%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG373-1 : TPTP v8.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n004.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 : Mon Jun 24 03:41:30 EDT 2024 % Result : Unsatisfiable 0.66s 0.75s % Output : CNFRefutation 0.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : ALG373-1 : TPTP v8.2.0. Released v4.1.0. % 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Jun 19 17:39:24 EDT 2024 % 0.14/0.34 % CPUTime : % 0.51/0.58 start to proof:theBenchmark % 0.57/0.72 %------------------------------------------- % 0.57/0.72 % File :CSE---1.7 % 0.57/0.72 % Problem :theBenchmark % 0.57/0.72 % Transform :cnf % 0.57/0.72 % Format :tptp:raw % 0.57/0.72 % Command :java -jar mcs_scs.jar %d %s % 0.57/0.72 % 0.57/0.72 % Result :Theorem 0.020000s % 0.57/0.72 % Output :CNFRefutation 0.020000s % 0.57/0.72 %------------------------------------------- % 0.57/0.72 %------------------------------------------------------------------------------ % 0.57/0.72 % File : ALG373-1 : TPTP v8.2.0. Released v4.1.0. % 0.57/0.72 % Domain : General Algebra % 0.57/0.72 % Problem : Fundamental theorem of algebra 0393_80 % 0.57/0.72 % Version : Especial. % 0.57/0.72 % English : % 0.57/0.72 % 0.57/0.72 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.57/0.72 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.57/0.72 % Source : [Nip10] % 0.57/0.72 % Names : Fundamental_Theorem_Algebra-0393_80 [Nip10] % 0.57/0.72 % 0.57/0.72 % Status : Unsatisfiable % 0.57/0.72 % Rating : 0.10 v8.2.0, 0.14 v8.1.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.30 v5.5.0, 0.40 v5.3.0, 0.44 v5.2.0, 0.38 v5.1.0, 0.47 v5.0.0, 0.36 v4.1.0 % 0.57/0.72 % Syntax : Number of clauses : 485 ( 117 unt; 55 nHn; 351 RR) % 0.57/0.72 % Number of literals : 1191 ( 178 equ; 666 neg) % 0.57/0.72 % Maximal clause size : 6 ( 2 avg) % 0.57/0.72 % Maximal term depth : 4 ( 1 avg) % 0.57/0.72 % Number of predicates : 48 ( 47 usr; 0 prp; 1-3 aty) % 0.57/0.72 % Number of functors : 35 ( 35 usr; 5 con; 0-3 aty) % 0.57/0.72 % Number of variables : 1015 ( 53 sgn) % 0.57/0.72 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.57/0.72 % 0.57/0.72 % Comments : % 0.57/0.72 %------------------------------------------------------------------------------ % 0.57/0.72 cnf(cls_mult__right_Opos__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.72 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_mult__left_Opos__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.72 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_scaleR__right_Opos__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.72 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_mult_Opos__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.72 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_mult__left_Ononneg__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.72 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_mult__right_Ononneg__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.72 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_mult_Ononneg__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.72 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(V_vskULp,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_scaleR__right_Ononneg__bounded_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.72 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1(V_vskULu,V_r,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_le__number__of__eq__not__less_1,axiom, % 0.57/0.72 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.72 | ~ class_Int_Onumber(T_a) % 0.57/0.72 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 0.57/0.72 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_le__number__of__eq__not__less_0,axiom, % 0.57/0.72 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.72 | ~ class_Int_Onumber(T_a) % 0.57/0.72 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) % 0.57/0.72 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_eq__number__of_0,axiom, % 0.57/0.72 ( ~ class_Int_Oring__char__0(T_a) % 0.57/0.72 | ~ class_Int_Onumber__ring(T_a) % 0.57/0.72 | c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a) % 0.57/0.72 | V_x = V_y ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_abs__number__of_1,axiom, % 0.57/0.72 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.72 | ~ class_Int_Onumber__ring(T_a) % 0.57/0.72 | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_x,T_a) % 0.57/0.72 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.72 % 0.57/0.72 cnf(cls_of__real__eq__iff_0,axiom, % 0.57/0.72 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.73 | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a) % 0.57/0.73 | V_x = V_y ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_norm__eq__zero_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 0.57/0.73 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_no__zero__divirors__neq0_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_no__zero__divisors_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__eq__0__iff_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_real__mult__order_0,axiom, % 0.57/0.73 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__neg__neg_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__pos__pos_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_zero__less__mult__pos_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_zero__less__mult__pos2_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_of__real_Ozero_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.73 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_of__real__0_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.73 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__le__zero__iff_0,axiom, % 0.57/0.73 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.73 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__of__nonneg_0,axiom, % 0.57/0.73 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__mult_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__eq__mult_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__eq__mult_1,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 0.57/0.73 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__eq__mult_2,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.73 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__eq__mult_3,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 0.57/0.73 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.73 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR__right_Ononneg__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_r,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1(V_vskULu,V_r,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR__right_Opos__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_r,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR__right_Obounded_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_r,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1(V_vskULm,V_r,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__left_Opos__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__right_Ononneg__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult_Ononneg__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(V_vskULp,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__right_Obounded_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__left_Ononneg__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult_Opos__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__right_Opos__bounded_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__left_Obounded_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult_Obounded_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.73 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(V_vskULj,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__number__of_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.73 | ~ class_Int_Onumber__ring(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__le__mult_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 0.57/0.73 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__mult__less_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_class__semiring_Omul__c_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_real__mult__commute_0,axiom, % 0.57/0.73 c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.73 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__eq__0_1,axiom, % 0.57/0.73 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR__conv__of__real_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.73 | c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_r,T_a),V_x,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_real__vector_Oscale__scale_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.73 | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR_Ozero__right_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR_Ozero__left_0,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.73 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR__eq__0__iff_2,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.73 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_scaleR__eq__0__iff_1,axiom, % 0.57/0.73 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.73 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__of__pos_0,axiom, % 0.57/0.73 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.73 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__strict__right__mono_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__strict__left__mono_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_real__mult__less__mono2_0,axiom, % 0.57/0.73 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_real__mult__less__iff1_1,axiom, % 0.57/0.73 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_real__mult__less__iff1_0,axiom, % 0.57/0.73 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_abs__less__iff_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__le__imp__less_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.73 | ~ c_lessequals(V_c,V_d,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__le__less__imp__less_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.57/0.73 