TSTP Solution File: SWW233+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW233+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:44:31 EDT 2023
% Result : Theorem 21.75s 3.20s
% Output : CNFRefutation 22.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW233+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 : n029.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 : Tue May 30 11:13:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.43 % Drodi V3.5.1
% 21.75/3.20 % Refutation found
% 21.75/3.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 21.75/3.20 % SZS output start CNFRefutation for theBenchmark
% 21.75/3.20 fof(f4,axiom,(
% 21.75/3.20 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f6,axiom,(
% 21.75/3.20 (! [V_w,V_z] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f7,axiom,(
% 21.75/3.20 (! [V_k,V_j,V_i] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f8,axiom,(
% 21.75/3.20 (! [V_w,V_z] :( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)=> V_z = V_w ) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f14,axiom,(
% 21.75/3.20 v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f31,axiom,(
% 21.75/3.20 (! [V_a,T_a] :( class_Groups_Oordered__ab__group__add__abs(T_a)=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f33,axiom,(
% 21.75/3.20 (! [V_a,T_a] :( class_Groups_Oordered__ab__group__add__abs(T_a)=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f34,axiom,(
% 21.75/3.20 (! [T_a] :( class_Rings_Olinordered__semidom(T_a)=> ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f38,axiom,(
% 21.75/3.20 (! [V_b,V_a,T_a] :( class_Groups_Oordered__comm__monoid__add(T_a)=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f40,axiom,(
% 21.75/3.20 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f44,axiom,(
% 21.75/3.20 (! [V_c,V_a,V_b,T_a] :( class_Groups_Ocancel__semigroup__add(T_a)=> ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)=> V_b = V_c ) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f55,axiom,(
% 21.75/3.20 (! [V_a,T_a] :( class_Groups_Ocomm__monoid__add(T_a)=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f70,axiom,(
% 21.75/3.20 (! [V_a,T_a] :( class_Groups_Oordered__ab__group__add__abs(T_a)=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f77,axiom,(
% 21.75/3.20 (! [V_c,V_b,V_a,T_a] :( class_Groups_Oordered__comm__monoid__add(T_a)=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) )),
% 21.75/3.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.20 fof(f190,axiom,(
% 21.75/3.20 (! [V_y_2,V_x_2,V_za_2] :( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) )),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f191,axiom,(
% 21.75/3.22 (! [V_y_2,V_x_2,V_za_2] :( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) )),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f758,axiom,(
% 21.75/3.22 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f770,axiom,(
% 21.75/3.22 (! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) )),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1008,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1012,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1016,axiom,(
% 21.75/3.22 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1024,axiom,(
% 21.75/3.22 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1029,axiom,(
% 21.75/3.22 class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1033,axiom,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1035,axiom,(
% 21.75/3.22 class_Rings_Olinordered__idom(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1047,axiom,(
% 21.75/3.22 class_Groups_Omonoid__add(tc_Int_Oint) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1066,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1069,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1071,axiom,(
% 21.75/3.22 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1074,axiom,(
% 21.75/3.22 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1079,axiom,(
% 21.75/3.22 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1082,axiom,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1091,axiom,(
% 21.75/3.22 class_Groups_Omonoid__add(tc_Nat_Onat) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1105,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1111,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1112,axiom,(
% 21.75/3.22 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1114,axiom,(
% 21.75/3.22 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1125,axiom,(
% 21.75/3.22 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1127,axiom,(
% 21.75/3.22 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1134,axiom,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1136,axiom,(
% 21.75/3.22 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1142,axiom,(
% 21.75/3.22 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1178,axiom,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1261,conjecture,(
% 21.75/3.22 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
% 21.75/3.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.75/3.22 fof(f1262,negated_conjecture,(
% 21.75/3.22 ~(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) )),
% 21.75/3.22 inference(negated_conjecture,[status(cth)],[f1261])).
% 21.75/3.22 fof(f1270,plain,(
% 21.75/3.22 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f4])).
% 21.75/3.22 fof(f1272,plain,(
% 21.75/3.22 ![X0,X1]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f6])).
% 21.75/3.22 fof(f1273,plain,(
% 21.75/3.22 ![V_k,V_j,V_i]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 21.75/3.22 fof(f1274,plain,(
% 21.75/3.22 ![V_j,V_i]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)|(![V_k]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1273])).
% 21.75/3.22 fof(f1275,plain,(
% 21.75/3.22 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X2))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1274])).
% 21.75/3.22 fof(f1276,plain,(
% 21.75/3.22 ![V_w,V_z]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)|(~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)|V_z=V_w))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 21.75/3.22 fof(f1277,plain,(
% 21.75/3.22 ![X0,X1]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)|X0=X1)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1276])).
% 21.75/3.22 fof(f1299,plain,(
% 21.75/3.22 ~v_cs____=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f14])).
