TSTP Solution File: SWW285+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW285+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 : Wed May 31 12:44:36 EDT 2023
% Result : Theorem 3.60s 0.92s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW285+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue May 30 10:58:16 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.12/0.37 % Drodi V3.5.1
% 3.60/0.92 % Refutation found
% 3.60/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.60/0.92 % SZS output start CNFRefutation for theBenchmark
% 3.60/0.92 fof(f2,axiom,(
% 3.60/0.92 v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f11,axiom,(
% 3.60/0.92 (! [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) ) )),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f20,axiom,(
% 3.60/0.92 (! [V_a,T_a] :( class_Rings_Ocomm__semiring__0(T_a)=> c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f25,axiom,(
% 3.60/0.92 (! [V_qa_2,V_pa_2,V_a_2,T_a] :( class_Fields_Ofield(T_a)=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_qa_2)<=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)=> V_qa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_qa_2) ) ) ) ) )),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f31,axiom,(
% 3.60/0.92 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f34,axiom,(
% 3.60/0.92 c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f53,axiom,(
% 3.60/0.92 (! [V_x,V_n,V_p,T_a] :( class_Rings_Ocomm__semiring__1(T_a)=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ) )),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f84,axiom,(
% 3.60/0.92 (! [V_p,V_a,T_a] :( class_Rings_Oidom(T_a)=> ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)=> c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )& ( V_a != c_Groups_Ozero__class_Ozero(T_a)=> c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)) = c_Polynomial_Odegree(T_a,V_p) ) ) ) )),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f98,axiom,(
% 3.60/0.92 (! [V_n_2,V_a_2,T_a] :( ( class_Power_Opower(T_a)& class_Rings_Omult__zero(T_a)& class_Rings_Ono__zero__divisors(T_a)& class_Rings_Ozero__neq__one(T_a) )=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)<=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) )),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1099,axiom,(
% 3.60/0.92 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1101,axiom,(
% 3.60/0.92 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1102,axiom,(
% 3.60/0.92 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1107,axiom,(
% 3.60/0.92 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1113,axiom,(
% 3.60/0.92 class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1118,axiom,(
% 3.60/0.92 class_Fields_Ofield(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1119,axiom,(
% 3.60/0.92 class_Power_Opower(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1122,axiom,(
% 3.60/0.92 class_Rings_Oidom(tc_Complex_Ocomplex) ),
% 3.60/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.60/0.92 fof(f1185,plain,(
% 3.60/0.92 v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f2])).
% 3.60/0.92 fof(f1221,plain,(
% 3.60/0.92 ![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))),
% 3.60/0.92 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 3.60/0.92 fof(f1222,plain,(
% 3.60/0.92 ![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)))),
% 3.60/0.92 inference(miniscoping,[status(esa)],[f1221])).
% 3.60/0.92 fof(f1223,plain,(
% 3.60/0.92 ![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))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1222])).
% 3.60/0.92 fof(f1261,plain,(
% 3.60/0.92 ![V_a,T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),
% 3.60/0.92 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 3.60/0.92 fof(f1262,plain,(
% 3.60/0.92 ![T_a]: (~class_Rings_Ocomm__semiring__0(T_a)|(![V_a]: c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),
% 3.60/0.92 inference(miniscoping,[status(esa)],[f1261])).
% 3.60/0.92 fof(f1263,plain,(
% 3.60/0.92 ![X0,X1]: (~class_Rings_Ocomm__semiring__0(X0)|c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1262])).
% 3.60/0.92 fof(f1281,plain,(
% 3.60/0.92 ![V_qa_2,V_pa_2,V_a_2,T_a]: (~class_Fields_Ofield(T_a)|(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_qa_2)<=>((~V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_qa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))&(V_a_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_qa_2)))))),
% 3.60/0.92 inference(pre_NNF_transformation,[status(esa)],[f25])).
% 3.60/0.92 fof(f1282,plain,(
% 3.60/0.92 ![V_qa_2,V_pa_2,V_a_2,T_a]: (~class_Fields_Ofield(T_a)|((~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_qa_2)|((~V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_qa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))&(V_a_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_qa_2))))&(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_qa_2)|((V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~V_qa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|(~V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_qa_2))))))),
% 3.60/0.92 inference(NNF_transformation,[status(esa)],[f1281])).