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__strict__mono_H_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__imp__less__right_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__less__imp__less__left_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__right__less__imp__less_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.57/0.73 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.73 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.73 % 0.57/0.73 cnf(cls_mult__left__less__imp__less_0,axiom, % 0.57/0.73 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__strict__mono_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__right__le__imp__le_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left__le__imp__le_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_a,V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,V_a,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_b,V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__ge__self_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__le__D1_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_lessequals(V_a,V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__of__neg_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__if_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__if__lattice_0,axiom, % 0.57/0.74 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.74 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__minus__le__zero_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__of__nonpos_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__equal__zero_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.57/0.74 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_minus__zero_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.74 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_minus__mult__commute_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oring(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.74 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__minus__cancel_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_minus__mult__minus_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oring(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_square__eq__iff_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__right_Ominus_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult_Ominus__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left_Ominus_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult_Ominus__left_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__equal__zero_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.57/0.74 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 0.57/0.74 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_minus__mult__right_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oring(T_a) % 0.57/0.74 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_minus__mult__left_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oring(T_a) % 0.57/0.74 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.74 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.74 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_square__eq__iff_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 0.57/0.74 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 0.57/0.74 | V_a = V_b ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_scaleR__minus__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.74 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_scaleR_Ominus__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.74 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.57/0.74 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__le__interval__iff_1,axiom, % 0.57/0.74 ( c_lessequals(V_x,V_r,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__le__cancel__iff2_1,axiom, % 0.57/0.74 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__le__cancel__iff2_0,axiom, % 0.57/0.74 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__le__cancel__iff1_1,axiom, % 0.57/0.74 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__le__cancel__iff1_0,axiom, % 0.57/0.74 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__mult__ineq_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__le__zero__iff_1,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__le__zero__iff_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.74 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__mult__less_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__less__norm__iff_1,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) % 0.57/0.74 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__less__norm__iff_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__abs__def_0,axiom, % 0.57/0.74 ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__norm__cancel_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__Re__le__cmod_0,axiom, % 0.57/0.74 c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_less__minus__self__iff_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_less__minus__self__iff_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__0__less__iff__less_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__0__less__iff__less_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__less__iff_2,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__less__iff_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__less__0__iff__less_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__less__0__iff__less_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__ge__minus__self_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__less__eq__nonneg_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_neg__less__eq__nonneg_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_less__eq__neg__nonpos_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_less__eq__neg__nonpos_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_minus__le__self__iff_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left__idem_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__0__iff_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__0__iff_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__0__iff_2,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__0__iff_3,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__neg__pos_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__pos__neg_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__pos__neg2_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__mono1_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left__mono_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__right__mono_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left__mono__neg_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__right__mono__neg_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__idem_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_of__real__eq__0__iff_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.74 | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.74 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_of__real__mult_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.74 | c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_split__mult__pos__le_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_split__mult__pos__le_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__nonpos__nonpos_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__square_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__mult__iff_4,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__mult__iff_5,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__nonneg__nonneg_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__assoc_0,axiom, % 0.57/0.74 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Omul__a_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__mult__iff_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__mult__iff_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__mult__iff_2,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__le__mult__iff_3,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__mono_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(V_c,V_d,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__mono_H_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.74 | ~ c_lessequals(V_c,V_d,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__sum__squares__cancel__a_0,axiom, % 0.57/0.74 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__sum__squares__cancel__a_1,axiom, % 0.57/0.74 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_poly__bound__exists_0,axiom, % 0.57/0.74 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_not__square__less__zero_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__0__iff_4,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__le__0__iff_5,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_split__mult__neg__le_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_split__mult__neg__le_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__nonneg__nonpos_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__nonpos__nonneg_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.57/0.74 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__le__zero__iff_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_scaleR__eq__0__iff_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.74 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.74 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.74 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult_OscaleR__left_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_a,T_a),V_b,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left_OscaleR_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult_OscaleR__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__right_OscaleR_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_xa,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__scaleR__left_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__scaleR__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_x,c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__scaleR_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_rabs__ratiotest__lemma_0,axiom, % 0.57/0.74 