% 21.75/3.22 fof(f1351,plain,(
% 21.75/3.22 ![V_a,T_a]: (~class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 21.75/3.22 fof(f1352,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Oordered__ab__group__add__abs(T_a)|(![V_a]: c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1351])).
% 21.75/3.22 fof(f1353,plain,(
% 21.75/3.22 ![X0,X1]: (~class_Groups_Oordered__ab__group__add__abs(X0)|c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1)))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1352])).
% 21.75/3.22 fof(f1359,plain,(
% 21.75/3.22 ![V_a,T_a]: (~class_Groups_Oordered__ab__group__add__abs(T_a)|(~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 21.75/3.22 fof(f1360,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Oordered__ab__group__add__abs(T_a)|(![V_a]: (~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1359])).
% 21.75/3.22 fof(f1361,plain,(
% 21.75/3.22 ![X0,X1]: (~class_Groups_Oordered__ab__group__add__abs(X0)|~c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)|c_Groups_Oabs__class_Oabs(X0,X1)=X1)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1360])).
% 21.75/3.22 fof(f1362,plain,(
% 21.75/3.22 ![T_a]: (~class_Rings_Olinordered__semidom(T_a)|~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 21.75/3.22 fof(f1363,plain,(
% 21.75/3.22 ![X0]: (~class_Rings_Olinordered__semidom(X0)|~c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1362])).
% 21.75/3.22 fof(f1376,plain,(
% 21.75/3.22 ![V_b,V_a,T_a]: (~class_Groups_Oordered__comm__monoid__add(T_a)|(~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|(~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 21.75/3.22 fof(f1377,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Oordered__comm__monoid__add(T_a)|(![V_a]: (~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|(![V_b]: (~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1376])).
% 21.75/3.22 fof(f1378,plain,(
% 21.75/3.22 ![X0,X1,X2]: (~class_Groups_Oordered__comm__monoid__add(X0)|~c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)|~c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)|c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,X1,X2)))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1377])).
% 21.75/3.22 fof(f1380,plain,(
% 21.75/3.22 ~c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f40])).
% 21.75/3.22 fof(f1390,plain,(
% 21.75/3.22 ![V_c,V_a,V_b,T_a]: (~class_Groups_Ocancel__semigroup__add(T_a)|(~c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f44])).
% 21.75/3.22 fof(f1391,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Ocancel__semigroup__add(T_a)|(![V_c,V_b]: ((![V_a]: ~c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a))|V_b=V_c)))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1390])).
% 21.75/3.22 fof(f1392,plain,(
% 21.75/3.22 ![X0,X1,X2,X3]: (~class_Groups_Ocancel__semigroup__add(X0)|~c_Groups_Oplus__class_Oplus(X0,X1,X2)=c_Groups_Oplus__class_Oplus(X0,X3,X2)|X1=X3)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1391])).
% 21.75/3.22 fof(f1431,plain,(
% 21.75/3.22 ![V_a,T_a]: (~class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a)),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f55])).
% 21.75/3.22 fof(f1432,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Ocomm__monoid__add(T_a)|(![V_a]: c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1431])).
% 21.75/3.22 fof(f1433,plain,(
% 21.75/3.22 ![X0,X1]: (~class_Groups_Ocomm__monoid__add(X0)|c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1)=X1)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1432])).
% 21.75/3.22 fof(f1480,plain,(
% 21.75/3.22 ![V_a,T_a]: (~class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f70])).
% 21.75/3.22 fof(f1481,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Oordered__ab__group__add__abs(T_a)|(![V_a]: c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1480])).
% 21.75/3.22 fof(f1482,plain,(
% 21.75/3.22 ![X0,X1]: (~class_Groups_Oordered__ab__group__add__abs(X0)|c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Oabs__class_Oabs(X0,X1)))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1481])).
% 21.75/3.22 fof(f1500,plain,(
% 21.75/3.22 ![V_c,V_b,V_a,T_a]: (~class_Groups_Oordered__comm__monoid__add(T_a)|(~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|(~c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f77])).
% 21.75/3.22 fof(f1501,plain,(
% 21.75/3.22 ![T_a]: (~class_Groups_Oordered__comm__monoid__add(T_a)|(![V_a]: (~c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|(![V_c,V_b]: (~c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1500])).
% 21.75/3.22 fof(f1502,plain,(
% 21.75/3.22 ![X0,X1,X2,X3]: (~class_Groups_Oordered__comm__monoid__add(X0)|~c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)|~c_Orderings_Oord__class_Oless__eq(X0,X2,X3)|c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Oplus__class_Oplus(X0,X1,X3)))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1501])).
% 21.75/3.22 fof(f1902,plain,(
% 21.75/3.22 ![V_y_2,V_x_2,V_za_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f190])).
