(f1217,plain,(
% 26.43/3.69 ![X0,X1]: (~class_Rings_Ocomm__semiring__0(X0)|hAPP(c_Polynomial_Opoly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1)=c_Groups_Ozero__class_Ozero(X0))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1216])).
% 26.43/3.69 fof(f1234,plain,(
% 26.43/3.69 ![X0]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X0))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f22])).
% 26.43/3.69 fof(f1447,plain,(
% 26.43/3.69 ![V_r,V_q,V_c,V_p,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))=c_Polynomial_OpCons(T_a,V_r,V_q)|(V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)&V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c))))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f81])).
% 26.43/3.69 fof(f1448,plain,(
% 26.43/3.69 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_r,V_q,V_c,V_p]: (~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))=c_Polynomial_OpCons(T_a,V_r,V_q)|(V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)&V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))))),
% 26.43/3.69 inference(miniscoping,[status(esa)],[f1447])).
% 26.43/3.69 fof(f1449,plain,(
% 26.43/3.69 ![X0,X1,X2,X3,X4]: (~class_Rings_Ocomm__semiring__0(X0)|~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),X1,c_Polynomial_Osmult(X0,X2,X3))=c_Polynomial_OpCons(X0,X4,X3)|X4=hAPP(c_Polynomial_Opoly(X0,X1),X2))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1448])).
% 26.43/3.69 fof(f1464,plain,(
% 26.43/3.69 ![V_p,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f86])).
% 26.43/3.69 fof(f1465,plain,(
% 26.43/3.69 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_p]: c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),
% 26.43/3.69 inference(miniscoping,[status(esa)],[f1464])).
% 26.43/3.69 fof(f1466,plain,(
% 26.43/3.69 ![X0,X1]: (~class_Rings_Ocomm__semiring__0(X0)|c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1465])).
% 26.43/3.69 fof(f1550,plain,(
% 26.43/3.69 ![X0]: (~c_Nat_OSuc(X0)=X0)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f118])).
% 26.43/3.69 fof(f1555,plain,(
% 26.43/3.69 ![V_a,T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a)),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f121])).
% 26.43/3.69 fof(f1556,plain,(
% 26.43/3.69 ![T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|(![V_a]: c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a))),
% 26.43/3.69 inference(miniscoping,[status(esa)],[f1555])).
% 26.43/3.69 fof(f1557,plain,(
% 26.43/3.69 ![X0,X1]: (~class_Rings_Ocomm__semiring__1(X0)|c_Groups_Oplus__class_Oplus(X0,X1,c_Groups_Ozero__class_Ozero(X0))=X1)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1556])).
% 26.43/3.69 fof(f1591,plain,(
% 26.43/3.69 ![V_n,V_m]: (~V_m=V_n|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f135])).
% 26.43/3.69 fof(f1592,plain,(
% 26.43/3.69 ![X0,X1]: (~X0=X1|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1591])).
% 26.43/3.69 fof(f2831,plain,(
% 26.43/3.69 ![T_a]: (~class_Rings_Ozero__neq__one(T_a)|~c_Groups_Oone__class_Oone(T_a)=c_Groups_Ozero__class_Ozero(T_a))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f506])).
% 26.43/3.69 fof(f2832,plain,(
% 26.43/3.69 ![X0]: (~class_Rings_Ozero__neq__one(X0)|~c_Groups_Oone__class_Oone(X0)=c_Groups_Ozero__class_Ozero(X0))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f2831])).
% 26.43/3.69 fof(f3073,plain,(
% 26.43/3.69 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f594])).
% 26.43/3.69 fof(f4587,plain,(
% 26.43/3.69 class_Rings_Olinordered__semidom(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1020])).
% 26.43/3.69 fof(f4595,plain,(
% 26.43/3.69 class_Rings_Ocomm__semiring__0(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1028])).
% 26.43/3.69 fof(f4598,plain,(
% 26.43/3.69 class_Rings_Ozero__neq__one(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1031])).
% 26.43/3.69 fof(f4599,plain,(
% 26.43/3.69 class_Orderings_Opreorder(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1032])).
% 26.43/3.69 fof(f4600,plain,(
% 26.43/3.69 class_Orderings_Olinorder(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1033])).
% 26.43/3.69 fof(f4605,plain,(
% 26.43/3.69 class_Orderings_Oorder(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1038])).
% 26.43/3.69 fof(f4609,plain,(
% 26.43/3.69 class_Groups_Ozero(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1042])).