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_c,c_HOL_Oabs__class_Oabs(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.74 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__of__real_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 0.57/0.74 | c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__idempotent_0,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_zero__less__abs__iff_1,axiom, % 0.57/0.74 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.74 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 0.57/0.74 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_scaleR_OscaleR__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_scaleR__left__commute_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.74 | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_scaleR__right_OscaleR_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_RealVector_OscaleR__class_OscaleR(V_ra,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_ra,V_x,T_a),T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_not__real__square__gt__zero_1,axiom, % 0.57/0.74 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__zero_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.74 | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_norm__mult_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 0.57/0.74 | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__left__cancel_0,axiom, % 0.57/0.74 ( c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal) % 0.57/0.74 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 0.57/0.74 | V_a = V_b ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_real__mult__right__cancel_0,axiom, % 0.57/0.74 ( c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal) % 0.57/0.74 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 0.57/0.74 | V_a = V_b ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_abs__mult__self_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__left_Ozero_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult_Ozero__left_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult_Ozero__right_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__right_Ozero_0,axiom, % 0.57/0.74 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_class__semiring_Omul__0_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__zero__left_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__zero__right_0,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 0.57/0.74 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.74 % 0.57/0.74 cnf(cls_mult__eq__0__iff_1,axiom, % 0.57/0.74 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.57/0.75 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mult__eq__0__iff_2,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.57/0.75 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__mult__pos_0,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.75 | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__not__less__zero_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__abs__def_1,axiom, % 0.57/0.75 ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r % 0.57/0.75 | c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__if__lattice_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 0.57/0.75 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__if_1,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 0.57/0.75 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__eq__0_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.75 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_zero__less__abs__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR__cancel__left_1,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR__cancel__right_1,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_norm__ratiotest__lemma_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.75 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.75 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Otimes__class_Otimes(V_c,c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR__cancel__left_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a) % 0.57/0.75 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 0.57/0.75 | V_x = V_y ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR__cancel__right_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a) % 0.57/0.75 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.57/0.75 | V_a = V_b ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_not__real__square__gt__zero_0,axiom, % 0.57/0.75 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 0.57/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__ge__zero_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__le__self__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_le__minus__self__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.75 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_le__minus__self__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.75 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__0__le__iff__le_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.75 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__0__le__iff__le_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__le__iff_2,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__leI_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__le__D2_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__le__0__iff__le_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__le__0__iff__le_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_norm__ge__zero_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_norm__not__less__zero_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_of__real_Ominus_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.75 | ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.75 | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_of__real__minus_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 0.57/0.75 | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR__minus__left_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR__left_Ominus_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_scaleR_Ominus__left_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.75 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__le__interval__iff_2,axiom, % 0.57/0.75 ( c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(V_x,V_r,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_abs__le__interval__iff_0,axiom, % 0.57/0.75 ( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__minus__mult__self__le_0,axiom, % 0.57/0.75 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_u,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_complex__Re__le__cmod_0,axiom, % 0.57/0.75 c_lessequals(c_Complex_ORe(V_x),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_poly__minus_0,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Ocomm__ring(T_a) % 0.57/0.75 | c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_rp_0,axiom, % 0.57/0.75 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_calculation_0,axiom, % 0.57/0.75 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__unknown__thm__rW8__1(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) % 0.57/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mth1_1,axiom, % 0.57/0.75 c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_sko__local__Xmth1__1(v_p,v_r),tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_poly__bound__exists_1,axiom, % 0.57/0.75 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),V_r,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_mth1_0,axiom, % 0.57/0.75 c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I9_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__le__linear_0,axiom, % 0.57/0.75 ( c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 0.57/0.75 | c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__linear_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_lessequals(V_y,V_x,T_a) % 0.57/0.75 | c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__asym_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__asym_H_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I6_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_lessequals(V_z,V_x,T_a) % 0.57/0.75 | ~ c_lessequals(V_z,V_y,T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I7_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.57/0.75 | ~ c_lessequals(V_z,V_y,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I8_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__trans_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_lessequals(V_x,V_z,T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_z,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__le__trans_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_z,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__le__less__trans_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__le__refl_0,axiom, % 0.57/0.75 c_lessequals(V_w,V_w,tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__le__trans_0,axiom, % 0.57/0.75 ( c_lessequals(V_i,V_k,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__eq__iff_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_lessequals(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__eq__refl_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_lessequals(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__imp__le_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_lessequals(V_x,V_y,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__less__def_0,axiom, % 0.57/0.75 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__le__less_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_lessequals(V_x,V_y,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_less__le__not__le_2,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | c_lessequals(V_y,V_x,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__irrefl_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__less__def_1,axiom, % 0.57/0.75 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__le_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__neq__iff_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_norm__minus__cancel_0,axiom, % 0.57/0.75 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 0.57/0.75 | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_complex__mod__minus__le__complex__mod_0,axiom, % 0.57/0.75 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I11_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.75 | V_a = V_b % 0.57/0.75 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I12_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.57/0.75 | ~ c_lessequals(V_b,V_a,T_a) % 0.57/0.75 | V_a = V_b ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__antisym__conv2_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__antisym__conv1_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__neq__le__trans_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.75 | ~ c_lessequals(V_a,V_b,T_a) % 0.57/0.75 | V_a = V_b ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__le__neq__trans_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.75 | V_a = V_b % 0.57/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__less__def_2,axiom, % 0.57/0.75 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__le__less_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__le_2,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.57/0.75 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | V_x = V_y ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__less__linear_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__antisym__conv_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__eq__iff_2,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__neqE_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | V_x = V_y ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__antisym_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | V_x = V_y % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_real__le__antisym_0,axiom, % 0.57/0.75 ( V_z = V_w % 0.57/0.75 | ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_compl__eq__compl__iff_0,axiom, % 0.57/0.75 ( ~ class_Lattices_Oboolean__algebra(T_a) % 0.57/0.75 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 0.57/0.75 | V_x = V_y ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__equal__iff__equal_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.75 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 0.57/0.75 | V_a = V_b ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__less__iff__less_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__less__iff__less_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_neg__le__iff__le_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(V_a,V_b,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_le__imp__neg__le_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_xt1_I10_J_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Oorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_order__less__trans_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_less__le__not__le_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Opreorder(T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_not__leE_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | c_lessequals(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__antisym__conv2_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_x,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__antisym__conv1_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 0.57/0.75 | c_lessequals(V_x,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__not__less_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.57/0.75 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__not__less_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_lessequals(V_y,V_x,T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__not__le_0,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.57/0.75 | c_lessequals(V_x,V_y,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_linorder__not__le_1,axiom, % 0.57/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.57/0.75 | ~ c_lessequals(V_x,V_y,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__equation__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.75 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_equation__minus__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.75 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_equation__minus__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.75 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_double__compl_0,axiom, % 0.57/0.75 ( ~ class_Lattices_Oboolean__algebra(T_a) % 0.57/0.75 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__minus_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.57/0.75 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__less__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__less__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_less__minus__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_less__minus__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.75 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__le__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_minus__le__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 0.57/0.75 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_le__minus__iff_1,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 0.57/0.75 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_le__minus__iff_0,axiom, % 0.57/0.75 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.57/0.75 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.57/0.75 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_CHAINED_0,axiom, % 0.57/0.75 ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal) % 0.57/0.75 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) % 0.57/0.75 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_conjecture_0,negated_conjecture, % 0.57/0.75 c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(V_xb),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_conjecture_1,negated_conjecture, % 0.57/0.75 c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(V_xb),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(V_xb),tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(cls_conjecture_2,negated_conjecture, % 0.57/0.75 ~ c_HOL_Oord__class_Oless(v_x(V_xb),V_xb,tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom, % 0.57/0.75 ( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) % 0.57/0.75 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom, % 0.57/0.75 ( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1)) % 0.57/0.75 | ~ class_OrderedGroup_Oab__group__add(T_1) ) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom, % 0.57/0.75 ( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) % 0.57/0.75 | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Oab__group__add(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 0.57/0.75 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 0.57/0.75 class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,axiom, % 0.57/0.75 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom, % 0.57/0.75 class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom, % 0.57/0.75 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Olordered__ring,axiom, % 0.57/0.75 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono1,axiom, % 0.57/0.75 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom, % 0.57/0.75 class_Ring__and__Field_Omult__zero(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono,axiom, % 0.57/0.75 class_Ring__and__Field_Omult__mono(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom, % 0.57/0.75 class_OrderedGroup_Ogroup__add(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oabs__if,axiom, % 0.57/0.75 class_Ring__and__Field_Oabs__if(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oring,axiom, % 0.57/0.75 class_Ring__and__Field_Oring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom, % 0.57/0.75 class_Ring__and__Field_Oidom(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom, % 0.57/0.75 class_Orderings_Opreorder(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom, % 0.57/0.75 class_Orderings_Olinorder(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Orderings_Oorder,axiom, % 0.57/0.75 class_Orderings_Oorder(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom, % 0.57/0.75 class_Int_Oring__char__0(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom, % 0.57/0.75 class_Int_Onumber__ring(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_Int__Oint__Int_Onumber,axiom, % 0.57/0.75 class_Int_Onumber(tc_Int_Oint) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 0.57/0.75 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 0.57/0.75 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom, % 0.57/0.75 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 0.57/0.75 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom, % 0.57/0.75 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 0.57/0.75 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom, % 0.57/0.75 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 0.57/0.75 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom, % 0.57/0.75 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 0.57/0.75 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom, % 0.57/0.75 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom, % 0.57/0.75 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom, % 0.57/0.75 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom, % 0.57/0.75 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom, % 0.57/0.75 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom, % 0.57/0.75 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom, % 0.57/0.75 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom, % 0.57/0.75 class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom, % 0.57/0.75 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom, % 0.57/0.75 class_RealVector_Oreal__vector(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom, % 0.57/0.75 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom, % 0.57/0.75 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom, % 0.57/0.75 class_Ring__and__Field_Oring(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom, % 0.57/0.75 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom, % 0.57/0.75 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom, % 