% 21.75/3.22 fof(f1903,plain,(
% 21.75/3.22 ![V_y_2,V_x_2,V_za_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))))),
% 21.75/3.22 inference(NNF_transformation,[status(esa)],[f1902])).
% 21.75/3.22 fof(f1904,plain,(
% 21.75/3.22 ![V_za_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|((![V_y_2,V_x_2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))&(![V_y_2,V_x_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1903])).
% 21.75/3.22 fof(f1905,plain,(
% 21.75/3.22 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1904])).
% 21.75/3.22 fof(f1907,plain,(
% 21.75/3.22 ![V_y_2,V_x_2,V_za_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))<=>c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))),
% 21.75/3.22 inference(pre_NNF_transformation,[status(esa)],[f191])).
% 21.75/3.22 fof(f1908,plain,(
% 21.75/3.22 ![V_y_2,V_x_2,V_za_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|((~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))&(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))))),
% 21.75/3.22 inference(NNF_transformation,[status(esa)],[f1907])).
% 21.75/3.22 fof(f1909,plain,(
% 21.75/3.22 ![V_za_2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|((![V_y_2,V_x_2]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))&(![V_y_2,V_x_2]: (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))))),
% 21.75/3.22 inference(miniscoping,[status(esa)],[f1908])).
% 21.75/3.22 fof(f1910,plain,(
% 21.75/3.22 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1909])).
% 21.75/3.22 fof(f3677,plain,(
% 21.75/3.22 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f758])).
% 21.75/3.22 fof(f3696,plain,(
% 21.75/3.22 ![X0]: (~c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(X0))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f770])).
% 21.75/3.22 fof(f4402,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1008])).
% 21.75/3.22 fof(f4406,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1012])).
% 21.75/3.22 fof(f4410,plain,(
% 21.75/3.22 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1016])).
% 21.75/3.22 fof(f4418,plain,(
% 21.75/3.22 class_Groups_Ocancel__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1024])).
% 21.75/3.22 fof(f4423,plain,(
% 21.75/3.22 class_Groups_Oab__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1029])).
% 21.75/3.22 fof(f4427,plain,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1033])).
% 21.75/3.22 fof(f4429,plain,(
% 21.75/3.22 class_Rings_Olinordered__idom(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1035])).
% 21.75/3.22 fof(f4441,plain,(
% 21.75/3.22 class_Groups_Omonoid__add(tc_Int_Oint)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1047])).
% 21.75/3.22 fof(f4460,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1066])).
% 21.75/3.22 fof(f4463,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1069])).
% 21.75/3.22 fof(f4465,plain,(
% 21.75/3.22 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1071])).
% 21.75/3.22 fof(f4468,plain,(
% 21.75/3.22 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1074])).
% 21.75/3.22 fof(f4473,plain,(
% 21.75/3.22 class_Groups_Oab__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1079])).
% 21.75/3.22 fof(f4476,plain,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1082])).
% 21.75/3.22 fof(f4485,plain,(
% 21.75/3.22 class_Groups_Omonoid__add(tc_Nat_Onat)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1091])).
% 21.75/3.22 fof(f4499,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1105])).
% 21.75/3.22 fof(f4505,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1111])).
% 21.75/3.22 fof(f4506,plain,(
% 21.75/3.22 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1112])).
% 21.75/3.22 fof(f4508,plain,(
% 21.75/3.22 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1114])).
% 21.75/3.22 fof(f4519,plain,(
% 21.75/3.22 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1125])).
% 21.75/3.22 fof(f4521,plain,(
% 21.75/3.22 class_Rings_Olinordered__semidom(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1127])).
% 21.75/3.22 fof(f4528,plain,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1134])).
% 21.75/3.22 fof(f4530,plain,(
% 21.75/3.22 class_Rings_Olinordered__idom(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1136])).
% 21.75/3.22 fof(f4536,plain,(
% 21.75/3.22 class_Rings_Ozero__neq__one(tc_RealDef_Oreal)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1142])).
% 21.75/3.22 fof(f4572,plain,(
% 21.75/3.22 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex)),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1178])).
% 21.75/3.22 fof(f4713,plain,(
% 21.75/3.22 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
% 21.75/3.22 inference(cnf_transformation,[status(esa)],[f1262])).
% 21.75/3.22 fof(f4777,plain,(
% 21.75/3.22 spl0_0 <=> v_cs____=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f4778,plain,(
% 21.75/3.22 v_cs____=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))|~spl0_0),
% 21.75/3.22 inference(component_clause,[status(thm)],[f4777])).
% 21.75/3.22 fof(f4920,plain,(
% 21.75/3.22 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)),
% 21.75/3.22 inference(resolution,[status(thm)],[f1272,f4713])).
% 21.75/3.22 fof(f4921,plain,(
% 21.75/3.22 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,v_r____))),
% 21.75/3.22 inference(resolution,[status(thm)],[f1275,f4920])).