% 26.43/3.69 fof(f4612,plain,(
% 26.43/3.69 class_HOL_Oequal(tc_Nat_Onat)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1045])).
% 26.43/3.69 fof(f4614,plain,(
% 26.43/3.69 class_Orderings_Opreorder(tc_HOL_Obool)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1047])).
% 26.43/3.69 fof(f4615,plain,(
% 26.43/3.69 class_Orderings_Oorder(tc_HOL_Obool)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1048])).
% 26.43/3.69 fof(f4619,plain,(
% 26.43/3.69 class_HOL_Oequal(tc_HOL_Obool)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1052])).
% 26.43/3.69 fof(f4637,plain,(
% 26.43/3.69 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1070])).
% 26.43/3.69 fof(f4638,plain,(
% 26.43/3.69 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1071])).
% 26.43/3.69 fof(f4643,plain,(
% 26.43/3.69 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1076])).
% 26.43/3.69 fof(f4651,plain,(
% 26.43/3.69 class_Int_Oring__char__0(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1084])).
% 26.43/3.69 fof(f4659,plain,(
% 26.43/3.69 class_Rings_Oidom(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1092])).
% 26.43/3.69 fof(f4719,plain,(
% 26.43/3.69 ![T_1]: (~class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)))),
% 26.43/3.69 inference(pre_NNF_transformation,[status(esa)],[f1124])).
% 26.43/3.69 fof(f4720,plain,(
% 26.43/3.69 ![X0]: (~class_Rings_Ocomm__semiring__1(X0)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f4719])).
% 26.43/3.69 fof(f4785,plain,(
% 26.43/3.69 ~c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 26.43/3.69 inference(cnf_transformation,[status(esa)],[f1160])).
% 26.43/3.69 fof(f4872,plain,(
% 26.43/3.69 ![X0]: (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0))),
% 26.43/3.69 inference(destructive_equality_resolution,[status(esa)],[f1592])).
% 26.43/3.69 fof(f5013,plain,(
% 26.43/3.69 ![X0]: (X0=v_d____|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),X0)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f1164,f1166])).
% 26.43/3.69 fof(f5014,plain,(
% 26.43/3.69 ![X0]: (X0=v_d____|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),X0)=v_d____)),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f1164,f5013])).
% 26.43/3.69 fof(f5106,plain,(
% 26.43/3.69 spl0_11 <=> class_Int_Oring__char__0(tc_Complex_Ocomplex)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f5108,plain,(
% 26.43/3.69 ~class_Int_Oring__char__0(tc_Complex_Ocomplex)|spl0_11),
% 26.43/3.69 inference(component_clause,[status(thm)],[f5106])).
% 26.43/3.69 fof(f5109,plain,(
% 26.43/3.69 spl0_12 <=> ~c_Polynomial_Opoly(tc_Complex_Ocomplex,X0)=c_Polynomial_Opoly(tc_Complex_Ocomplex,X1)|X0=X1),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f5110,plain,(
% 26.43/3.69 ![X0,X1]: (~c_Polynomial_Opoly(tc_Complex_Ocomplex,X0)=c_Polynomial_Opoly(tc_Complex_Ocomplex,X1)|X0=X1|~spl0_12)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f5109])).
% 26.43/3.69 fof(f5112,plain,(
% 26.43/3.69 ![X0,X1]: (~class_Int_Oring__char__0(tc_Complex_Ocomplex)|~c_Polynomial_Opoly(tc_Complex_Ocomplex,X0)=c_Polynomial_Opoly(tc_Complex_Ocomplex,X1)|X0=X1)),
% 26.43/3.69 inference(resolution,[status(thm)],[f1208,f4659])).
% 26.43/3.69 fof(f5113,plain,(
% 26.43/3.69 ~spl0_11|spl0_12),
% 26.43/3.69 inference(split_clause,[status(thm)],[f5112,f5106,f5109])).
% 26.43/3.69 fof(f5114,plain,(
% 26.43/3.69 $false|spl0_11),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f5108,f4651])).
% 26.43/3.69 fof(f5115,plain,(
% 26.43/3.69 spl0_11),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f5114])).
% 26.43/3.69 fof(f5116,plain,(
% 26.43/3.69 ![X0]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 26.43/3.69 inference(resolution,[status(thm)],[f1217,f4638])).
% 26.43/3.69 fof(f5117,plain,(
% 26.43/3.69 ![X0]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0)=v_d____)),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f1164,f5116])).