% 3.60/0.92 fof(f1283,plain,(
% 3.60/0.92 ![T_a]: (~class_Fields_Ofield(T_a)|((![V_qa_2,V_pa_2,V_a_2]: (~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_qa_2)|((~V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_qa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))&(V_a_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_qa_2)))))&(![V_qa_2,V_pa_2,V_a_2]: (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_qa_2)|((V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~V_qa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|(~V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_qa_2)))))))),
% 3.60/0.92 inference(miniscoping,[status(esa)],[f1282])).
% 3.60/0.92 fof(f1284,plain,(
% 3.60/0.92 ![X0,X1,X2,X3]: (~class_Fields_Ofield(X0)|~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),X3)|~X1=c_Groups_Ozero__class_Ozero(X0)|X3=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1283])).
% 3.60/0.92 fof(f1309,plain,(
% 3.60/0.92 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f31])).
% 3.60/0.92 fof(f1316,plain,(
% 3.60/0.92 c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f34])).
% 3.60/0.92 fof(f1378,plain,(
% 3.60/0.92 ![V_x,V_n,V_p,T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n))),
% 3.60/0.92 inference(pre_NNF_transformation,[status(esa)],[f53])).
% 3.60/0.92 fof(f1379,plain,(
% 3.60/0.92 ![T_a]: (~class_Rings_Ocomm__semiring__1(T_a)|(![V_x,V_n,V_p]: hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)))),
% 3.60/0.92 inference(miniscoping,[status(esa)],[f1378])).
% 3.60/0.92 fof(f1380,plain,(
% 3.60/0.92 ![X0,X1,X2,X3]: (~class_Rings_Ocomm__semiring__1(X0)|hAPP(c_Polynomial_Opoly(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X0)),X1),X2)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(X0),hAPP(c_Polynomial_Opoly(X0,X1),X3)),X2))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1379])).
% 3.60/0.92 fof(f1474,plain,(
% 3.60/0.92 ![V_p,V_a,T_a]: (~class_Rings_Oidom(T_a)|((~V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Polynomial_Odegree(T_a,V_p))))),
% 3.60/0.92 inference(pre_NNF_transformation,[status(esa)],[f84])).
% 3.60/0.92 fof(f1475,plain,(
% 3.60/0.92 ![T_a]: (~class_Rings_Oidom(T_a)|((![V_a]: (~V_a=c_Groups_Ozero__class_Ozero(T_a)|(![V_p]: c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(![V_a]: (V_a=c_Groups_Ozero__class_Ozero(T_a)|(![V_p]: c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Polynomial_Odegree(T_a,V_p))))))),
% 3.60/0.92 inference(miniscoping,[status(esa)],[f1474])).
% 3.60/0.92 fof(f1476,plain,(
% 3.60/0.92 ![X0,X1,X2]: (~class_Rings_Oidom(X0)|~X1=c_Groups_Ozero__class_Ozero(X0)|c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,X1,X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1475])).
% 3.60/0.92 fof(f1523,plain,(
% 3.60/0.92 ![V_n_2,V_a_2,T_a]: ((((~class_Power_Opower(T_a)|~class_Rings_Omult__zero(T_a))|~class_Rings_Ono__zero__divisors(T_a))|~class_Rings_Ozero__neq__one(T_a))|(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)<=>(V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 3.60/0.92 inference(pre_NNF_transformation,[status(esa)],[f98])).
% 3.60/0.92 fof(f1524,plain,(
% 3.60/0.92 ![V_n_2,V_a_2,T_a]: ((((~class_Power_Opower(T_a)|~class_Rings_Omult__zero(T_a))|~class_Rings_Ono__zero__divisors(T_a))|~class_Rings_Ozero__neq__one(T_a))|((~hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|(V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|(~V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 3.60/0.92 inference(NNF_transformation,[status(esa)],[f1523])).
% 3.60/0.92 fof(f1525,plain,(
% 3.60/0.92 ![T_a]: ((((~class_Power_Opower(T_a)|~class_Rings_Omult__zero(T_a))|~class_Rings_Ono__zero__divisors(T_a))|~class_Rings_Ozero__neq__one(T_a))|((![V_n_2,V_a_2]: (~hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|(V_a_2=c_Groups_Ozero__class_Ozero(T_a)&~V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(![V_n_2,V_a_2]: (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|(~V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 3.60/0.92 inference(miniscoping,[status(esa)],[f1524])).
% 3.60/0.92 fof(f1527,plain,(
% 3.60/0.92 ![X0,X1,X2]: (~class_Power_Opower(X0)|~class_Rings_Omult__zero(X0)|~class_Rings_Ono__zero__divisors(X0)|~class_Rings_Ozero__neq__one(X0)|~hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)=c_Groups_Ozero__class_Ozero(X0)|~X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1525])).