% 21.75/3.22 fof(f4924,plain,(
% 21.75/3.22 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____)),
% 21.75/3.22 inference(resolution,[status(thm)],[f4921,f1270])).
% 21.75/3.22 fof(f4933,plain,(
% 21.75/3.22 ![X0]: (~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,v_r____))),
% 21.75/3.22 inference(resolution,[status(thm)],[f4924,f1275])).
% 21.75/3.22 fof(f5634,plain,(
% 21.75/3.22 spl0_22 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f5636,plain,(
% 21.75/3.22 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))|spl0_22),
% 21.75/3.22 inference(component_clause,[status(thm)],[f5634])).
% 21.75/3.22 fof(f5637,plain,(
% 21.75/3.22 spl0_23 <=> v_r____=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f5638,plain,(
% 21.75/3.22 v_r____=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))|~spl0_23),
% 21.75/3.22 inference(component_clause,[status(thm)],[f5637])).
% 21.75/3.22 fof(f5640,plain,(
% 21.75/3.22 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)))|v_r____=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),
% 21.75/3.22 inference(resolution,[status(thm)],[f1277,f4924])).
% 21.75/3.22 fof(f5641,plain,(
% 21.75/3.22 ~spl0_22|spl0_23),
% 21.75/3.22 inference(split_clause,[status(thm)],[f5640,f5634,f5637])).
% 21.75/3.22 fof(f5800,plain,(
% 21.75/3.22 ![X0,X1,X2]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1)))),
% 21.75/3.22 inference(resolution,[status(thm)],[f1905,f1272])).
% 21.75/3.22 fof(f5818,plain,(
% 21.75/3.22 spl0_38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f6254,plain,(
% 21.75/3.22 spl0_111 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,v_r____)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f7355,plain,(
% 21.75/3.22 spl0_226 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f7356,plain,(
% 21.75/3.22 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____)|~spl0_226),
% 21.75/3.22 inference(component_clause,[status(thm)],[f7355])).
% 21.75/3.22 fof(f7434,plain,(
% 21.75/3.22 spl0_241 <=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f7436,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|spl0_241),
% 21.75/3.22 inference(component_clause,[status(thm)],[f7434])).
% 21.75/3.22 fof(f9296,plain,(
% 21.75/3.22 $false|spl0_241),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f4506,f7436])).
% 21.75/3.22 fof(f9297,plain,(
% 21.75/3.22 spl0_241),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f9296])).
% 21.75/3.22 fof(f9552,plain,(
% 21.75/3.22 spl0_454 <=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f9554,plain,(
% 21.75/3.22 ~class_Rings_Olinordered__semidom(tc_RealDef_Oreal)|spl0_454),
% 21.75/3.22 inference(component_clause,[status(thm)],[f9552])).
% 21.75/3.22 fof(f9567,plain,(
% 21.75/3.22 spl0_457 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f9570,plain,(
% 21.75/3.22 ~class_Rings_Olinordered__semidom(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
% 21.75/3.22 inference(resolution,[status(thm)],[f1363,f1272])).
% 21.75/3.22 fof(f9571,plain,(
% 21.75/3.22 ~spl0_454|spl0_457),
% 21.75/3.22 inference(split_clause,[status(thm)],[f9570,f9552,f9567])).
% 21.75/3.22 fof(f9573,plain,(
% 21.75/3.22 $false|spl0_454),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f9554,f4521])).
% 21.75/3.22 fof(f9574,plain,(
% 21.75/3.22 spl0_454),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f9573])).
% 21.75/3.22 fof(f9623,plain,(
% 21.75/3.22 spl0_466 <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f9624,plain,(
% 21.75/3.22 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~spl0_466),
% 21.75/3.22 inference(component_clause,[status(thm)],[f9623])).
% 21.75/3.22 fof(f9649,plain,(
% 21.75/3.22 $false|~spl0_466),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f9624,f1380])).
% 21.75/3.22 fof(f9650,plain,(
% 21.75/3.22 ~spl0_466),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f9649])).
% 21.75/3.22 fof(f10004,plain,(
% 21.75/3.22 spl0_536 <=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f10006,plain,(
% 21.75/3.22 ~class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)|spl0_536),
% 21.75/3.22 inference(component_clause,[status(thm)],[f10004])).
% 21.75/3.22 fof(f10007,plain,(
% 21.75/3.22 spl0_537 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f10009,plain,(
% 21.75/3.22 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))|spl0_537),
% 21.75/3.22 inference(component_clause,[status(thm)],[f10007])).
% 21.75/3.22 fof(f10014,plain,(
% 21.75/3.22 ~class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____))|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r____)),
% 21.75/3.22 inference(resolution,[status(thm)],[f1378,f4933])).