% 26.43/3.69 fof(f5131,plain,(
% 26.43/3.69 ![X0]: (~hAPP(X0,sk0_0(X0,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))=v_d____|X0=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 26.43/3.69 inference(paramodulation,[status(thm)],[f5117,f1163])).
% 26.43/3.69 fof(f5258,plain,(
% 26.43/3.69 spl0_23 <=> c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f5259,plain,(
% 26.43/3.69 c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))|~spl0_23),
% 26.43/3.69 inference(component_clause,[status(thm)],[f5258])).
% 26.43/3.69 fof(f5261,plain,(
% 26.43/3.69 spl0_24 <=> sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f5262,plain,(
% 26.43/3.69 sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))=v_d____|~spl0_24),
% 26.43/3.69 inference(component_clause,[status(thm)],[f5261])).
% 26.43/3.69 fof(f5264,plain,(
% 26.43/3.69 c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))|sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))=v_d____),
% 26.43/3.69 inference(resolution,[status(thm)],[f5131,f5014])).
% 26.43/3.69 fof(f5265,plain,(
% 26.43/3.69 spl0_23|spl0_24),
% 26.43/3.69 inference(split_clause,[status(thm)],[f5264,f5258,f5261])).
% 26.43/3.69 fof(f5313,plain,(
% 26.43/3.69 ![X0]: (~hAPP(X0,sk0_0(X0,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))=v_d____|X0=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 26.43/3.69 inference(paramodulation,[status(thm)],[f5117,f1163])).
% 26.43/3.69 fof(f5577,plain,(
% 26.43/3.69 ![X0]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_d____)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X0))),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f1164,f1234])).
% 26.43/3.69 fof(f5702,plain,(
% 26.43/3.69 ![X0,X1]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X0)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X1))),
% 26.43/3.69 inference(paramodulation,[status(thm)],[f5577,f5577])).
% 26.43/3.69 fof(f6017,plain,(
% 26.43/3.69 spl0_78 <=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),v_d____)=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f6019,plain,(
% 26.43/3.69 ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),v_d____)=v_d____|spl0_78),
% 26.43/3.69 inference(component_clause,[status(thm)],[f6017])).
% 26.43/3.69 fof(f6045,plain,(
% 26.43/3.69 spl0_82 <=> c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f6046,plain,(
% 26.43/3.69 c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))|~spl0_82),
% 26.43/3.69 inference(component_clause,[status(thm)],[f6045])).
% 26.43/3.69 fof(f6111,plain,(
% 26.43/3.69 class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 26.43/3.69 inference(resolution,[status(thm)],[f4720,f4637])).
% 26.43/3.69 fof(f6633,plain,(
% 26.43/3.69 spl0_125 <=> ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X0)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_d____)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f6634,plain,(
% 26.43/3.69 ![X0]: (~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X0)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_d____)|~spl0_125)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f6633])).
% 26.43/3.69 fof(f6870,plain,(
% 26.43/3.69 ~c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 26.43/3.69 inference(resolution,[status(thm)],[f2832,f4598])).
% 26.43/3.69 fof(f6871,plain,(
% 26.43/3.69 ~c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 26.43/3.69 inference(resolution,[status(thm)],[f2832,f4643])).
% 26.43/3.69 fof(f6872,plain,(
% 26.43/3.69 ~c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=v_d____),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f1164,f6871])).
% 26.43/3.69 fof(f7097,plain,(
% 26.43/3.69 spl0_160 <=> X0=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f7098,plain,(
% 26.43/3.69 ![X0]: (X0=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))|~spl0_160)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f7097])).
% 26.43/3.69 fof(f7595,plain,(
% 26.43/3.69 ![X0]: (c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 26.43/3.69 inference(resolution,[status(thm)],[f1466,f4638])).
% 26.43/3.69 fof(f7596,plain,(
% 26.43/3.69 ![X0]: (c_Polynomial_Osmult(tc_Complex_Ocomplex,v_d____,X0)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f1164,f7595])).
% 26.43/3.69 fof(f7660,plain,(
% 26.43/3.69 ![X0]: (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))=X0)),
% 26.43/3.69 inference(resolution,[status(thm)],[f1557,f6111])).
% 26.43/3.69 fof(f8109,plain,(
% 26.43/3.69 $false|~spl0_82),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f6046,f4785])).
% 26.43/3.69 fof(f8110,plain,(
% 26.43/3.69 ~spl0_82),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f8109])).