% 3.60/0.92 fof(f4514,plain,(
% 3.60/0.92 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1099])).
% 3.60/0.92 fof(f4516,plain,(
% 3.60/0.92 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1101])).
% 3.60/0.92 fof(f4517,plain,(
% 3.60/0.92 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1102])).
% 3.60/0.92 fof(f4522,plain,(
% 3.60/0.92 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1107])).
% 3.60/0.92 fof(f4528,plain,(
% 3.60/0.92 class_Rings_Omult__zero(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1113])).
% 3.60/0.92 fof(f4533,plain,(
% 3.60/0.92 class_Fields_Ofield(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1118])).
% 3.60/0.92 fof(f4534,plain,(
% 3.60/0.92 class_Power_Opower(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1119])).
% 3.60/0.92 fof(f4537,plain,(
% 3.60/0.92 class_Rings_Oidom(tc_Complex_Ocomplex)),
% 3.60/0.92 inference(cnf_transformation,[status(esa)],[f1122])).
% 3.60/0.92 fof(f4697,plain,(
% 3.60/0.92 ![X0,X1,X2]: (~class_Fields_Ofield(X0)|~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1),X2)|X2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))),
% 3.60/0.92 inference(destructive_equality_resolution,[status(esa)],[f1284])).
% 3.60/0.92 fof(f4704,plain,(
% 3.60/0.92 ![X0,X1]: (~class_Rings_Oidom(X0)|c_Polynomial_Odegree(X0,c_Polynomial_Osmult(X0,c_Groups_Ozero__class_Ozero(X0),X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 3.60/0.92 inference(destructive_equality_resolution,[status(esa)],[f1476])).
% 3.60/0.92 fof(f4705,plain,(
% 3.60/0.92 ![X0,X1]: (~class_Power_Opower(X0)|~class_Rings_Omult__zero(X0)|~class_Rings_Ono__zero__divisors(X0)|~class_Rings_Ozero__neq__one(X0)|~hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(X0))),
% 3.60/0.92 inference(destructive_equality_resolution,[status(esa)],[f1527])).
% 3.60/0.92 fof(f4849,plain,(
% 3.60/0.92 spl0_4 <=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f4851,plain,(
% 3.60/0.92 ~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)|spl0_4),
% 3.60/0.92 inference(component_clause,[status(thm)],[f4849])).
% 3.60/0.92 fof(f4860,plain,(
% 3.60/0.92 spl0_7 <=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f4861,plain,(
% 3.60/0.92 ![X0]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|~spl0_7)),
% 3.60/0.92 inference(component_clause,[status(thm)],[f4860])).
% 3.60/0.92 fof(f4924,plain,(
% 3.60/0.92 ![X0]: (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 3.60/0.92 inference(paramodulation,[status(thm)],[f1185,f1223])).
% 3.60/0.92 fof(f4925,plain,(
% 3.60/0.92 ~spl0_4|spl0_7),
% 3.60/0.92 inference(split_clause,[status(thm)],[f4924,f4849,f4860])).
% 3.60/0.92 fof(f4947,plain,(
% 3.60/0.92 spl0_21 <=> class_Rings_Oidom(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f4949,plain,(
% 3.60/0.92 ~class_Rings_Oidom(tc_Complex_Ocomplex)|spl0_21),
% 3.60/0.92 inference(component_clause,[status(thm)],[f4947])).
% 3.60/0.92 fof(f4950,plain,(
% 3.60/0.92 spl0_22 <=> c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f4951,plain,(
% 3.60/0.92 ![X0]: (c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))|~spl0_22)),
% 3.60/0.92 inference(component_clause,[status(thm)],[f4950])).
% 3.60/0.92 fof(f4967,plain,(
% 3.60/0.92 $false|spl0_4),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f4517,f4851])).
% 3.60/0.92 fof(f4968,plain,(
% 3.60/0.92 spl0_4),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f4967])).
% 3.60/0.92 fof(f4989,plain,(
% 3.60/0.92 ![X0]: (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)|c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 3.60/0.92 inference(paramodulation,[status(thm)],[f1185,f1263])).
% 3.60/0.92 fof(f4990,plain,(
% 3.60/0.92 ~spl0_4|spl0_22),
% 3.60/0.92 inference(split_clause,[status(thm)],[f4989,f4849,f4950])).
% 3.60/0.92 fof(f4991,plain,(
% 3.60/0.92 ![X0]: (c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_p)=v_p|~spl0_22)),
% 3.60/0.92 inference(forward_demodulation,[status(thm)],[f1185,f4951])).