% 21.75/3.22 fof(f10015,plain,(
% 21.75/3.22 ~spl0_536|~spl0_457|~spl0_537|spl0_226),
% 21.75/3.22 inference(split_clause,[status(thm)],[f10014,f10004,f9567,f10007,f7355])).
% 21.75/3.22 fof(f10054,plain,(
% 21.75/3.22 $false|spl0_536),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f10006,f4508])).
% 21.75/3.22 fof(f10055,plain,(
% 21.75/3.22 spl0_536),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f10054])).
% 21.75/3.22 fof(f10168,plain,(
% 21.75/3.22 spl0_559 <=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)=v_r____),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f10169,plain,(
% 21.75/3.22 c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)=v_r____|~spl0_559),
% 21.75/3.22 inference(component_clause,[status(thm)],[f10168])).
% 21.75/3.22 fof(f10171,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)=v_r____|~spl0_226),
% 21.75/3.22 inference(resolution,[status(thm)],[f7356,f1361])).
% 21.75/3.22 fof(f10172,plain,(
% 21.75/3.22 ~spl0_241|spl0_559|~spl0_226),
% 21.75/3.22 inference(split_clause,[status(thm)],[f10171,f7434,f10168,f7355])).
% 21.75/3.22 fof(f10368,plain,(
% 21.75/3.22 ~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____))|~spl0_559|spl0_22),
% 21.75/3.22 inference(backward_demodulation,[status(thm)],[f10169,f5636])).
% 21.75/3.22 fof(f10738,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|spl0_537),
% 21.75/3.22 inference(resolution,[status(thm)],[f10009,f1353])).
% 21.75/3.22 fof(f10739,plain,(
% 21.75/3.22 ~spl0_241|spl0_537),
% 21.75/3.22 inference(split_clause,[status(thm)],[f10738,f7434,f10007])).
% 21.75/3.22 fof(f10783,plain,(
% 21.75/3.22 spl0_621 <=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____)=v_r____),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f10784,plain,(
% 21.75/3.22 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____)=v_r____|~spl0_621),
% 21.75/3.22 inference(component_clause,[status(thm)],[f10783])).
% 21.75/3.22 fof(f11289,plain,(
% 21.75/3.22 spl0_653 <=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f11291,plain,(
% 21.75/3.22 ~class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex)|spl0_653),
% 21.75/3.22 inference(component_clause,[status(thm)],[f11289])).
% 21.75/3.22 fof(f11923,plain,(
% 21.75/3.22 v_r____=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____)|~spl0_559|~spl0_23),
% 21.75/3.22 inference(forward_demodulation,[status(thm)],[f10169,f5638])).
% 21.75/3.22 fof(f11936,plain,(
% 21.75/3.22 spl0_729 <=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f11938,plain,(
% 21.75/3.22 ~class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)|spl0_729),
% 21.75/3.22 inference(component_clause,[status(thm)],[f11936])).
% 21.75/3.22 fof(f11953,plain,(
% 21.75/3.22 spl0_732 <=> ~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,v_r____)=v_r____|X0=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f11954,plain,(
% 21.75/3.22 ![X0]: (~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,v_r____)=v_r____|X0=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~spl0_732)),
% 21.75/3.22 inference(component_clause,[status(thm)],[f11953])).
% 21.75/3.22 fof(f11956,plain,(
% 21.75/3.22 ![X0]: (~class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal)|~c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,v_r____)=v_r____|X0=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~spl0_621)),
% 21.75/3.22 inference(paramodulation,[status(thm)],[f10784,f1392])).
% 21.75/3.22 fof(f11957,plain,(
% 21.75/3.22 ~spl0_729|spl0_732|~spl0_621),
% 21.75/3.22 inference(split_clause,[status(thm)],[f11956,f11936,f11953,f10783])).
% 21.75/3.22 fof(f11976,plain,(
% 21.75/3.22 $false|spl0_729),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f11938,f4519])).
% 21.75/3.22 fof(f11977,plain,(
% 21.75/3.22 spl0_729),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f11976])).
% 21.75/3.22 fof(f11992,plain,(
% 21.75/3.22 spl0_736 <=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f11994,plain,(
% 21.75/3.22 ~class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)|spl0_736),
% 21.75/3.22 inference(component_clause,[status(thm)],[f11992])).
% 21.75/3.22 fof(f11995,plain,(
% 21.75/3.22 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|~class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal)|~spl0_732),
% 21.75/3.22 inference(resolution,[status(thm)],[f11954,f1433])).
% 21.75/3.22 fof(f11996,plain,(
% 21.75/3.22 spl0_466|~spl0_736|~spl0_732),
% 21.75/3.22 inference(split_clause,[status(thm)],[f11995,f9623,f11992,f11953])).
% 21.75/3.22 fof(f12001,plain,(
% 21.75/3.22 spl0_621|~spl0_559|~spl0_23),
% 21.75/3.22 inference(split_clause,[status(thm)],[f11923,f10783,f10168,f5637])).