% 26.43/3.69 fof(f8358,plain,(
% 26.43/3.69 spl0_227 <=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f8360,plain,(
% 26.43/3.69 ~class_Rings_Ocomm__semiring__0(tc_Nat_Onat)|spl0_227),
% 26.43/3.69 inference(component_clause,[status(thm)],[f8358])).
% 26.43/3.69 fof(f8366,plain,(
% 26.43/3.69 spl0_229 <=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f8368,plain,(
% 26.43/3.69 ~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)|spl0_229),
% 26.43/3.69 inference(component_clause,[status(thm)],[f8366])).
% 26.43/3.69 fof(f8374,plain,(
% 26.43/3.69 $false|spl0_229),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f8368,f4638])).
% 26.43/3.69 fof(f8375,plain,(
% 26.43/3.69 spl0_229),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f8374])).
% 26.43/3.69 fof(f8376,plain,(
% 26.43/3.69 $false|spl0_227),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f8360,f4595])).
% 26.43/3.69 fof(f8377,plain,(
% 26.43/3.69 spl0_227),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f8376])).
% 26.43/3.69 fof(f8923,plain,(
% 26.43/3.69 spl0_273 <=> ~X0=hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_d____)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f8924,plain,(
% 26.43/3.69 ![X0]: (~X0=hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_d____)|~spl0_273)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f8923])).
% 26.43/3.69 fof(f8933,plain,(
% 26.43/3.69 $false|~spl0_273),
% 26.43/3.69 inference(destructive_equality_resolution,[status(esa)],[f8924])).
% 26.43/3.69 fof(f8934,plain,(
% 26.43/3.69 ~spl0_273),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f8933])).
% 26.43/3.69 fof(f8942,plain,(
% 26.43/3.69 spl0_275 <=> ~v_p=X0),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f8943,plain,(
% 26.43/3.69 ![X0]: (~v_p=X0|~spl0_275)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f8942])).
% 26.43/3.69 fof(f8959,plain,(
% 26.43/3.69 $false|~spl0_275),
% 26.43/3.69 inference(destructive_equality_resolution,[status(esa)],[f8943])).
% 26.43/3.69 fof(f8960,plain,(
% 26.43/3.69 ~spl0_275),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f8959])).
% 26.43/3.69 fof(f9208,plain,(
% 26.43/3.69 spl0_300 <=> X0=tc_Complex_Ocomplex),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f9209,plain,(
% 26.43/3.69 ![X0]: (X0=tc_Complex_Ocomplex|~spl0_300)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f9208])).
% 26.43/3.69 fof(f9229,plain,(
% 26.43/3.69 $false|~spl0_300),
% 26.43/3.69 inference(resolution,[status(thm)],[f9209,f1550])).
% 26.43/3.69 fof(f9230,plain,(
% 26.43/3.69 ~spl0_300),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f9229])).
% 26.43/3.69 fof(f10018,plain,(
% 26.43/3.69 $false|~spl0_160),
% 26.43/3.69 inference(resolution,[status(thm)],[f7098,f1550])).
% 26.43/3.69 fof(f10019,plain,(
% 26.43/3.69 ~spl0_160),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f10018])).
% 26.43/3.69 fof(f10025,plain,(
% 26.43/3.69 spl0_313 <=> ~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))=c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)|X1=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),v_d____)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f10026,plain,(
% 26.43/3.69 ![X0,X1,X2]: (~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))=c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)|X1=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),v_d____)|~spl0_313)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f10025])).
% 26.43/3.69 fof(f10028,plain,(
% 26.43/3.69 ![X0,X1,X2]: (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)|~c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))=c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)|X1=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),v_d____))),
% 26.43/3.69 inference(paramodulation,[status(thm)],[f7596,f1449])).
% 26.43/3.69 fof(f10029,plain,(
% 26.43/3.69 ~spl0_229|spl0_313),
% 26.43/3.69 inference(split_clause,[status(thm)],[f10028,f8366,f10025])).
% 26.43/3.69 fof(f10378,plain,(
% 26.43/3.69 spl0_319 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f10379,plain,(
% 26.43/3.69 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~spl0_319),
% 26.43/3.69 inference(component_clause,[status(thm)],[f10378])).
% 26.43/3.69 fof(f10388,plain,(
% 26.43/3.69 spl0_321 <=> ~c_Groups_Oone__class_Oone(tc_Nat_Onat)=X0),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f10389,plain,(
% 26.43/3.69 ![X0]: (~c_Groups_Oone__class_Oone(tc_Nat_Onat)=X0|~spl0_321)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f10388])).