0.57/0.75 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 0.57/0.75 % 0.57/0.75 cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom, % 0.57/0.75 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_RealDef__Oreal__Int_Oring__char__0,axiom, % 0.66/0.75 class_Int_Oring__char__0(tc_RealDef_Oreal) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom, % 0.66/0.75 class_Int_Onumber__ring(tc_RealDef_Oreal) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_RealDef__Oreal__Int_Onumber,axiom, % 0.66/0.75 class_Int_Onumber(tc_RealDef_Oreal) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom, % 0.66/0.75 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom, % 0.66/0.75 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom, % 0.66/0.75 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom, % 0.66/0.75 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.66/0.75 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom, % 0.66/0.75 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom, % 0.66/0.75 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom, % 0.66/0.75 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom, % 0.66/0.75 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom, % 0.66/0.75 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom, % 0.66/0.75 class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,axiom, % 0.66/0.75 class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__vector,axiom, % 0.66/0.75 class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom, % 0.66/0.75 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom, % 0.66/0.75 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom, % 0.66/0.75 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom, % 0.66/0.75 class_Int_Oring__char__0(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom, % 0.66/0.75 class_Int_Onumber__ring(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom, % 0.66/0.75 class_Int_Onumber(tc_Complex_Ocomplex) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom, % 0.66/0.75 ( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 0.66/0.75 ( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,axiom, % 0.66/0.75 ( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom, % 0.66/0.75 ( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,axiom, % 0.66/0.75 ( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs,axiom, % 0.66/0.75 ( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom, % 0.66/0.75 ( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.66/0.75 ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom, % 0.66/0.75 ( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,axiom, % 0.66/0.75 ( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom, % 0.66/0.75 ( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom, % 0.66/0.75 ( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,axiom, % 0.66/0.75 ( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom, % 0.66/0.75 ( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom, % 0.66/0.75 ( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_OrderedGroup_Oab__group__add(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom, % 0.66/0.75 ( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom, % 0.66/0.75 ( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom, % 0.66/0.75 ( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom, % 0.66/0.75 ( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Int_Oring__char__0,axiom, % 0.66/0.75 ( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom, % 0.66/0.75 ( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ). % 0.66/0.75 % 0.66/0.75 cnf(clsarity_Polynomial__Opoly__Int_Onumber,axiom, % 0.66/0.75 ( class_Int_Onumber(tc_Polynomial_Opoly(T_1)) % 0.66/0.75 | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ). % 0.66/0.75 % 0.66/0.75 %------------------------------------------------------------------------------ % 0.66/0.75 %------------------------------------------- % 0.66/0.75 % Proof found % 0.66/0.75 % SZS status Theorem for theBenchmark % 0.66/0.75 % SZS output start Proof % 0.66/0.75 %ClaNum:599(EqnAxiom:114) % 0.66/0.75 %VarNum:2592(SingletonVarNum:852) % 0.66/0.75 %MaxLitNum:6 % 0.66/0.75 %MaxfuncDepth:3 % 0.66/0.75 %SharedTerms:122 % 0.66/0.75 %goalClause: 220 224 230 % 0.66/0.75 %singleGoalClaCount:3 % 0.66/0.75 [115]P1(a1) % 0.66/0.75 [116]P1(a2) % 0.66/0.75 [117]P22(a1) % 0.66/0.75 [118]P22(a2) % 0.66/0.75 [119]P2(a1) % 0.66/0.75 [120]P2(a26) % 0.66/0.75 [121]P3(a1) % 0.66/0.75 [122]P3(a2) % 0.66/0.75 [123]P3(a26) % 0.66/0.75 [124]P6(a1) % 0.66/0.75 [125]P6(a2) % 0.66/0.75 [126]P6(a26) % 0.66/0.75 [127]P7(a1) % 0.66/0.75 [128]P7(a2) % 0.66/0.75 [129]P7(a26) % 0.66/0.75 [130]P25(a1) % 0.66/0.75 [131]P25(a26) % 0.66/0.75 [132]P18(a1) % 0.66/0.75 [133]P18(a2) % 0.66/0.75 [134]P26(a1) % 0.66/0.75 [135]P26(a2) % 0.66/0.75 [136]P26(a26) % 0.66/0.75 [137]P39(a1) % 0.66/0.75 [138]P39(a2) % 0.66/0.75 [139]P39(a26) % 0.66/0.75 [140]P40(a1) % 0.66/0.75 [141]P40(a26) % 0.66/0.75 [142]P41(a1) % 0.66/0.75 [143]P41(a26) % 0.66/0.75 [144]P27(a1) % 0.66/0.75 [145]P27(a2) % 0.66/0.75 [146]P27(a26) % 0.66/0.75 [147]P8(a1) % 0.66/0.75 [148]P8(a26) % 0.66/0.75 [149]P43(a1) % 0.66/0.75 [150]P43(a26) % 0.66/0.75 [151]P33(a1) % 0.66/0.75 [152]P33(a26) % 0.66/0.75 [153]P28(a1) % 0.66/0.75 [154]P28(a2) % 0.66/0.75 [155]P38(a1) % 0.66/0.75 [156]P38(a26) % 0.66/0.75 [157]P42(a1) % 0.66/0.75 [158]P42(a26) % 0.66/0.75 [159]P29(a1) % 0.66/0.75 [160]P29(a26) % 0.66/0.75 [161]P9(a1) % 0.66/0.75 [162]P9(a26) % 0.66/0.75 [163]P16(a1) % 0.66/0.75 [164]P16(a26) % 0.66/0.75 [165]P10(a1) % 0.66/0.75 [166]P10(a2) % 0.66/0.75 [167]P10(a26) % 0.66/0.75 [168]P46(a1) % 0.66/0.75 [169]P46(a2) % 0.66/0.75 [170]P46(a26) % 0.66/0.75 [171]P34(a1) % 0.66/0.75 [172]P34(a2) % 0.66/0.75 [173]P34(a26) % 0.66/0.75 [174]P17(a1) % 0.66/0.75 [175]P17(a26) % 0.66/0.75 [176]P15(a1) % 0.66/0.75 [177]P15(a26) % 0.66/0.75 [178]P35(a1) % 0.66/0.75 [179]P35(a26) % 0.66/0.75 [180]P36(a1) % 0.66/0.75 [181]P36(a26) % 0.66/0.75 [182]P44(a1) % 0.66/0.75 [183]P44(a26) % 0.66/0.75 [184]P45(a1) % 0.66/0.75 [185]P45(a26) % 0.66/0.75 [186]P11(a1) % 0.66/0.75 [187]P11(a2) % 0.66/0.75 [188]P11(a26) % 0.66/0.75 [189]P47(a1) % 0.66/0.75 [190]P47(a26) % 0.66/0.75 [191]P19(a1) % 0.66/0.75 [192]P19(a2) % 0.66/0.75 [193]P23(a1) % 0.66/0.75 [194]P23(a2) % 0.66/0.75 [195]P24(a1) % 0.66/0.75 [196]P24(a2) % 0.66/0.75 [197]P37(a1) % 0.66/0.75 [198]P37(a2) % 0.66/0.75 [199]P37(a26) % 0.66/0.75 [200]P30(a1) % 0.66/0.75 [201]P30(a2) % 0.66/0.75 [202]P30(a26) % 0.66/0.75 [203]P20(a1) % 0.66/0.75 [204]P20(a26) % 0.66/0.75 [205]P21(a1) % 0.66/0.75 [206]P21(a26) % 0.66/0.75 [207]P31(a1) % 0.66/0.75 [208]P31(a2) % 0.66/0.75 [209]P31(a26) % 0.66/0.75 [210]P12(a1) % 0.66/0.75 [211]P12(a2) % 0.66/0.75 [212]P12(a26) % 0.66/0.75 [213]P32(a1) % 0.66/0.75 [214]P32(a2) % 0.66/0.75 [215]P32(a26) % 0.66/0.75 [217]P4(f3(a1),a28,a1) % 0.66/0.75 [223]P4(f9(f32(a29,a28),a2),a28,a1) % 0.66/0.75 [231]~P5(f3(a1),f5(f3(a1),f3(a1),a1),a1) % 0.66/0.75 [226]E(f9(f10(a29,f32(a29,a28),a2),a2),f8(f33(a29,a28),a1)) % 0.66/0.75 [216]P4(x2161,x2161,a1) % 0.66/0.75 [229]~P5(x2291,x2291,a1) % 0.66/0.75 [218]P4(f4(x2181),f9(x2181,a2),a1) % 0.66/0.75 [230]~P5(f34(x2301),x2301,a1) % 0.66/0.75 [220]P4(f9(f31(x2201),a2),a28,a1) % 0.66/0.75 [222]P4(f6(f4(x2221),a1),f9(x2221,a2),a1) % 0.66/0.75 [225]P4(f8(f9(x2251,a2),a1),f9(x2251,a2),a1) % 0.66/0.75 [224]E(f9(f10(a29,f31(x2241),a2),a2),f8(f34(x2241),a1)) % 0.66/0.75 [219]P5(f3(a1),f30(x2191,x2192),a1) % 0.66/0.75 [221]E(f5(x2211,x2212,a1),f5(x2212,x2211,a1)) % 0.66/0.75 [228]P4(f8(f5(x2281,x2281,a1),a1),f5(x2282,x2282,a1),a1) % 0.66/0.75 [227]E(f5(f5(x2271,x2272,a1),x2273,a1),f5(x2271,f5(x2272,x2273,a1),a1)) % 0.66/0.75 [232]~P25(x2321)+P2(f27(x2321)) % 0.66/0.75 [233]~P32(x2331)+P3(f27(x2331)) % 0.66/0.75 [234]~P25(x2341)+P6(f27(x2341)) % 0.66/0.75 [235]~P32(x2351)+P7(f27(x2351)) % 0.66/0.75 [236]~P25(x2361)+P25(f27(x2361)) % 0.66/0.75 [237]~P34(x2371)+P26(f27(x2371)) % 0.66/0.75 [238]~P34(x2381)+P39(f27(x2381)) % 0.66/0.75 [239]~P25(x2391)+P40(f27(x2391)) % 0.66/0.75 [240]~P25(x2401)+P41(f27(x2401)) % 0.66/0.75 [241]~P27(x2411)+P27(f27(x2411)) % 0.66/0.75 [242]~P25(x2421)+P8(f27(x2421)) % 0.66/0.75 [243]~P25(x2431)+P43(f27(x2431)) % 0.66/0.75 [244]~P25(x2441)+P38(f27(x2441)) % 0.66/0.75 [245]~P25(x2451)+P42(f27(x2451)) % 0.66/0.75 [246]~P25(x2461)+P29(f27(x2461)) % 0.66/0.75 [247]~P25(x2471)+P16(f27(x2471)) % 0.66/0.75 [248]~P12(x2481)+P10(f27(x2481)) % 0.66/0.75 [249]~P30(x2491)+P46(f27(x2491)) % 0.66/0.75 [250]~P34(x2501)+P34(f27(x2501)) % 0.66/0.75 [251]~P25(x2511)+P17(f27(x2511)) % 0.66/0.75 [252]~P25(x2521)+P35(f27(x2521)) % 0.66/0.75 [253]~P25(x2531)+P36(f27(x2531)) % 0.66/0.75 [254]~P25(x2541)+P44(f27(x2541)) % 0.66/0.75 [255]~P25(x2551)+P45(f27(x2551)) % 0.66/0.75 [256]~P31(x2561)+P11(f27(x2561)) % 0.66/0.75 [257]~P25(x2571)+P47(f27(x2571)) % 0.66/0.75 [258]~P31(x2581)+P37(f27(x2581)) % 0.66/0.75 [259]~P30(x2591)+P30(f27(x2591)) % 0.66/0.75 [260]~P25(x2601)+P20(f27(x2601)) % 0.66/0.75 [261]~P25(x2611)+P21(f27(x2611)) % 0.66/0.75 [262]~P31(x2621)+P31(f27(x2621)) % 0.66/0.75 [263]~P12(x2631)+P12(f27(x2631)) % 0.66/0.75 [264]~P32(x2641)+P32(f27(x2641)) % 0.66/0.75 [297]E(f6(x2971,a1),x2971)+P5(x2971,f3(a1),a1) % 0.66/0.75 [336]E(f8(x3361,a1),f6(x3361,a1))+~P5(x3361,f3(a1),a1) % 0.66/0.75 [379]E(x3791,f3(a1))+P5(f3(a1),f5(x3791,x3791,a1),a1) % 0.66/0.75 [265]~P18(x2651)+E(f12(f3(a1),x2651),f3(x2651)) % 0.66/0.75 [266]~P22(x2661)+E(f9(f3(x2661),x2661),f3(a1)) % 0.66/0.75 [268]~P8(x2681)+E(f6(f3(x2681),x2681),f3(x2681)) % 0.66/0.75 [269]~P16(x2691)+E(f8(f3(x2691),x2691),f3(x2691)) % 0.66/0.75 [270]~P10(x2701)+E(f8(f3(x2701),x2701),f3(x2701)) % 0.66/0.75 [329]~P22(x3291)+P4(f9(f3(x3291),x3291),f3(a1),a1) % 0.66/0.75 [330]~P8(x3301)+P4(f6(f3(x3301),x3301),f3(x3301),x3301) % 0.66/0.75 [377]~P22(x3771)+~P5(f3(a1),f9(f3(x3771),x3771),a1) % 0.66/0.75 [378]~P8(x3781)+~P5(f3(x3781),f6(f3(x3781),x3781),x3781) % 0.66/0.75 [292]~P20(x2922)+P4(x2921,x2921,x2922) % 0.66/0.75 [293]~P21(x2932)+P4(x2931,x2931,x2932) % 0.66/0.75 [323]~P5(x3232,x3232,x3231)+~P2(x3231) % 0.66/0.75 [324]~P5(x3242,x3242,x3241)+~P20(x3241) % 0.66/0.75 [325]~P5(x3252,x3252,x3251)+~P21(x3251) % 0.66/0.75 [331]P4(x3312,x3311,a1)+P4(x3311,x3312,a1) % 0.66/0.75 [358]~P5(x3581,x3582,a1)+P4(x3581,x3582,a1) % 0.66/0.75 [294]~P14(x2942)+E(f5(x2941,x2941,x2942),x2941) % 0.66/0.75 [313]~P8(x3132)+P4(x3131,f6(x3131,x3132),x3132) % 0.66/0.75 [314]~P1(x3142)+P5(f3(a1),f14(x3141,x3142),a1) % 0.66/0.75 [315]~P1(x3152)+P5(f3(a1),f15(x3151,x3152),a1) % 0.66/0.75 [316]~P1(x3162)+P5(f3(a1),f16(x3161,x3162),a1) % 0.66/0.75 [317]~P1(x3172)+P4(f3(a1),f19(x3171,x3172),a1) % 0.66/0.75 [318]~P1(x3182)+P4(f3(a1),f21(x3181,x3182),a1) % 0.66/0.75 [319]~P1(x3192)+P4(f3(a1),f17(x3191,x3192),a1) % 0.66/0.75 [320]~P22(x3202)+P4(f3(a1),f9(x3201,x3202),a1) % 0.66/0.75 [326]~P8(x3261)+P4(f3(x3261),f6(x3262,x3261),x3261) % 0.66/0.75 [337]~P8(x3372)+P4(f8(x3371,x3372),f6(x3371,x3372),x3372) % 0.66/0.75 [357]~P22(x3571)+~P5(f9(x3572,x3571),f3(a1),a1) % 0.66/0.75 [363]~P8(x3631)+~P5(f6(x3632,x3631),f3(x3631),x3631) % 0.66/0.75 [389]P4(x3891,x3892,a1)+~P4(f6(x3891,a1),x3892,a1) % 0.66/0.75 [390]~P40(x3901)+P4(f3(x3901),f5(x3902,x3902,x3901),x3901) % 0.66/0.75 [420]~P4(f6(x4202,a1),x4201,a1)+P4(f8(x4201,a1),x4202,a1) % 0.66/0.75 [471]~P40(x4711)+~P5(f5(x4712,x4712,x4711),f3(x4711),x4711) % 0.66/0.75 [281]~P10(x2812)+E(f8(f8(x2811,x2812),x2812),x2811) % 0.66/0.75 [282]~P13(x2822)+E(f8(f8(x2821,x2822),x2822),x2821) % 0.66/0.75 [286]~P23(x2862)+E(f9(f12(x2861,x2862),x2862),f6(x2861,a1)) % 0.66/0.75 [287]~P22(x2872)+E(f6(f9(x2871,x2872),a1),f9(x2871,x2872)) % 0.66/0.75 [289]~P8(x2892)+E(f6(f6(x2891,x2892),x2892),f6(x2891,x2892)) % 0.66/0.75 [290]~P8(x2902)+E(f6(f8(x2901,x2902),x2902),f6(x2901,x2902)) % 0.66/0.75 [291]~P22(x2912)+E(f9(f8(x2911,x2912),x2912),f9(x2911,x2912)) % 0.66/0.75 [295]~P22(x2952)+E(f13(f3(a1),x2951,x2952),f3(x2952)) % 0.66/0.75 [296]~P28(x2962)+E(f13(f3(a1),x2961,x2962),f3(x2962)) % 0.66/0.75 [299]~P1(x2992)+E(f5(x2991,f3(x2992),x2992),f3(x2992)) % 0.66/0.75 [300]~P39(x3002)+E(f5(x3001,f3(x3002),x3002),f3(x3002)) % 0.66/0.75 [301]~P27(x3012)+E(f5(x3011,f3(x3012),x3012),f3(x3012)) % 0.66/0.75 [302]~P37(x3022)+E(f5(x3021,f3(x3022),x3022),f3(x3022)) % 0.66/0.75 [303]~P22(x3032)+E(f13(x3031,f3(x3032),x3032),f3(x3032)) % 0.66/0.75 [304]~P28(x3042)+E(f13(x3041,f3(x3042),x3042),f3(x3042)) % 0.66/0.75 [306]~P1(x3061)+E(f5(f3(x3061),x3062,x3061),f3(x3061)) % 0.66/0.75 [307]~P39(x3071)+E(f5(f3(x3071),x3072,x3071),f3(x3071)) % 0.66/0.75 [309]~P27(x3091)+E(f5(f3(x3091),x3092,x3091),f3(x3091)) % 0.66/0.75 [310]~P37(x3101)+E(f5(f3(x3101),x3102,x3101),f3(x3101)) % 0.66/0.75 [312]~P18(x3122)+E(f12(f8(x3121,a1),x3122),f8(f12(x3121,x3122),x3122)) % 0.66/0.75 [364]~P8(x3642)+P4(f8(f6(x3641,x3642),x3642),f3(x3642),x3642) % 0.66/0.75 [381]~P25(x3812)+E(f5(f6(x3811,x3812),f6(x3811,x3812),x3812),f5(x3811,x3811,x3812)) % 0.66/0.75 [383]~P34(x3832)+E(f5(f8(x3831,x3832),f8(x3831,x3832),x3832),f5(x3831,x3831,x3832)) % 0.66/0.75 [469]E(x4691,f3(a1))+~E(f5(x4692,x4692,a1),f8(f5(x4691,x4691,a1),a1)) % 0.66/0.75 [470]E(x4701,f3(a1))+~E(f5(x4701,x4701,a1),f8(f5(x4702,x4702,a1),a1)) % 0.66/0.75 [339]~P27(x3393)+E(f5(x3391,x3392,x3393),f5(x3392,x3391,x3393)) % 0.66/0.75 [385]~P22(x3853)+P5(f3(a1),f23(x3851,x3852,x3853),a1) % 0.66/0.75 [386]~P22(x3863)+P4(f3(a1),f24(x3861,x3862,x3863),a1) % 0.66/0.75 [352]~P28(x3522)+E(f13(f3(a1),x3521,x3522),f13(f3(a1),x3523,x3522)) % 0.66/0.75 [353]~P28(x3532)+E(f13(x3531,f3(x3532),x3532),f13(x3533,f3(x3532),x3532)) % 0.66/0.75 [362]~P18(x3622)+E(f5(f12(x3621,x3622),x3623,x3622),f13(x3621,x3623,x3622)) % 0.66/0.75 [380]~P46(x3802)+E(f5(f8(x3801,x3802),x3803,x3802),f5(x3801,f8(x3803,x3802),x3802)) % 0.66/0.75 [382]~P46(x3822)+E(f5(f8(x3821,x3822),f8(x3823,x3822),x3822),f5(x3821,x3823,x3822)) % 0.66/0.75 [429]~P22(x4293)+E(f13(f8(x4291,a1),x4292,x4293),f8(f13(x4291,x4292,x4293),x4293)) % 0.66/0.75 [431]~P28(x4313)+E(f13(f8(x4311,a1),x4312,x4313),f8(f13(x4311,x4312,x4313),x4313)) % 0.66/0.75 [432]~P46(x4323)+E(f5(x4321,f8(x4322,x4323),x4323),f8(f5(x4321,x4322,x4323),x4323)) % 0.66/0.75 [433]~P46(x4332)+E(f5(f8(x4331,x4332),x4333,x4332),f8(f5(x4331,x4333,x4332),x4332)) % 0.66/0.75 [435]~P1(x4353)+E(f5(x4351,f8(x4352,x4353),x4353),f8(f5(x4351,x4352,x4353),x4353)) % 0.66/0.75 [436]~P22(x4363)+E(f13(x4361,f8(x4362,x4363),x4363),f8(f13(x4361,x4362,x4363),x4363)) % 0.66/0.75 [437]~P28(x4373)+E(f13(x4371,f8(x4372,x4373),x4373),f8(f13(x4371,x4372,x4373),x4373)) % 0.66/0.75 [439]~P1(x4392)+E(f5(f8(x4391,x4392),x4393,x4392),f8(f5(x4391,x4393,x4392),x4392)) % 0.66/0.75 [452]~P14(x4523)+E(f5(x4521,f5(x4521,x4522,x4523),x4523),f5(x4521,x4522,x4523)) % 0.66/0.75 [454]~P22(x4543)+E(f9(f13(x4541,x4542,x4543),x4543),f5(f6(x4541,a1),f9(x4542,x4543),a1)) % 0.66/0.75 [458]~P18(x4582)+E(f5(f12(x4581,x4582),f12(x4583,x4582),x4582),f12(f5(x4581,x4583,a1),x4582)) % 0.66/0.75 [459]~P24(x4592)+E(f5(f9(x4591,x4592),f9(x4593,x4592),a1),f9(f5(x4591,x4593,x4592),x4592)) % 0.66/0.75 [460]~P25(x4602)+E(f5(f6(x4601,x4602),f6(x4603,x4602),x4602),f6(f5(x4601,x4603,x4602),x4602)) % 0.66/0.75 [528]~P4(f9(x5282,a2),x5283,a1)+P4(f9(f10(x5281,x5282,a2),a2),f30(x5281,x5283),a1) % 0.66/0.75 [553]~P1(x5533)+P4(f9(f5(x5531,x5532,x5533),x5533),f5(f9(x5532,x5533),f14(x5531,x5533),a1),a1) % 0.66/0.75 [554]~P1(x5543)+P4(f9(f5(x5541,x5542,x5543),x5543),f5(f9(x5542,x5543),f21(x5541,x5543),a1),a1) % 0.66/0.75 [555]~P1(x5553)+P4(f9(f5(x5551,x5552,x5553),x5553),f5(f9(x5552,x5553),f22(x5551,x5553),a1),a1) % 0.66/0.75 [556]~P1(x5563)+P4(f9(f5(x5561,x5562,x5563),x5563),f5(f9(x5561,x5563),f15(x5562,x5563),a1),a1) % 0.66/0.75 [557]~P1(x5573)+P4(f9(f5(x5571,x5572,x5573),x5573),f5(f9(x5571,x5573),f19(x5572,x5573),a1),a1) % 0.66/0.75 [558]~P1(x5583)+P4(f9(f5(x5581,x5582,x5583),x5583),f5(f9(x5581,x5583),f9(x5582,x5583),a1),a1) % 0.66/0.75 [559]~P1(x5593)+P4(f9(f5(x5591,x5592,x5593),x5593),f5(f9(x5591,x5593),f20(x5592,x5593),a1),a1) % 0.66/0.75 [560]~P33(x5603)+P4(f6(f5(x5601,x5602,x5603),x5603),f5(f6(x5601,x5603),f6(x5602,x5603),x5603),x5603) % 0.66/0.75 [450]~P30(x4502)+E(f10(f8(x4501,f27(x4502)),x4503,x4502),f8(f10(x4501,x4503,x4502),x4502)) % 0.66/0.75 [477]~P28(x4774)+E(f13(x4771,f13(x4772,x4773,x4774),x4774),f13(f5(x4771,x4772,a1),x4773,x4774)) % 0.66/0.75 [478]~P27(x4784)+E(f5(x4781,f5(x4782,x4783,x4784),x4784),f5(x4782,f5(x4781,x4783,x4784),x4784)) % 0.66/0.75 [480]~P1(x4804)+E(f13(x4801,f5(x4802,x4803,x4804),x4804),f5(x4802,f13(x4801,x4803,x4804),x4804)) % 0.66/0.75 [481]~P19(x4814)+E(f13(x4811,f5(x4812,x4813,x4814),x4814),f5(x4812,f13(x4811,x4813,x4814),x4814)) % 0.66/0.75 [483]~P22(x4834)+E(f13(x4831,f13(x4832,x4833,x4834),x4834),f13(x4832,f13(x4831,x4833,x4834),x4834)) % 0.66/0.75 [484]~P28(x4844)+E(f13(x4841,f13(x4842,x4843,x4844),x4844),f13(x4842,f13(x4841,x4843,x4844),x4844)) % 0.66/0.75 [487]~P27(x4873)+E(f5(f5(x4871,x4872,x4873),x4874,x4873),f5(x4871,f5(x4872,x4874,x4873),x4873)) % 0.66/0.75 [488]~P11(x4883)+E(f5(f5(x4881,x4882,x4883),x4884,x4883),f5(x4881,f5(x4882,x4884,x4883),x4883)) % 0.66/0.75 [490]~P1(x4904)+E(f13(x4901,f5(x4902,x4903,x4904),x4904),f5(f13(x4901,x4902,x4904),x4903,x4904)) % 0.66/0.75 [491]~P19(x4914)+E(f13(x4911,f5(x4912,x4913,x4914),x4914),f5(f13(x4911,x4912,x4914),x4913,x4914)) % 0.66/0.75 [492]~P27(x4923)+E(f5(f5(x4921,x4922,x4923),x4924,x4923),f5(f5(x4921,x4924,x4923),x4922,x4923)) % 0.66/0.75 [593]~P22(x5933)+P4(f9(f13(x5931,x5932,x5933),x5933),f5(f9(x5932,x5933),f23(x5934,x5931,x5933),a1),a1) % 0.66/0.75 [594]~P22(x5943)+P4(f9(f13(x5941,x5942,x5943),x5943),f5(f9(x5942,x5943),f24(x5944,x5941,x5943),a1),a1) % 0.66/0.75 [595]~P22(x5953)+P4(f9(f13(x5951,x5952,x5953),x5953),f5(f9(x5952,x5953),f25(x5954,x5951,x5953),a1),a1) % 0.66/0.75 [597]~P1(x5973)+P4(f9(f5(x5971,x5972,x5973),x5973),f5(f5(f9(x5971,x5973),f9(x5972,x5973),a1),f16(x5974,x5973),a1),a1) % 0.66/0.75 [598]~P1(x5983)+P4(f9(f5(x5981,x5982,x5983),x5983),f5(f5(f9(x5981,x5983),f9(x5982,x5983),a1),f17(x5984,x5983),a1),a1) % 0.66/0.75 [599]~P1(x5993)+P4(f9(f5(x5991,x5992,x5993),x5993),f5(f5(f9(x5991,x5993),f9(x5992,x5993),a1),f18(x5994,x5993),a1),a1) % 0.66/0.75 [563]~P27(x5633)+E(f5(f5(x5631,x5632,x5633),f5(x5634,x5635,x5633),x5633),f5(f5(x5631,x5634,x5633),f5(x5632,x5635,x5633),x5633)) % 0.66/0.75 [360]E(x3601,x3602)+P5(x3601,x3602,a1)+~P4(x3601,x3602,a1) % 0.66/0.75 [384]E(x3841,x3842)+~P4(x3842,x3841,a1)+~P4(x3841,x3842,a1) % 0.66/0.75 [272]~P16(x2722)+~E(f8(x2721,x2722),x2721)+E(x2721,f3(x2722)) % 0.66/0.75 [273]~P22(x2732)+E(x2731,f3(x2732))+~E(f9(x2731,x2732),f3(a1)) % 0.66/0.75 [274]~P18(x2742)+~E(f12(x2741,x2742),f3(x2742))+E(x2741,f3(a1)) % 0.66/0.75 [275]~P8(x2752)+~E(f6(x2751,x2752),f3(x2752))+E(x2751,f3(x2752)) % 0.66/0.75 [276]~P10(x2762)+~E(f8(x2761,x2762),f3(x2762))+E(x2761,f3(x2762)) % 0.66/0.75 [277]~P10(x2771)+~E(f8(x2772,x2771),f3(x2771))+E(f3(x2771),x2772) % 0.66/0.75 [311]~P29(x3112)+P5(x3111,f3(x3112),x3112)+E(f6(x3111,x3112),x3111) % 0.66/0.75 [327]~P22(x3272)+E(x3271,f3(x3272))+P5(f3(a1),f9(x3271,x3272),a1) % 0.66/0.75 [328]~P8(x3282)+P5(f3(x3282),f6(x3281,x3282),x3282)+E(x3281,f3(x3282)) % 0.66/0.75 [345]~P8(x3452)+~P5(f3(x3452),x3451,x3452)+E(f6(x3451,x3452),x3451) % 0.66/0.75 [346]~P8(x3462)+~P4(f3(x3462),x3461,x3462)+E(f6(x3461,x3462),x3461) % 0.66/0.75 [354]~P8(x3542)+~P5(x3541,f3(x3542),x3542)+E(f8(x3541,x3542),f6(x3541,x3542)) % 0.66/0.75 [355]~P8(x3552)+~P4(x3551,f3(x3552),x3552)+E(f8(x3551,x3552),f6(x3551,x3552)) % 0.66/0.75 [356]~P29(x3562)+~P5(x3561,f3(x3562),x3562)+E(f8(x3561,x3562),f6(x3561,x3562)) % 0.66/0.75 [361]~P22(x3612)+E(x3611,f3(x3612))+~P4(f9(x3611,x3612),f3(a1),a1) % 0.66/0.75 [367]~P8(x3672)+~P4(f6(x3671,x3672),f3(x3672),x3672)+E(x3671,f3(x3672)) % 0.66/0.75 [402]~P25(x4022)+~P5(x4021,f3(x4022),x4022)+P5(x4021,f8(x4021,x4022),x4022) % 0.66/0.75 [403]~P16(x4032)+~P4(x4031,f3(x4032),x4032)+P4(x4031,f8(x4031,x4032),x4032) % 0.66/0.75 [404]~P15(x4042)+~P4(x4041,f3(x4042),x4042)+P4(x4041,f8(x4041,x4042),x4042) % 0.66/0.75 [405]~P16(x4052)+~P4(f3(x4052),x4051,x4052)+P4(f8(x4051,x4052),x4051,x4052) % 0.66/0.75 [406]~P15(x4062)+~P4(f3(x4062),x4061,x4062)+P4(f8(x4061,x4062),x4061,x4062) % 0.66/0.75 [411]~P17(x4111)+~P5(x4112,f3(x4111),x4111)+P5(f3(x4111),f8(x4112,x4111),x4111) % 0.66/0.75 [412]~P17(x4121)+~P4(x4122,f3(x4121),x4121)+P4(f3(x4121),f8(x4122,x4121),x4121) % 0.66/0.75 [413]~P17(x4132)+~P5(f3(x4132),x4131,x4132)+P5(f8(x4131,x4132),f3(x4132),x4132) % 0.66/0.75 [414]~P17(x4142)+~P4(f3(x4142),x4141,x4142)+P4(f8(x4141,x4142),f3(x4142),x4142) % 