% 21.75/3.22 fof(f12035,plain,(
% 21.75/3.22 $false|spl0_736),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f11994,f4528])).
% 21.75/3.22 fof(f12036,plain,(
% 21.75/3.22 spl0_736),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f12035])).
% 21.75/3.22 fof(f12043,plain,(
% 21.75/3.22 $false|spl0_653),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f11291,f4572])).
% 21.75/3.22 fof(f12044,plain,(
% 21.75/3.22 spl0_653),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f12043])).
% 21.75/3.22 fof(f12836,plain,(
% 21.75/3.22 spl0_800 <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f12838,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)|spl0_800),
% 21.75/3.22 inference(component_clause,[status(thm)],[f12836])).
% 21.75/3.22 fof(f12868,plain,(
% 21.75/3.22 spl0_806 <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f12870,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)|spl0_806),
% 21.75/3.22 inference(component_clause,[status(thm)],[f12868])).
% 21.75/3.22 fof(f12900,plain,(
% 21.75/3.22 spl0_812 <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f12902,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)|spl0_812),
% 21.75/3.22 inference(component_clause,[status(thm)],[f12900])).
% 21.75/3.22 fof(f12947,plain,(
% 21.75/3.22 $false|spl0_806),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f12870,f4460])).
% 21.75/3.22 fof(f12948,plain,(
% 21.75/3.22 spl0_806),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f12947])).
% 21.75/3.22 fof(f12949,plain,(
% 21.75/3.22 $false|spl0_800),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f12838,f4402])).
% 21.75/3.22 fof(f12950,plain,(
% 21.75/3.22 spl0_800),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f12949])).
% 21.75/3.22 fof(f12951,plain,(
% 21.75/3.22 $false|spl0_812),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f12902,f4499])).
% 21.75/3.22 fof(f12952,plain,(
% 21.75/3.22 spl0_812),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f12951])).
% 21.75/3.22 fof(f13225,plain,(
% 21.75/3.22 spl0_866 <=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f13227,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)|spl0_866),
% 21.75/3.22 inference(component_clause,[status(thm)],[f13225])).
% 21.75/3.22 fof(f13238,plain,(
% 21.75/3.22 spl0_867 <=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f13240,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)|spl0_867),
% 21.75/3.22 inference(component_clause,[status(thm)],[f13238])).
% 21.75/3.22 fof(f13251,plain,(
% 21.75/3.22 spl0_868 <=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f13253,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal)|spl0_868),
% 21.75/3.22 inference(component_clause,[status(thm)],[f13251])).
% 21.75/3.22 fof(f13398,plain,(
% 21.75/3.22 $false|spl0_867),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f13240,f4463])).
% 21.75/3.22 fof(f13399,plain,(
% 21.75/3.22 spl0_867),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f13398])).
% 21.75/3.22 fof(f13400,plain,(
% 21.75/3.22 $false|spl0_866),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f13227,f4406])).
% 21.75/3.22 fof(f13401,plain,(
% 21.75/3.22 spl0_866),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f13400])).
% 21.75/3.22 fof(f13402,plain,(
% 21.75/3.22 $false|spl0_868),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f13253,f4505])).
% 21.75/3.22 fof(f13403,plain,(
% 21.75/3.22 spl0_868),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f13402])).
% 21.75/3.22 fof(f14471,plain,(
% 21.75/3.22 ![X0,X1]: (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1)|~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0))),
% 21.75/3.22 inference(resolution,[status(thm)],[f5800,f1910])).
% 21.75/3.22 fof(f14472,plain,(
% 21.75/3.22 spl0_38),
% 21.75/3.22 inference(split_clause,[status(thm)],[f14471,f5818])).
% 21.75/3.22 fof(f14560,plain,(
% 21.75/3.22 $false|~spl0_0),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f4778,f1299])).
% 21.75/3.22 fof(f14561,plain,(
% 21.75/3.22 ~spl0_0),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f14560])).
% 21.75/3.22 fof(f14570,plain,(
% 21.75/3.22 spl0_986 <=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14572,plain,(
% 21.75/3.22 ~class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)|spl0_986),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14570])).
% 21.75/3.22 fof(f14578,plain,(
% 21.75/3.22 spl0_988 <=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14580,plain,(
% 21.75/3.22 ~class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)|spl0_988),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14578])).
% 21.75/3.22 fof(f14591,plain,(
% 21.75/3.22 spl0_989 <=> class_Groups_Omonoid__add(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14593,plain,(
% 21.75/3.22 ~class_Groups_Omonoid__add(tc_Nat_Onat)|spl0_989),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14591])).
% 21.75/3.22 fof(f14596,plain,(
% 21.75/3.22 spl0_990 <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14598,plain,(
% 21.75/3.22 ~class_Groups_Ocomm__monoid__add(tc_Nat_Onat)|spl0_990),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14596])).