% 26.43/3.69 fof(f10393,plain,(
% 26.43/3.69 $false|~spl0_319),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f10379,f6870])).
% 26.43/3.69 fof(f10394,plain,(
% 26.43/3.69 ~spl0_319),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f10393])).
% 26.43/3.69 fof(f10414,plain,(
% 26.43/3.69 spl0_323 <=> ~c_Groups_Oone__class_Oone(tc_Nat_Onat)=X0|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f10415,plain,(
% 26.43/3.69 ![X0]: (~c_Groups_Oone__class_Oone(tc_Nat_Onat)=X0|X0=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_323)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f10414])).
% 26.43/3.69 fof(f10477,plain,(
% 26.43/3.69 spl0_332 <=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f10478,plain,(
% 26.43/3.69 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=v_d____|~spl0_332),
% 26.43/3.69 inference(component_clause,[status(thm)],[f10477])).
% 26.43/3.69 fof(f10651,plain,(
% 26.43/3.69 spl0_341 <=> ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0)=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f10652,plain,(
% 26.43/3.69 ![X0]: (~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0)=v_d____|~spl0_341)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f10651])).
% 26.43/3.69 fof(f10681,plain,(
% 26.43/3.69 $false|~spl0_332),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f10478,f6872])).
% 26.43/3.69 fof(f10682,plain,(
% 26.43/3.69 ~spl0_332),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f10681])).
% 26.43/3.69 fof(f11005,plain,(
% 26.43/3.69 spl0_347 <=> ~X0=X0),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f11006,plain,(
% 26.43/3.69 ![X0]: (~X0=X0|~spl0_347)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f11005])).
% 26.43/3.69 fof(f11324,plain,(
% 26.43/3.69 $false|~spl0_347),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f11006])).
% 26.43/3.69 fof(f11325,plain,(
% 26.43/3.69 ~spl0_347),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11324])).
% 26.43/3.69 fof(f11354,plain,(
% 26.43/3.69 spl0_358 <=> v_d____=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f11356,plain,(
% 26.43/3.69 ~v_d____=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))|spl0_358),
% 26.43/3.69 inference(component_clause,[status(thm)],[f11354])).
% 26.43/3.69 fof(f11359,plain,(
% 26.43/3.69 ~v_d____=v_d____|spl0_358),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f5117,f11356])).
% 26.43/3.69 fof(f11360,plain,(
% 26.43/3.69 $false|spl0_358),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f11359])).
% 26.43/3.69 fof(f11361,plain,(
% 26.43/3.69 spl0_358),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11360])).
% 26.43/3.69 fof(f11370,plain,(
% 26.43/3.69 c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))|~spl0_23|~spl0_12),
% 26.43/3.69 inference(resolution,[status(thm)],[f5259,f5110])).
% 26.43/3.69 fof(f11371,plain,(
% 26.43/3.69 spl0_82|~spl0_23|~spl0_12),
% 26.43/3.69 inference(split_clause,[status(thm)],[f11370,f6045,f5258,f5109])).
% 26.43/3.69 fof(f11399,plain,(
% 26.43/3.69 ~v_d____=v_d____|~spl0_341),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f5117,f10652])).
% 26.43/3.69 fof(f11400,plain,(
% 26.43/3.69 $false|~spl0_341),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f11399])).
% 26.43/3.69 fof(f11401,plain,(
% 26.43/3.69 ~spl0_341),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11400])).
% 26.43/3.69 fof(f11404,plain,(
% 26.43/3.69 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_323),
% 26.43/3.69 inference(destructive_equality_resolution,[status(esa)],[f10415])).
% 26.43/3.69 fof(f11405,plain,(
% 26.43/3.69 $false|~spl0_323),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f11404,f6870])).
% 26.43/3.69 fof(f11406,plain,(
% 26.43/3.69 ~spl0_323),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11405])).
% 26.43/3.69 fof(f11407,plain,(
% 26.43/3.69 $false|~spl0_321),
% 26.43/3.69 inference(destructive_equality_resolution,[status(esa)],[f10389])).
% 26.43/3.69 fof(f11408,plain,(
% 26.43/3.69 ~spl0_321),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11407])).
% 26.43/3.69 fof(f11418,plain,(
% 26.43/3.69 $false|~spl0_125),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f6634,f5702])).
% 26.43/3.69 fof(f11419,plain,(
% 26.43/3.69 ~spl0_125),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11418])).