% 3.60/0.92 fof(f5251,plain,(
% 3.60/0.92 spl0_63 <=> class_Fields_Ofield(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f5253,plain,(
% 3.60/0.92 ~class_Fields_Ofield(tc_Complex_Ocomplex)|spl0_63),
% 3.60/0.92 inference(component_clause,[status(thm)],[f5251])).
% 3.60/0.92 fof(f5254,plain,(
% 3.60/0.92 spl0_64 <=> ~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,X0)|X0=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f5255,plain,(
% 3.60/0.92 ![X0]: (~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,X0)|X0=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))|~spl0_64)),
% 3.60/0.92 inference(component_clause,[status(thm)],[f5254])).
% 3.60/0.92 fof(f5257,plain,(
% 3.60/0.92 ![X0]: (~class_Fields_Ofield(tc_Complex_Ocomplex)|~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,X0)|X0=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))|~spl0_22)),
% 3.60/0.92 inference(paramodulation,[status(thm)],[f4991,f4697])).
% 3.60/0.92 fof(f5258,plain,(
% 3.60/0.92 ~spl0_63|spl0_64|~spl0_22),
% 3.60/0.92 inference(split_clause,[status(thm)],[f5257,f5251,f5254,f4950])).
% 3.60/0.92 fof(f5267,plain,(
% 3.60/0.92 $false|spl0_63),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f5253,f4533])).
% 3.60/0.92 fof(f5268,plain,(
% 3.60/0.92 spl0_63),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f5267])).
% 3.60/0.92 fof(f5269,plain,(
% 3.60/0.92 ![X0]: (~c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,X0)|X0=v_p|~spl0_64)),
% 3.60/0.92 inference(forward_demodulation,[status(thm)],[f1185,f5255])).
% 3.60/0.92 fof(f5293,plain,(
% 3.60/0.92 $false|spl0_21),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f4949,f4537])).
% 3.60/0.92 fof(f5294,plain,(
% 3.60/0.92 spl0_21),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f5293])).
% 3.60/0.92 fof(f5861,plain,(
% 3.60/0.92 c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),v_p,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____))),
% 3.60/0.92 inference(forward_demodulation,[status(thm)],[f1309,f1316])).
% 3.60/0.92 fof(f5862,plain,(
% 3.60/0.92 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____)=v_p|~spl0_64),
% 3.60/0.92 inference(resolution,[status(thm)],[f5861,f5269])).
% 3.60/0.92 fof(f5874,plain,(
% 3.60/0.92 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))=v_p|~spl0_64),
% 3.60/0.92 inference(backward_demodulation,[status(thm)],[f5862,f1309])).
% 3.60/0.92 fof(f7108,plain,(
% 3.60/0.92 spl0_224 <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f7110,plain,(
% 3.60/0.92 ~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)|spl0_224),
% 3.60/0.92 inference(component_clause,[status(thm)],[f7108])).
% 3.60/0.92 fof(f8295,plain,(
% 3.60/0.92 spl0_368 <=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f8296,plain,(
% 3.60/0.92 ![X0]: (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))|~spl0_368)),
% 3.60/0.92 inference(component_clause,[status(thm)],[f8295])).
% 3.60/0.92 fof(f8298,plain,(
% 3.60/0.92 ![X0]: (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))|~spl0_64)),
% 3.60/0.92 inference(paramodulation,[status(thm)],[f5874,f1380])).
% 3.60/0.92 fof(f8299,plain,(
% 3.60/0.92 ~spl0_224|spl0_368|~spl0_64),
% 3.60/0.92 inference(split_clause,[status(thm)],[f8298,f7108,f8295,f5254])).
% 3.60/0.92 fof(f8300,plain,(
% 3.60/0.92 $false|spl0_224),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f7110,f4516])).
% 3.60/0.92 fof(f8301,plain,(
% 3.60/0.92 spl0_224),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f8300])).
% 3.60/0.92 fof(f8302,plain,(
% 3.60/0.92 ![X0]: (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))|~spl0_7|~spl0_368)),
% 3.60/0.92 inference(forward_demodulation,[status(thm)],[f4861,f8296])).
% 3.60/0.92 fof(f11061,plain,(
% 3.60/0.92 spl0_611 <=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f11062,plain,(
% 3.60/0.92 c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_611),
% 3.60/0.92 inference(component_clause,[status(thm)],[f11061])).