% 21.75/3.22 fof(f14665,plain,(
% 21.75/3.22 spl0_1001 <=> class_Groups_Oab__semigroup__add(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14667,plain,(
% 21.75/3.22 ~class_Groups_Oab__semigroup__add(tc_Nat_Onat)|spl0_1001),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14665])).
% 21.75/3.22 fof(f14717,plain,(
% 21.75/3.22 $false|spl0_1001),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14667,f4473])).
% 21.75/3.22 fof(f14718,plain,(
% 21.75/3.22 spl0_1001),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f14717])).
% 21.75/3.22 fof(f14719,plain,(
% 21.75/3.22 $false|spl0_988),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14580,f4465])).
% 21.75/3.22 fof(f14720,plain,(
% 21.75/3.22 spl0_988),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f14719])).
% 21.75/3.22 fof(f14721,plain,(
% 21.75/3.22 $false|spl0_990),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14598,f4476])).
% 21.75/3.22 fof(f14722,plain,(
% 21.75/3.22 spl0_990),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f14721])).
% 21.75/3.22 fof(f14723,plain,(
% 21.75/3.22 $false|spl0_989),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14593,f4485])).
% 21.75/3.22 fof(f14724,plain,(
% 21.75/3.22 spl0_989),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f14723])).
% 21.75/3.22 fof(f14725,plain,(
% 21.75/3.22 $false|spl0_986),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14572,f4468])).
% 21.75/3.22 fof(f14726,plain,(
% 21.75/3.22 spl0_986),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f14725])).
% 21.75/3.22 fof(f14864,plain,(
% 21.75/3.22 spl0_1026 <=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14866,plain,(
% 21.75/3.22 ~class_Groups_Ocancel__semigroup__add(tc_Int_Oint)|spl0_1026),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14864])).
% 21.75/3.22 fof(f14872,plain,(
% 21.75/3.22 spl0_1028 <=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14874,plain,(
% 21.75/3.22 ~class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)|spl0_1028),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14872])).
% 21.75/3.22 fof(f14885,plain,(
% 21.75/3.22 spl0_1029 <=> class_Groups_Omonoid__add(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14887,plain,(
% 21.75/3.22 ~class_Groups_Omonoid__add(tc_Int_Oint)|spl0_1029),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14885])).
% 21.75/3.22 fof(f14890,plain,(
% 21.75/3.22 spl0_1030 <=> class_Groups_Ocomm__monoid__add(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14892,plain,(
% 21.75/3.22 ~class_Groups_Ocomm__monoid__add(tc_Int_Oint)|spl0_1030),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14890])).
% 21.75/3.22 fof(f14959,plain,(
% 21.75/3.22 spl0_1041 <=> class_Groups_Oab__semigroup__add(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f14961,plain,(
% 21.75/3.22 ~class_Groups_Oab__semigroup__add(tc_Int_Oint)|spl0_1041),
% 21.75/3.22 inference(component_clause,[status(thm)],[f14959])).
% 21.75/3.22 fof(f15011,plain,(
% 21.75/3.22 $false|spl0_1041),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14961,f4423])).
% 21.75/3.22 fof(f15012,plain,(
% 21.75/3.22 spl0_1041),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15011])).
% 21.75/3.22 fof(f15013,plain,(
% 21.75/3.22 $false|spl0_1028),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14874,f4410])).
% 21.75/3.22 fof(f15014,plain,(
% 21.75/3.22 spl0_1028),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15013])).
% 21.75/3.22 fof(f15015,plain,(
% 21.75/3.22 $false|spl0_1030),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14892,f4427])).
% 21.75/3.22 fof(f15016,plain,(
% 21.75/3.22 spl0_1030),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15015])).
% 21.75/3.22 fof(f15017,plain,(
% 21.75/3.22 $false|spl0_1029),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14887,f4441])).
% 21.75/3.22 fof(f15018,plain,(
% 21.75/3.22 spl0_1029),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15017])).
% 21.75/3.22 fof(f15019,plain,(
% 21.75/3.22 $false|spl0_1026),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f14866,f4418])).
% 21.75/3.22 fof(f15020,plain,(
% 21.75/3.22 spl0_1026),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15019])).
% 21.75/3.22 fof(f15152,plain,(
% 21.75/3.22 spl0_1066 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f15153,plain,(
% 21.75/3.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~spl0_1066),
% 21.75/3.22 inference(component_clause,[status(thm)],[f15152])).
% 21.75/3.22 fof(f15197,plain,(
% 21.75/3.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))|~spl0_1066),
% 21.75/3.22 inference(forward_demodulation,[status(thm)],[f3677,f15153])).
% 21.75/3.22 fof(f15198,plain,(
% 21.75/3.22 $false|~spl0_1066),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f15197,f3696])).