% 26.43/3.69 fof(f11441,plain,(
% 26.43/3.69 spl0_365 <=> ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f11442,plain,(
% 26.43/3.69 ![X0,X1]: (~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)=v_d____|~spl0_365)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f11441])).
% 26.43/3.69 fof(f11453,plain,(
% 26.43/3.69 $false|~spl0_365),
% 26.43/3.69 inference(backward_subsumption_resolution,[status(thm)],[f5117,f11442])).
% 26.43/3.69 fof(f11454,plain,(
% 26.43/3.69 ~spl0_365),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11453])).
% 26.43/3.69 fof(f11582,plain,(
% 26.43/3.69 spl0_370 <=> class_Rings_Olinordered__semidom(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f11584,plain,(
% 26.43/3.69 ~class_Rings_Olinordered__semidom(tc_Nat_Onat)|spl0_370),
% 26.43/3.69 inference(component_clause,[status(thm)],[f11582])).
% 26.43/3.69 fof(f11595,plain,(
% 26.43/3.69 $false|spl0_370),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f11584,f4587])).
% 26.43/3.69 fof(f11596,plain,(
% 26.43/3.69 spl0_370),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11595])).
% 26.43/3.69 fof(f11896,plain,(
% 26.43/3.69 spl0_377 <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f11898,plain,(
% 26.43/3.69 ~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)|spl0_377),
% 26.43/3.69 inference(component_clause,[status(thm)],[f11896])).
% 26.43/3.69 fof(f11926,plain,(
% 26.43/3.69 $false|spl0_377),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f11898,f4637])).
% 26.43/3.69 fof(f11927,plain,(
% 26.43/3.69 spl0_377),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f11926])).
% 26.43/3.69 fof(f12547,plain,(
% 26.43/3.69 ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____)),v_d____)=v_d____|c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))=c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))|~spl0_24),
% 26.43/3.69 inference(paramodulation,[status(thm)],[f5262,f5313])).
% 26.43/3.69 fof(f12548,plain,(
% 26.43/3.69 ~spl0_78|spl0_23|~spl0_24),
% 26.43/3.69 inference(split_clause,[status(thm)],[f12547,f6017,f5258,f5261])).
% 26.43/3.69 fof(f13007,plain,(
% 26.43/3.69 spl0_414 <=> class_HOL_Oequal(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f13009,plain,(
% 26.43/3.69 ~class_HOL_Oequal(tc_Nat_Onat)|spl0_414),
% 26.43/3.69 inference(component_clause,[status(thm)],[f13007])).
% 26.43/3.69 fof(f13012,plain,(
% 26.43/3.69 spl0_415 <=> class_HOL_Oequal(tc_HOL_Obool)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f13014,plain,(
% 26.43/3.69 ~class_HOL_Oequal(tc_HOL_Obool)|spl0_415),
% 26.43/3.69 inference(component_clause,[status(thm)],[f13012])).
% 26.43/3.69 fof(f13017,plain,(
% 26.43/3.69 $false|spl0_415),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f13014,f4619])).
% 26.43/3.69 fof(f13018,plain,(
% 26.43/3.69 spl0_415),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f13017])).
% 26.43/3.69 fof(f13019,plain,(
% 26.43/3.69 $false|spl0_414),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f13009,f4612])).
% 26.43/3.69 fof(f13020,plain,(
% 26.43/3.69 spl0_414),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f13019])).
% 26.43/3.69 fof(f13527,plain,(
% 26.43/3.69 spl0_420 <=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f13529,plain,(
% 26.43/3.69 ~c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|spl0_420),
% 26.43/3.69 inference(component_clause,[status(thm)],[f13527])).
% 26.43/3.69 fof(f13532,plain,(
% 26.43/3.69 ~c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|spl0_420),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f3073,f13529])).
% 26.43/3.69 fof(f13533,plain,(
% 26.43/3.69 $false|spl0_420),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f13532])).
% 26.43/3.69 fof(f13534,plain,(
% 26.43/3.69 spl0_420),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f13533])).
% 26.43/3.69 fof(f13537,plain,(
% 26.43/3.69 spl0_421 <=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____)))=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f13539,plain,(
% 26.43/3.69 ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____)))=v_d____|spl0_421),
% 26.43/3.69 inference(component_clause,[status(thm)],[f13537])).
% 26.43/3.69 fof(f13542,plain,(
% 26.43/3.69 ~v_d____=v_d____|spl0_421),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f5117,f13539])).
% 26.43/3.69 fof(f13543,plain,(
% 26.43/3.69 $false|spl0_421),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f13542])).