0.66/0.75 [415]~P25(x4152)+~P5(x4151,f8(x4151,x4152),x4152)+P5(x4151,f3(x4152),x4152) % 0.66/0.75 [416]~P16(x4162)+~P4(x4161,f8(x4161,x4162),x4162)+P4(x4161,f3(x4162),x4162) % 0.66/0.75 [417]~P15(x4172)+~P4(x4171,f8(x4171,x4172),x4172)+P4(x4171,f3(x4172),x4172) % 0.66/0.75 [418]~P16(x4181)+~P4(f8(x4182,x4181),x4182,x4181)+P4(f3(x4181),x4182,x4181) % 0.66/0.75 [419]~P15(x4191)+~P4(f8(x4192,x4191),x4192,x4191)+P4(f3(x4191),x4192,x4191) % 0.66/0.75 [425]~P17(x4252)+~P5(f3(x4252),f8(x4251,x4252),x4252)+P5(x4251,f3(x4252),x4252) % 0.66/0.75 [426]~P17(x4262)+~P4(f3(x4262),f8(x4261,x4262),x4262)+P4(x4261,f3(x4262),x4262) % 0.66/0.75 [427]~P17(x4271)+~P5(f8(x4272,x4271),f3(x4271),x4271)+P5(f3(x4271),x4272,x4271) % 0.66/0.75 [428]~P17(x4281)+~P4(f8(x4282,x4281),f3(x4281),x4281)+P4(f3(x4281),x4282,x4281) % 0.66/0.75 [472]~P4(x4721,x4722,a1)+~P4(f8(x4722,a1),x4721,a1)+P4(f6(x4721,a1),x4722,a1) % 0.66/0.75 [493]~P5(f3(a1),x4932,a1)+~P5(f3(a1),x4931,a1)+P5(f3(a1),f5(x4931,x4932,a1),a1) % 0.66/0.75 [513]P5(x5131,f7(a1),a1)+~P4(f9(x5132,a2),a28,a1)+~E(f9(f10(a29,x5132,a2),a2),f8(x5131,a1)) % 0.66/0.75 [342]P4(x3422,x3421,x3423)+~P2(x3423)+P5(x3421,x3422,x3423) % 0.66/0.75 [344]P4(x3442,x3441,x3443)+~P2(x3443)+P4(x3441,x3442,x3443) % 0.66/0.75 [365]~P20(x3653)+~P5(x3651,x3652,x3653)+P4(x3651,x3652,x3653) % 0.66/0.75 [366]~P21(x3663)+~P5(x3661,x3662,x3663)+P4(x3661,x3662,x3663) % 0.66/0.75 [391]~P5(x3913,x3912,x3911)+~P2(x3911)+~P5(x3912,x3913,x3911) % 0.66/0.75 [393]~P4(x3933,x3932,x3931)+~P2(x3931)+~P5(x3932,x3933,x3931) % 0.66/0.75 [395]~P5(x3953,x3952,x3951)+~P20(x3951)+~P5(x3952,x3953,x3951) % 0.66/0.75 [397]~P5(x3973,x3972,x3971)+~P21(x3971)+~P5(x3972,x3973,x3971) % 0.66/0.75 [398]~P4(x3983,x3982,x3981)+~P21(x3981)+~P5(x3982,x3983,x3981) % 0.66/0.75 [451]~P4(x4511,x4513,a1)+P4(x4511,x4512,a1)+~P4(x4513,x4512,a1) % 0.66/0.75 [283]~P18(x2833)+E(x2831,x2832)+~E(f12(x2831,x2833),f12(x2832,x2833)) % 0.66/0.75 [284]~P10(x2843)+E(x2841,x2842)+~E(f8(x2841,x2843),f8(x2842,x2843)) % 0.66/0.75 [285]~P13(x2853)+E(x2851,x2852)+~E(f8(x2851,x2853),f8(x2852,x2853)) % 0.66/0.75 [387]E(x3871,x3872)+~E(f5(x3873,x3871,a1),f5(x3873,x3872,a1))+E(x3873,f3(a1)) % 0.66/0.75 [388]E(x3881,x3882)+~E(f5(x3881,x3883,a1),f5(x3882,x3883,a1))+E(x3883,f3(a1)) % 0.66/0.75 [409]~P25(x4093)+P5(x4091,x4092,x4093)+~P5(f6(x4091,x4093),x4092,x4093) % 0.66/0.75 [410]~P8(x4103)+P4(x4101,x4102,x4103)+~P4(f6(x4101,x4103),x4102,x4103) % 0.66/0.75 [422]~P17(x4222)+~P5(x4223,x4221,x4222)+P5(f8(x4221,x4222),f8(x4223,x4222),x4222) % 0.66/0.75 [423]~P17(x4232)+~P4(x4233,x4231,x4232)+P4(f8(x4231,x4232),f8(x4233,x4232),x4232) % 0.66/0.75 [441]~P17(x4413)+~P5(x4412,f8(x4411,x4413),x4413)+P5(x4411,f8(x4412,x4413),x4413) % 0.66/0.75 [443]~P17(x4433)+~P4(x4432,f8(x4431,x4433),x4433)+P4(x4431,f8(x4432,x4433),x4433) % 0.66/0.75 [444]~P25(x4442)+~P5(f6(x4441,x4442),x4443,x4442)+P5(f8(x4441,x4442),x4443,x4442) % 0.66/0.75 [446]~P17(x4462)+~P5(f8(x4463,x4462),x4461,x4462)+P5(f8(x4461,x4462),x4463,x4462) % 0.66/0.75 [447]~P8(x4472)+~P4(f6(x4471,x4472),x4473,x4472)+P4(f8(x4471,x4472),x4473,x4472) % 0.66/0.75 [449]~P17(x4492)+~P4(f8(x4493,x4492),x4491,x4492)+P4(f8(x4491,x4492),x4493,x4492) % 0.66/0.75 [455]~P17(x4553)+P5(x4551,x4552,x4553)+~P5(f8(x4552,x4553),f8(x4551,x4553),x4553) % 0.66/0.75 [456]~P17(x4563)+P4(x4561,x4562,x4563)+~P4(f8(x4562,x4563),f8(x4561,x4563),x4563) % 0.66/0.75 [529]~P5(x5291,x5293,a1)+P5(f5(x5291,x5292,a1),f5(x5293,x5292,a1),a1)+~P5(f3(a1),x5292,a1) % 0.66/0.75 [530]~P5(x5302,x5303,a1)+P5(f5(x5301,x5302,a1),f5(x5301,x5303,a1),a1)+~P5(f3(a1),x5301,a1) % 0.66/0.75 [531]~P4(x5311,x5313,a1)+P4(f5(x5311,x5312,a1),f5(x5313,x5312,a1),a1)+~P5(f3(a1),x5312,a1) % 0.66/0.75 [532]~P4(x5322,x5323,a1)+P4(f5(x5321,x5322,a1),f5(x5321,x5323,a1),a1)+~P5(f3(a1),x5321,a1) % 0.66/0.75 [570]P5(x5701,x5702,a1)+~P5(f5(x5701,x5703,a1),f5(x5702,x5703,a1),a1)+~P5(f3(a1),x5703,a1) % 0.66/0.75 [571]P4(x5711,x5712,a1)+~P4(f5(x5713,x5711,a1),f5(x5713,x5712,a1),a1)+~P5(f3(a1),x5713,a1) % 0.66/0.75 [572]P4(x5721,x5722,a1)+~P4(f5(x5721,x5723,a1),f5(x5722,x5723,a1),a1)+~P5(f3(a1),x5723,a1) % 0.66/0.75 [476]~P25(x4762)+~P4(f3(x4762),x4763,x4762)+E(f5(f6(x4761,x4762),x4763,x4762),f6(f5(x4761,x4763,x4762),x4762)) % 0.66/0.75 [533]E(x5331,f3(a1))+~P4(x5332,f3(a1),a1)+~P4(f6(x5331,a1),f5(x5332,f6(x5333,a1),a1),a1) % 0.66/0.75 [321]~P2(x3212)+~P9(x3212)+P5(x3211,f3(x3212),x3212)+E(f6(x3211,x3212),x3211) % 0.66/0.75 [359]~P2(x3592)+~P9(x3592)+~P5(x3591,f3(x3592),x3592)+E(f8(x3591,x3592),f6(x3591,x3592)) % 0.66/0.75 [376]~P7(x3762)+~P25(x3762)+P5(f11(x3761,x3762),f3(x3762),x3762)+E(f6(f11(x3761,x3762),x3762),f11(x3761,x3762)) % 0.66/0.75 [457]~P7(x4572)+~P25(x4572)+~P5(f11(x4571,x4572),f3(x4572),x4572)+E(f8(f11(x4571,x4572),x4572),f6(f11(x4571,x4572),x4572)) % 0.66/0.75 [350]P5(x3501,x3502,x3503)+~P2(x3503)+E(x3501,x3502)+P5(x3502,x3501,x3503) % 0.66/0.75 [351]P5(x3511,x3512,x3513)+~P25(x3513)+E(x3511,x3512)+P5(x3512,x3511,x3513) % 0.66/0.75 [369]~P2(x3693)+~P4(x3691,x3692,x3693)+E(x3691,x3692)+P5(x3691,x3692,x3693) % 0.66/0.75 [375]~P20(x3753)+~P4(x3751,x3752,x3753)+E(x3751,x3752)+P5(x3751,x3752,x3753) % 0.66/0.75 [401]~P4(x4012,x4011,x4013)+~P4(x4011,x4012,x4013)+E(x4011,x4012)+~P20(x4013) % 0.66/0.75 [424]P4(x4242,x4241,x4243)+~P21(x4243)+~P4(x4241,x4242,x4243)+P5(x4241,x4242,x4243) % 0.66/0.75 [288]~P6(x2883)+~P7(x2883)+E(x2881,x2882)+~E(f11(x2881,x2883),f11(x2882,x2883)) % 0.66/0.75 [332]~P28(x3322)+~E(f13(x3323,x3321,x3322),f3(x3322))+E(x3321,f3(x3322))+E(x3323,f3(a1)) % 0.66/0.75 [334]~P26(x3342)+~E(f5(x3343,x3341,x3342),f3(x3342))+E(x3341,f3(x3342))+E(x3343,f3(x3342)) % 0.66/0.75 [335]~P39(x3352)+~E(f5(x3353,x3351,x3352),f3(x3352))+E(x3351,f3(x3352))+E(x3353,f3(x3352)) % 0.66/0.75 [421]~P34(x4213)+E(x4211,x4212)+~E(f5(x4211,x4211,x4213),f5(x4212,x4212,x4213))+E(x4211,f8(x4212,x4213)) % 0.66/0.75 [473]~P25(x4732)+~P5(x4731,x4733,x4732)+~P5(f8(x4731,x4732),x4733,x4732)+P5(f6(x4731,x4732),x4733,x4732) % 0.66/0.75 [475]~P8(x4752)+~P4(x4751,x4753,x4752)+~P4(f8(x4751,x4752),x4753,x4752)+P4(f6(x4751,x4752),x4753,x4752) % 0.66/0.75 [495]~P40(x4951)+~P5(x4953,f3(x4951),x4951)+~P5(x4952,f3(x4951),x4951)+P5(f3(x4951),f5(x4952,x4953,x4951),x4951) % 0.66/0.75 [496]~P40(x4961)+~P4(x4963,f3(x4961),x4961)+~P4(x4962,f3(x4961),x4961)+P4(f3(x4961),f5(x4962,x4963,x4961),x4961) % 0.66/0.75 [498]~P44(x4981)+~P4(x4983,f3(x4981),x4981)+~P4(x4982,f3(x4981),x4981)+P4(f3(x4981),f5(x4982,x4983,x4981),x4981) % 0.66/0.75 [499]~P41(x4991)+~P5(f3(x4991),x4993,x4991)+~P5(f3(x4991),x4992,x4991)+P5(f3(x4991),f5(x4992,x4993,x4991),x4991) % 0.66/0.75 [500]~P40(x5001)+~P4(f3(x5001),x5003,x5001)+~P4(f3(x5001),x5002,x5001)+P4(f3(x5001),f5(x5002,x5003,x5001),x5001) % 0.66/0.75 [501]~P44(x5011)+~P4(f3(x5011),x5013,x5011)+~P4(f3(x5011),x5012,x5011)+P4(f3(x5011),f5(x5012,x5013,x5011),x5011) % 0.66/0.75 [502]~P45(x5021)+~P4(f3(x5021),x5023,x5021)+~P4(f3(x5021),x5022,x5021)+P4(f3(x5021),f5(x5022,x5023,x5021),x5021) % 0.66/0.75 [503]~P41(x5033)+~P5(x5032,f3(x5033),x5033)+~P5(f3(x5033),x5031,x5033)+P5(f5(x5031,x5032,x5033),f3(x5033),x5033) % 0.66/0.76 [505]~P41(x5053)+~P5(x5051,f3(x5053),x5053)+~P5(f3(x5053),x5052,x5053)+P5(f5(x5051,x5052,x5053),f3(x5053),x5053) % 0.66/0.76 [506]~P40(x5063)+~P4(x5062,f3(x5063),x5063)+~P4(f3(x5063),x5061,x5063)+P4(f5(x5061,x5062,x5063),f3(x5063),x5063) % 0.66/0.76 [507]~P40(x5073)+~P4(x5071,f3(x5073),x5073)+~P4(f3(x5073),x5072,x5073)+P4(f5(x5071,x5072,x5073),f3(x5073),x5073) % 0.66/0.76 [509]~P45(x5093)+~P4(x5092,f3(x5093),x5093)+~P4(f3(x5093),x5091,x5093)+P4(f5(x5091,x5092,x5093),f3(x5093),x5093) % 0.66/0.76 [512]~P45(x5123)+~P4(x5121,f3(x5123),x5123)+~P4(f3(x5123),x5122,x5123)+P4(f5(x5121,x5122,x5123),f3(x5123),x5123) % 0.66/0.76 [514]~P40(x5142)+~P4(f5(x5143,x5141,x5142),f3(x5142),x5142)+P4(x5141,f3(x5142),x5142)+P4(x5143,f3(x5142),x5142) % 0.66/0.76 [515]~P40(x5152)+~P4(f3(x5152),f5(x5153,x5151,x5152),x5152)+P4(x5151,f3(x5152),x5152)+P4(f3(x5152),x5153,x5152) % 0.66/0.76 [516]~P40(x5162)+~P4(f3(x5162),f5(x5161,x5163,x5162),x5162)+P4(x5161,f3(x5162),x5162)+P4(f3(x5162),x5163,x5162) % 0.66/0.76 [517]~P40(x5172)+~P4(f3(x5172),f5(x5173,x5171,x5172),x5172)+P4(x5171,f3(x5172),x5172)+P4(f3(x5172),x5171,x5172) % 0.66/0.76 [518]~P40(x5182)+~P4(f3(x5182),f5(x5181,x5183,x5182),x5182)+P4(x5181,f3(x5182),x5182)+P4(f3(x5182),x5181,x5182) % 0.66/0.76 [519]~P40(x5192)+~P4(f5(x5193,x5191,x5192),f3(x5192),x5192)+P4(x5191,f3(x5192),x5192)+P4(f3(x5192),x5191,x5192) % 0.66/0.76 [520]~P40(x5202)+~P4(f5(x5201,x5203,x5202),f3(x5202),x5202)+P4(x5201,f3(x5202),x5202)+P4(f3(x5202),x5201,x5202) % 0.66/0.76 [521]~P40(x5211)+~P4(f5(x5212,x5213,x5211),f3(x5211),x5211)+P4(f3(x5211),x5212,x5211)+P4(f3(x5211),x5213,x5211) % 0.66/0.76 [526]~P41(x5261)+~P5(f3(x5261),f5(x5263,x5262,x5261),x5261)+P5(f3(x5261),x5262,x5261)+~P5(f3(x5261),x5263,x5261) % 0.66/0.76 [527]~P41(x5271)+~P5(f3(x5271),f5(x5272,x5273,x5271),x5271)+P5(f3(x5271),x5272,x5271)+~P5(f3(x5271),x5273,x5271) % 0.66/0.76 [522]~P43(x5222)+~P4(x5223,f3(x5222),x5222)+~P4(x5221,f3(x5222),x5222)+E(f5(f6(x5221,x5222),f6(x5223,x5222),x5222),f6(f5(x5221,x5223,x5222),x5222)) % 0.66/0.76 [523]~P43(x5232)+~P4(x5233,f3(x5232),x5232)+~P4(f3(x5232),x5231,x5232)+E(f5(f6(x5231,x5232),f6(x5233,x5232),x5232),f6(f5(x5231,x5233,x5232),x5232)) % 0.66/0.76 [524]~P43(x5242)+~P4(x5241,f3(x5242),x5242)+~P4(f3(x5242),x5243,x5242)+E(f5(f6(x5241,x5242),f6(x5243,x5242),x5242),f6(f5(x5241,x5243,x5242),x5242)) % 0.66/0.76 [525]~P43(x5252)+~P4(f3(x5252),x5253,x5252)+~P4(f3(x5252),x5251,x5252)+E(f5(f6(x5251,x5252),f6(x5253,x5252),x5252),f6(f5(x5251,x5253,x5252),x5252)) % 0.66/0.76 [461]~P20(x4613)+~P5(x4611,x4614,x4613)+P5(x4611,x4612,x4613)+~P5(x4614,x4612,x4613) % 0.66/0.76 [462]~P20(x4623)+~P4(x4621,x4624,x4623)+P5(x4621,x4622,x4623)+~P5(x4624,x4622,x4623) % 0.66/0.76 [463]~P20(x4633)+~P4(x4634,x4632,x4633)+P5(x4631,x4632,x4633)+~P5(x4631,x4634,x4633) % 0.66/0.76 [464]~P21(x4643)+~P5(x4641,x4644,x4643)+P5(x4641,x4642,x4643)+~P5(x4644,x4642,x4643) % 0.66/0.76 [465]~P21(x4653)+~P4(x4651,x4654,x4653)+P5(x4651,x4652,x4653)+~P5(x4654,x4652,x4653) % 0.66/0.76 [466]~P21(x4663)+~P4(x4664,x4662,x4663)+P5(x4661,x4662,x4663)+~P5(x4661,x4664,x4663) % 0.66/0.76 [467]~P20(x4673)+~P4(x4671,x4674,x4673)+P4(x4671,x4672,x4673)+~P4(x4674,x4672,x4673) % 