% 21.75/3.22 fof(f15199,plain,(
% 21.75/3.22 ~spl0_1066),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15198])).
% 21.75/3.22 fof(f15201,plain,(
% 21.75/3.22 spl0_1068 <=> c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f15203,plain,(
% 21.75/3.22 ~c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|spl0_1068),
% 21.75/3.22 inference(component_clause,[status(thm)],[f15201])).
% 21.75/3.22 fof(f15206,plain,(
% 21.75/3.22 $false|spl0_1068),
% 21.75/3.22 inference(trivial_equality_resolution,[status(esa)],[f15203])).
% 21.75/3.22 fof(f15207,plain,(
% 21.75/3.22 spl0_1068),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15206])).
% 21.75/3.22 fof(f15420,plain,(
% 21.75/3.22 ~class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,v_r____)|~spl0_559),
% 21.75/3.22 inference(paramodulation,[status(thm)],[f10169,f1482])).
% 21.75/3.22 fof(f15421,plain,(
% 21.75/3.22 ~spl0_241|spl0_111|~spl0_559),
% 21.75/3.22 inference(split_clause,[status(thm)],[f15420,f7434,f6254,f10168])).
% 21.75/3.22 fof(f15730,plain,(
% 21.75/3.22 spl0_1149 <=> class_Rings_Olinordered__idom(tc_Int_Oint)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f15732,plain,(
% 21.75/3.22 ~class_Rings_Olinordered__idom(tc_Int_Oint)|spl0_1149),
% 21.75/3.22 inference(component_clause,[status(thm)],[f15730])).
% 21.75/3.22 fof(f15738,plain,(
% 21.75/3.22 spl0_1151 <=> class_Rings_Olinordered__idom(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f15740,plain,(
% 21.75/3.22 ~class_Rings_Olinordered__idom(tc_RealDef_Oreal)|spl0_1151),
% 21.75/3.22 inference(component_clause,[status(thm)],[f15738])).
% 21.75/3.22 fof(f15745,plain,(
% 21.75/3.22 $false|spl0_1149),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f15732,f4429])).
% 21.75/3.22 fof(f15746,plain,(
% 21.75/3.22 spl0_1149),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15745])).
% 21.75/3.22 fof(f15747,plain,(
% 21.75/3.22 $false|spl0_1151),
% 21.75/3.22 inference(forward_subsumption_resolution,[status(thm)],[f15740,f4530])).
% 21.75/3.22 fof(f15748,plain,(
% 21.75/3.22 spl0_1151),
% 21.75/3.22 inference(contradiction_clause,[status(thm)],[f15747])).
% 21.75/3.22 fof(f16170,plain,(
% 21.75/3.22 spl0_1214 <=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal)),
% 21.75/3.22 introduced(split_symbol_definition)).
% 21.75/3.22 fof(f16172,plain,(
% 22.18/3.24 ~class_Rings_Ozero__neq__one(tc_RealDef_Oreal)|spl0_1214),
% 22.18/3.24 inference(component_clause,[status(thm)],[f16170])).
% 22.18/3.24 fof(f16179,plain,(
% 22.18/3.24 $false|spl0_1214),
% 22.18/3.24 inference(forward_subsumption_resolution,[status(thm)],[f16172,f4536])).
% 22.18/3.24 fof(f16180,plain,(
% 22.18/3.24 spl0_1214),
% 22.18/3.24 inference(contradiction_clause,[status(thm)],[f16179])).
% 22.18/3.24 fof(f18838,plain,(
% 22.18/3.24 ~class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|~c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,v_r____)|~spl0_559|spl0_22),
% 22.18/3.24 inference(resolution,[status(thm)],[f1502,f10368])).
% 22.18/3.24 fof(f18839,plain,(
% 22.18/3.24 ~spl0_536|~spl0_457|~spl0_111|~spl0_559|spl0_22),
% 22.18/3.24 inference(split_clause,[status(thm)],[f18838,f10004,f9567,f6254,f10168,f5634])).
% 22.18/3.24 fof(f18892,plain,(
% 22.18/3.24 $false),
% 22.18/3.24 inference(sat_refutation,[status(thm)],[f5641,f9297,f9571,f9574,f9650,f10015,f10055,f10172,f10739,f11957,f11977,f11996,f12001,f12036,f12044,f12948,f12950,f12952,f13399,f13401,f13403,f14472,f14561,f14718,f14720,f14722,f14724,f14726,f15012,f15014,f15016,f15018,f15020,f15199,f15207,f15421,f15746,f15748,f16180,f18839])).
% 22.18/3.24 % SZS output end CNFRefutation for theBenchmark.p
% 22.18/3.24 % Elapsed time: 2.899166 seconds
% 22.18/3.24 % CPU time: 22.251008 seconds
% 22.18/3.24 % Memory used: 287.176 MB
%------------------------------------------------------------------------------