% 26.43/3.69 fof(f13544,plain,(
% 26.43/3.69 spl0_421),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f13543])).
% 26.43/3.69 fof(f13640,plain,(
% 26.43/3.69 spl0_423 <=> c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f13642,plain,(
% 26.43/3.69 ~c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))|spl0_423),
% 26.43/3.69 inference(component_clause,[status(thm)],[f13640])).
% 26.43/3.69 fof(f13645,plain,(
% 26.43/3.69 ~c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))|spl0_423),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f3073,f13642])).
% 26.43/3.69 fof(f13646,plain,(
% 26.43/3.69 $false|spl0_423),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f13645])).
% 26.43/3.69 fof(f13647,plain,(
% 26.43/3.69 spl0_423),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f13646])).
% 26.43/3.69 fof(f13675,plain,(
% 26.43/3.69 spl0_425 <=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))))=v_d____),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f13677,plain,(
% 26.43/3.69 ~hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),sk0_0(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_d____,v_ds____))))=v_d____|spl0_425),
% 26.43/3.69 inference(component_clause,[status(thm)],[f13675])).
% 26.43/3.69 fof(f13680,plain,(
% 26.43/3.69 ~v_d____=v_d____|spl0_425),
% 26.43/3.69 inference(forward_demodulation,[status(thm)],[f5117,f13677])).
% 26.43/3.69 fof(f13681,plain,(
% 26.43/3.69 $false|spl0_425),
% 26.43/3.69 inference(trivial_equality_resolution,[status(esa)],[f13680])).
% 26.43/3.69 fof(f13682,plain,(
% 26.43/3.69 spl0_425),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f13681])).
% 26.43/3.69 fof(f14004,plain,(
% 26.43/3.69 spl0_437 <=> class_Orderings_Opreorder(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f14006,plain,(
% 26.43/3.69 ~class_Orderings_Opreorder(tc_Nat_Onat)|spl0_437),
% 26.43/3.69 inference(component_clause,[status(thm)],[f14004])).
% 26.43/3.69 fof(f14022,plain,(
% 26.43/3.69 $false|spl0_437),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f14006,f4599])).
% 26.43/3.69 fof(f14023,plain,(
% 26.43/3.69 spl0_437),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f14022])).
% 26.43/3.69 fof(f14077,plain,(
% 26.43/3.69 spl0_448 <=> class_Orderings_Olinorder(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f14079,plain,(
% 26.43/3.69 ~class_Orderings_Olinorder(tc_Nat_Onat)|spl0_448),
% 26.43/3.69 inference(component_clause,[status(thm)],[f14077])).
% 26.43/3.69 fof(f14082,plain,(
% 26.43/3.69 spl0_449 <=> class_Orderings_Oorder(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f14084,plain,(
% 26.43/3.69 ~class_Orderings_Oorder(tc_Nat_Onat)|spl0_449),
% 26.43/3.69 inference(component_clause,[status(thm)],[f14082])).
% 26.43/3.69 fof(f14089,plain,(
% 26.43/3.69 $false|spl0_449),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f14084,f4605])).
% 26.43/3.69 fof(f14090,plain,(
% 26.43/3.69 spl0_449),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f14089])).
% 26.43/3.69 fof(f14091,plain,(
% 26.43/3.69 $false|spl0_448),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f14079,f4600])).
% 26.43/3.69 fof(f14092,plain,(
% 26.43/3.69 spl0_448),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f14091])).
% 26.43/3.69 fof(f18895,plain,(
% 26.43/3.69 spl0_510 <=> class_Groups_Ozero(tc_Nat_Onat)),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f18897,plain,(
% 26.43/3.69 ~class_Groups_Ozero(tc_Nat_Onat)|spl0_510),
% 26.43/3.69 inference(component_clause,[status(thm)],[f18895])).
% 26.43/3.69 fof(f18903,plain,(
% 26.43/3.69 $false|spl0_510),
% 26.43/3.69 inference(forward_subsumption_resolution,[status(thm)],[f18897,f4609])).
% 26.43/3.69 fof(f18904,plain,(
% 26.43/3.69 spl0_510),
% 26.43/3.69 inference(contradiction_clause,[status(thm)],[f18903])).
% 26.43/3.69 fof(f25720,plain,(
% 26.43/3.69 spl0_633 <=> ~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),c_Nat_OSuc(X2))),
% 26.43/3.69 introduced(split_symbol_definition)).