% 3.60/0.92 fof(f11150,plain,(
% 3.60/0.92 ![X0]: (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_611|~spl0_7|~spl0_368)),
% 3.60/0.92 inference(backward_demodulation,[status(thm)],[f11062,f8302])).
% 3.60/0.92 fof(f13726,plain,(
% 3.60/0.92 ~class_Rings_Oidom(tc_Complex_Ocomplex)|c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~spl0_22),
% 3.60/0.92 inference(paramodulation,[status(thm)],[f4991,f4704])).
% 3.60/0.92 fof(f13727,plain,(
% 3.60/0.92 ~spl0_21|spl0_611|~spl0_22),
% 3.60/0.92 inference(split_clause,[status(thm)],[f13726,f4947,f11061,f4950])).
% 3.60/0.92 fof(f19710,plain,(
% 3.60/0.92 spl0_1572 <=> class_Power_Opower(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f19712,plain,(
% 3.60/0.92 ~class_Power_Opower(tc_Complex_Ocomplex)|spl0_1572),
% 3.60/0.92 inference(component_clause,[status(thm)],[f19710])).
% 3.60/0.92 fof(f19713,plain,(
% 3.60/0.92 spl0_1573 <=> class_Rings_Omult__zero(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f19715,plain,(
% 3.60/0.92 ~class_Rings_Omult__zero(tc_Complex_Ocomplex)|spl0_1573),
% 3.60/0.92 inference(component_clause,[status(thm)],[f19713])).
% 3.60/0.92 fof(f19716,plain,(
% 3.60/0.92 spl0_1574 <=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f19718,plain,(
% 3.60/0.92 ~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)|spl0_1574),
% 3.60/0.92 inference(component_clause,[status(thm)],[f19716])).
% 3.60/0.92 fof(f19719,plain,(
% 3.60/0.92 spl0_1575 <=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 3.60/0.92 introduced(split_symbol_definition)).
% 3.60/0.92 fof(f19721,plain,(
% 3.60/0.92 ~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)|spl0_1575),
% 3.60/0.92 inference(component_clause,[status(thm)],[f19719])).
% 3.60/0.92 fof(f19740,plain,(
% 3.60/0.92 $false|spl0_1575),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f19721,f4522])).
% 3.60/0.92 fof(f19741,plain,(
% 3.60/0.92 spl0_1575),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f19740])).
% 3.60/0.92 fof(f19742,plain,(
% 3.60/0.92 $false|spl0_1574),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f19718,f4514])).
% 3.60/0.92 fof(f19743,plain,(
% 3.60/0.92 spl0_1574),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f19742])).
% 3.60/0.92 fof(f19744,plain,(
% 3.60/0.92 $false|spl0_1573),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f19715,f4528])).
% 3.60/0.92 fof(f19745,plain,(
% 3.60/0.92 spl0_1573),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f19744])).
% 3.60/0.92 fof(f19746,plain,(
% 3.60/0.92 $false|spl0_1572),
% 3.60/0.92 inference(forward_subsumption_resolution,[status(thm)],[f19712,f4534])).
% 3.60/0.92 fof(f19747,plain,(
% 3.60/0.92 spl0_1572),
% 3.60/0.92 inference(contradiction_clause,[status(thm)],[f19746])).
% 3.60/0.92 fof(f19748,plain,(
% 3.60/0.92 ~class_Power_Opower(tc_Complex_Ocomplex)|~class_Rings_Omult__zero(tc_Complex_Ocomplex)|~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)|~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)|~spl0_611|~spl0_7|~spl0_368),
% 3.60/0.92 inference(resolution,[status(thm)],[f4705,f11150])).
% 3.60/0.92 fof(f19749,plain,(
% 3.60/0.92 ~spl0_1572|~spl0_1573|~spl0_1574|~spl0_1575|~spl0_611|~spl0_7|~spl0_368),
% 3.60/0.92 inference(split_clause,[status(thm)],[f19748,f19710,f19713,f19716,f19719,f11061,f4860,f8295])).
% 3.60/0.92 fof(f19754,plain,(
% 3.60/0.92 $false),
% 3.81/0.97 inference(sat_refutation,[status(thm)],[f4925,f4968,f4990,f5258,f5268,f5294,f8299,f8301,f13727,f19741,f19743,f19745,f19747,f19749])).
% 3.81/0.97 % SZS output end CNFRefutation for theBenchmark.p
% 3.81/0.97 % Elapsed time: 0.679936 seconds
% 3.81/0.97 % CPU time: 3.971067 seconds
% 3.81/0.97 % Memory used: 188.437 MB
%------------------------------------------------------------------------------