% 26.43/3.69 fof(f25721,plain,(
% 26.43/3.69 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X0))|~spl0_633)),
% 26.43/3.69 inference(component_clause,[status(thm)],[f25720])).
% 26.43/3.72 fof(f25758,plain,(
% 26.43/3.72 $false|~spl0_633),
% 26.43/3.72 inference(forward_subsumption_resolution,[status(thm)],[f25721,f4872])).
% 26.43/3.72 fof(f25759,plain,(
% 26.43/3.72 ~spl0_633),
% 26.43/3.72 inference(contradiction_clause,[status(thm)],[f25758])).
% 26.43/3.72 fof(f27466,plain,(
% 26.43/3.72 spl0_670 <=> class_Orderings_Oorder(tc_HOL_Obool)),
% 26.43/3.72 introduced(split_symbol_definition)).
% 26.43/3.72 fof(f27468,plain,(
% 26.43/3.72 ~class_Orderings_Oorder(tc_HOL_Obool)|spl0_670),
% 26.43/3.72 inference(component_clause,[status(thm)],[f27466])).
% 26.43/3.72 fof(f27471,plain,(
% 26.43/3.72 spl0_671 <=> class_Orderings_Opreorder(tc_HOL_Obool)),
% 26.43/3.72 introduced(split_symbol_definition)).
% 26.43/3.72 fof(f27473,plain,(
% 26.43/3.72 ~class_Orderings_Opreorder(tc_HOL_Obool)|spl0_671),
% 26.43/3.72 inference(component_clause,[status(thm)],[f27471])).
% 26.43/3.72 fof(f27476,plain,(
% 26.43/3.72 $false|spl0_671),
% 26.43/3.72 inference(forward_subsumption_resolution,[status(thm)],[f27473,f4614])).
% 26.43/3.72 fof(f27477,plain,(
% 26.43/3.72 spl0_671),
% 26.43/3.72 inference(contradiction_clause,[status(thm)],[f27476])).
% 26.43/3.72 fof(f27478,plain,(
% 26.43/3.72 $false|spl0_670),
% 26.43/3.72 inference(forward_subsumption_resolution,[status(thm)],[f27468,f4615])).
% 26.43/3.72 fof(f27479,plain,(
% 26.43/3.72 spl0_670),
% 26.43/3.72 inference(contradiction_clause,[status(thm)],[f27478])).
% 26.43/3.72 fof(f27518,plain,(
% 26.43/3.72 ![X0,X1,X2]: (~X0=c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)|X1=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),v_d____)|~spl0_313)),
% 26.43/3.72 inference(backward_demodulation,[status(thm)],[f7660,f10026])).
% 26.43/3.72 fof(f27519,plain,(
% 26.43/3.72 ![X0,X1]: (X0=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),v_d____)|~spl0_313)),
% 26.43/3.72 inference(destructive_equality_resolution,[status(esa)],[f27518])).
% 26.43/3.72 fof(f28467,plain,(
% 26.43/3.72 ~v_d____=v_d____|~spl0_313|spl0_78),
% 26.43/3.72 inference(backward_demodulation,[status(thm)],[f27519,f6019])).
% 26.43/3.72 fof(f28468,plain,(
% 26.43/3.72 $false|~spl0_313|spl0_78),
% 26.43/3.72 inference(trivial_equality_resolution,[status(esa)],[f28467])).
% 26.43/3.72 fof(f28469,plain,(
% 26.43/3.72 ~spl0_313|spl0_78),
% 26.43/3.72 inference(contradiction_clause,[status(thm)],[f28468])).
% 26.43/3.72 fof(f28470,plain,(
% 26.43/3.72 $false),
% 26.43/3.72 inference(sat_refutation,[status(thm)],[f5113,f5115,f5265,f8110,f8375,f8377,f8934,f8960,f9230,f10019,f10029,f10394,f10682,f11325,f11361,f11371,f11401,f11406,f11408,f11419,f11454,f11596,f11927,f12548,f13018,f13020,f13534,f13544,f13647,f13682,f14023,f14090,f14092,f18904,f25759,f27477,f27479,f28469])).
% 26.43/3.72 % SZS output end CNFRefutation for theBenchmark.p
% 26.91/3.79 % Elapsed time: 3.493457 seconds
% 26.91/3.79 % CPU time: 26.887882 seconds
% 26.91/3.79 % Total memory used: 451.522 MB
% 26.91/3.79 % Net memory used: 445.979 MB
%------------------------------------------------------------------------------