0.66/0.76 [468]~P21(x4683)+~P4(x4681,x4684,x4683)+P4(x4681,x4682,x4683)+~P4(x4684,x4682,x4683) % 0.66/0.76 [407]~P28(x4074)+E(x4071,x4072)+~E(f13(x4073,x4071,x4074),f13(x4073,x4072,x4074))+E(x4073,f3(a1)) % 0.66/0.76 [408]~P28(x4084)+E(x4081,x4082)+~E(f13(x4081,x4083,x4084),f13(x4082,x4083,x4084))+E(x4083,f3(x4084)) % 0.66/0.76 [535]~P40(x5353)+~P5(x5354,x5351,x5353)+~P5(x5352,f3(x5353),x5353)+P5(f5(x5351,x5352,x5353),f5(x5354,x5352,x5353),x5353) % 0.66/0.76 [538]~P40(x5383)+~P5(x5384,x5382,x5383)+~P5(x5381,f3(x5383),x5383)+P5(f5(x5381,x5382,x5383),f5(x5381,x5384,x5383),x5383) % 0.66/0.76 [539]~P44(x5393)+~P4(x5394,x5391,x5393)+~P4(x5392,f3(x5393),x5393)+P4(f5(x5391,x5392,x5393),f5(x5394,x5392,x5393),x5393) % 0.66/0.76 [540]~P40(x5403)+~P4(x5404,x5402,x5403)+~P5(x5401,f3(x5403),x5403)+P4(f5(x5401,x5402,x5403),f5(x5401,x5404,x5403),x5403) % 0.66/0.76 [541]~P44(x5413)+~P4(x5414,x5412,x5413)+~P4(x5411,f3(x5413),x5413)+P4(f5(x5411,x5412,x5413),f5(x5411,x5414,x5413),x5413) % 0.66/0.76 [542]~P40(x5423)+~P5(x5421,x5424,x5423)+~P5(f3(x5423),x5422,x5423)+P5(f5(x5421,x5422,x5423),f5(x5424,x5422,x5423),x5423) % 0.66/0.76 [543]~P41(x5433)+~P5(x5431,x5434,x5433)+~P5(f3(x5433),x5432,x5433)+P5(f5(x5431,x5432,x5433),f5(x5434,x5432,x5433),x5433) % 0.66/0.76 [545]~P40(x5453)+~P5(x5452,x5454,x5453)+~P5(f3(x5453),x5451,x5453)+P5(f5(x5451,x5452,x5453),f5(x5451,x5454,x5453),x5453) % 0.66/0.76 [546]~P41(x5463)+~P5(x5462,x5464,x5463)+~P5(f3(x5463),x5461,x5463)+P5(f5(x5461,x5462,x5463),f5(x5461,x5464,x5463),x5463) % 0.66/0.76 [547]~P38(x5473)+~P5(x5472,x5474,x5473)+~P5(f3(x5473),x5471,x5473)+P5(f5(x5471,x5472,x5473),f5(x5471,x5474,x5473),x5473) % 0.66/0.76 [548]~P36(x5483)+~P4(x5481,x5484,x5483)+~P4(f3(x5483),x5482,x5483)+P4(f5(x5481,x5482,x5483),f5(x5484,x5482,x5483),x5483) % 0.66/0.76 [549]~P40(x5493)+~P4(x5492,x5494,x5493)+~P5(f3(x5493),x5491,x5493)+P4(f5(x5491,x5492,x5493),f5(x5491,x5494,x5493),x5493) % 0.66/0.76 [550]~P35(x5503)+~P4(x5502,x5504,x5503)+~P4(f3(x5503),x5501,x5503)+P4(f5(x5501,x5502,x5503),f5(x5501,x5504,x5503),x5503) % 0.66/0.76 [551]~P36(x5513)+~P4(x5512,x5514,x5513)+~P4(f3(x5513),x5511,x5513)+P4(f5(x5511,x5512,x5513),f5(x5511,x5514,x5513),x5513) % 0.66/0.76 [561]P5(x5612,x5611,x5613)+~P40(x5613)+P5(x5611,x5612,x5613)+~P5(f5(x5614,x5611,x5613),f5(x5614,x5612,x5613),x5613) % 0.66/0.76 [562]P5(x5622,x5621,x5623)+~P40(x5623)+P5(x5621,x5622,x5623)+~P5(f5(x5621,x5624,x5623),f5(x5622,x5624,x5623),x5623) % 0.66/0.76 [564]~P40(x5643)+P5(x5641,x5642,x5643)+~P5(f5(x5641,x5644,x5643),f5(x5642,x5644,x5643),x5643)+P5(x5644,f3(x5643),x5643) % 0.66/0.76 [565]~P40(x5653)+P5(x5651,x5652,x5653)+~P5(f5(x5654,x5651,x5653),f5(x5654,x5652,x5653),x5653)+P5(x5654,f3(x5653),x5653) % 0.66/0.76 [566]~P40(x5663)+P5(x5661,x5662,x5663)+~P5(f5(x5664,x5662,x5663),f5(x5664,x5661,x5663),x5663)+P5(f3(x5663),x5664,x5663) % 0.66/0.76 [567]~P40(x5673)+P5(x5671,x5672,x5673)+~P5(f5(x5672,x5674,x5673),f5(x5671,x5674,x5673),x5673)+P5(f3(x5673),x5674,x5673) % 0.66/0.76 [568]~P40(x5682)+~P5(f5(x5683,x5681,x5682),f5(x5684,x5681,x5682),x5682)+P5(x5681,f3(x5682),x5682)+P5(f3(x5682),x5681,x5682) % 0.66/0.76 [569]~P40(x5692)+~P5(f5(x5691,x5693,x5692),f5(x5691,x5694,x5692),x5692)+P5(x5691,f3(x5692),x5692)+P5(f3(x5692),x5691,x5692) % 0.66/0.76 [573]~P40(x5733)+P5(x5731,x5732,x5733)+~P5(f5(x5734,x5732,x5733),f5(x5734,x5731,x5733),x5733)+~P5(x5734,f3(x5733),x5733) % 0.66/0.76 [574]~P40(x5743)+P4(x5741,x5742,x5743)+~P4(f5(x5744,x5742,x5743),f5(x5744,x5741,x5743),x5743)+~P5(x5744,f3(x5743),x5743) % 0.66/0.76 [575]~P40(x5753)+P5(x5751,x5752,x5753)+~P5(f5(x5754,x5751,x5753),f5(x5754,x5752,x5753),x5753)+~P5(f3(x5753),x5754,x5753) % 0.66/0.76 [576]~P41(x5763)+P5(x5761,x5762,x5763)+~P5(f5(x5764,x5761,x5763),f5(x5764,x5762,x5763),x5763)+~P4(f3(x5763),x5764,x5763) % 0.66/0.76 [577]~P41(x5773)+P5(x5771,x5772,x5773)+~P5(f5(x5771,x5774,x5773),f5(x5772,x5774,x5773),x5773)+~P4(f3(x5773),x5774,x5773) % 0.66/0.76 [578]~P42(x5783)+P5(x5781,x5782,x5783)+~P5(f5(x5784,x5781,x5783),f5(x5784,x5782,x5783),x5783)+~P4(f3(x5783),x5784,x5783) % 0.66/0.76 [579]~P42(x5793)+P5(x5791,x5792,x5793)+~P5(f5(x5791,x5794,x5793),f5(x5792,x5794,x5793),x5793)+~P4(f3(x5793),x5794,x5793) % 0.66/0.76 [580]~P40(x5803)+P4(x5801,x5802,x5803)+~P4(f5(x5804,x5801,x5803),f5(x5804,x5802,x5803),x5803)+~P5(f3(x5803),x5804,x5803) % 0.66/0.76 [581]~P41(x5813)+P4(x5811,x5812,x5813)+~P4(f5(x5814,x5811,x5813),f5(x5814,x5812,x5813),x5813)+~P5(f3(x5813),x5814,x5813) % 0.66/0.76 [582]~P41(x5823)+P4(x5821,x5822,x5823)+~P4(f5(x5821,x5824,x5823),f5(x5822,x5824,x5823),x5823)+~P5(f3(x5823),x5824,x5823) % 0.66/0.76 [552]~P22(x5522)+E(x5521,f3(x5522))+~P4(x5523,f3(a1),a1)+~P4(f9(x5521,x5522),f5(x5523,f9(x5524,x5522),a1),a1) % 0.66/0.76 [583]~P25(x5832)+~P5(f6(x5831,x5832),x5834,x5832)+~P5(f6(x5833,x5832),x5835,x5832)+P5(f5(f6(x5831,x5832),f6(x5833,x5832),x5832),f5(x5834,x5835,x5832),x5832) % 0.66/0.76 [592]~P1(x5923)+~P5(f9(x5922,x5923),x5925,a1)+~P5(f9(x5921,x5923),x5924,a1)+P5(f9(f5(x5921,x5922,x5923),x5923),f5(x5924,x5925,a1),a1) % 0.66/0.76 [584]~P41(x5843)+~P5(x5842,x5845,x5843)+~P5(x5841,x5844,x5843)+~P5(f3(x5843),x5844,x5843)+~P4(f3(x5843),x5842,x5843)+P5(f5(x5841,x5842,x5843),f5(x5844,x5845,x5843),x5843) % 0.66/0.76 [585]~P41(x5853)+~P5(x5852,x5855,x5853)+~P5(x5851,x5854,x5853)+~P4(f3(x5853),x5852,x5853)+~P4(f3(x5853),x5851,x5853)+P5(f5(x5851,x5852,x5853),f5(x5854,x5855,x5853),x5853) % 0.66/0.76 [586]~P41(x5863)+~P5(x5862,x5865,x5863)+~P4(x5861,x5864,x5863)+~P5(f3(x5863),x5861,x5863)+~P4(f3(x5863),x5862,x5863)+P5(f5(x5861,x5862,x5863),f5(x5864,x5865,x5863),x5863) % 0.66/0.76 [587]~P41(x5873)+~P5(x5871,x5874,x5873)+~P4(x5872,x5875,x5873)+~P5(f3(x5873),x5872,x5873)+~P4(f3(x5873),x5871,x5873)+P5(f5(x5871,x5872,x5873),f5(x5874,x5875,x5873),x5873) % 0.66/0.76 [588]~P47(x5883)+~P4(x5882,x5885,x5883)+~P4(x5881,x5884,x5883)+~P4(f3(x5883),x5884,x5883)+~P4(f3(x5883),x5882,x5883)+P4(f5(x5881,x5882,x5883),f5(x5884,x5885,x5883),x5883) % 0.66/0.76 [589]~P47(x5893)+~P4(x5892,x5895,x5893)+~P4(x5891,x5894,x5893)+~P4(f3(x5893),x5892,x5893)+~P4(f3(x5893),x5891,x5893)+P4(f5(x5891,x5892,x5893),f5(x5894,x5895,x5893),x5893) % 0.66/0.76 %EqnAxiom % 0.66/0.76 [1]E(x11,x11) % 0.66/0.76 [2]E(x22,x21)+~E(x21,x22) % 0.66/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.66/0.76 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 0.66/0.76 [5]~E(x51,x52)+E(f4(x51),f4(x52)) % 0.66/0.76 [6]~E(x61,x62)+E(f9(x61,x63),f9(x62,x63)) % 0.66/0.76 [7]~E(x71,x72)+E(f9(x73,x71),f9(x73,x72)) % 0.66/0.76 [8]~E(x81,x82)+E(f5(x81,x83,x84),f5(x82,x83,x84)) % 0.66/0.76 [9]~E(x91,x92)+E(f5(x93,x91,x94),f5(x93,x92,x94)) % 0.66/0.76 [10]~E(x101,x102)+E(f5(x103,x104,x101),f5(x103,x104,x102)) % 0.66/0.76 [11]~E(x111,x112)+E(f30(x111,x113),f30(x112,x113)) % 0.66/0.76 [12]~E(x121,x122)+E(f30(x123,x121),f30(x123,x122)) % 0.66/0.76 [13]~E(x131,x132)+E(f31(x131),f31(x132)) % 0.66/0.76 [14]~E(x141,x142)+E(f6(x141,x143),f6(x142,x143)) % 0.66/0.76 [15]~E(x151,x152)+E(f6(x153,x151),f6(x153,x152)) % 0.66/0.76 [16]~E(x161,x162)+E(f14(x161,x163),f14(x162,x163)) % 0.66/0.76 [17]~E(x171,x172)+E(f14(x173,x171),f14(x173,x172)) % 0.66/0.76 [18]~E(x181,x182)+E(f21(x181,x183),f21(x182,x183)) % 0.66/0.76 [19]~E(x191,x192)+E(f21(x193,x191),f21(x193,x192)) % 0.66/0.76 [20]~E(x201,x202)+E(f13(x201,x203,x204),f13(x202,x203,x204)) % 0.66/0.76 [21]~E(x211,x212)+E(f13(x213,x211,x214),f13(x213,x212,x214)) % 0.66/0.76 [22]~E(x221,x222)+E(f13(x223,x224,x221),f13(x223,x224,x222)) % 0.66/0.76 [23]~E(x231,x232)+E(f8(x231,x233),f8(x232,x233)) % 0.66/0.76 [24]~E(x241,x242)+E(f8(x243,x241),f8(x243,x242)) % 0.66/0.76 [25]~E(x251,x252)+E(f7(x251),f7(x252)) % 0.66/0.76 [26]~E(x261,x262)+E(f32(x261,x263),f32(x262,x263)) % 0.66/0.76 [27]~E(x271,x272)+E(f32(x273,x271),f32(x273,x272)) % 0.66/0.76 [28]~E(x281,x282)+E(f11(x281,x283),f11(x282,x283)) % 0.66/0.76 [29]~E(x291,x292)+E(f11(x293,x291),f11(x293,x292)) % 0.66/0.76 [30]~E(x301,x302)+E(f10(x301,x303,x304),f10(x302,x303,x304)) % 0.66/0.76 [31]~E(x311,x312)+E(f10(x313,x311,x314),f10(x313,x312,x314)) % 0.66/0.76 [32]~E(x321,x322)+E(f10(x323,x324,x321),f10(x323,x324,x322)) % 0.66/0.76 [33]~E(x331,x332)+E(f16(x331,x333),f16(x332,x333)) % 0.66/0.76 [34]~E(x341,x342)+E(f16(x343,x341),f16(x343,x342)) % 0.66/0.76 [35]~E(x351,x352)+E(f25(x351,x353,x354),f25(x352,x353,x354)) % 0.66/0.76 [36]~E(x361,x362)+E(f25(x363,x361,x364),f25(x363,x362,x364)) % 0.66/0.76 [37]~E(x371,x372)+E(f25(x373,x374,x371),f25(x373,x374,x372)) % 0.66/0.76 [38]~E(x381,x382)+E(f34(x381),f34(x382)) % 0.66/0.76 [39]~E(x391,x392)+E(f12(x391,x393),f12(x392,x393)) % 0.66/0.76 [40]~E(x401,x402)+E(f12(x403,x401),f12(x403,x402)) % 0.66/0.76 [41]~E(x411,x412)+E(f23(x411,x413,x414),f23(x412,x413,x414)) % 0.66/0.76 [42]~E(x421,x422)+E(f23(x423,x421,x424),f23(x423,x422,x424)) % 0.66/0.76 [43]~E(x431,x432)+E(f23(x433,x434,x431),f23(x433,x434,x432)) % 0.66/0.76 [44]~E(x441,x442)+E(f24(x441,x443,x444),f24(x442,x443,x444)) % 0.66/0.76 [45]~E(x451,x452)+E(f24(x453,x451,x454),f24(x453,x452,x454)) % 0.66/0.76 [46]~E(x461,x462)+E(f24(x463,x464,x461),f24(x463,x464,x462)) % 0.66/0.76 [47]~E(x471,x472)+E(f17(x471,x473),f17(x472,x473)) % 0.66/0.76 [48]~E(x481,x482)+E(f17(x483,x481),f17(x483,x482)) % 0.66/0.76 [49]~E(x491,x492)+E(f35(x491,x493),f35(x492,x493)) % 0.66/0.76 [50]~E(x501,x502)+E(f35(x503,x501),f35(x503,x502)) % 0.66/0.76 [51]~E(x511,x512)+E(f22(x511,x513),f22(x512,x513)) % 0.66/0.76 [52]~E(x521,x522)+E(f22(x523,x521),f22(x523,x522)) % 0.66/0.76 [53]~E(x531,x532)+E(f27(x531),f27(x532)) % 0.66/0.76 [54]~E(x541,x542)+E(f33(x541,x543),f33(x542,x543)) % 0.66/0.76 [55]~E(x551,x552)+E(f33(x553,x551),f33(x553,x552)) % 0.66/0.76 [56]~E(x561,x562)+E(f15(x561,x563),f15(x562,x563)) % 0.66/0.76 [57]~E(x571,x572)+E(f15(x573,x571),f15(x573,x572)) % 0.66/0.76 [58]~E(x581,x582)+E(f20(x581,x583),f20(x582,x583)) % 0.66/0.76 [59]~E(x591,x592)+E(f20(x593,x591),f20(x593,x592)) % 0.66/0.76 [60]~E(x601,x602)+E(f18(x601,x603),f18(x602,x603)) % 0.66/0.76 [61]~E(x611,x612)+E(f18(x613,x611),f18(x613,x612)) % 0.66/0.76 [62]~E(x621,x622)+E(f19(x621,x623),f19(x622,x623)) % 0.66/0.76 [63]~E(x631,x632)+E(f19(x633,x631),f19(x633,x632)) % 0.66/0.76 [64]~P1(x641)+P1(x642)+~E(x641,x642) % 0.66/0.76 [65]P4(x652,x653,x654)+~E(x651,x652)+~P4(x651,x653,x654) % 0.66/0.76 [66]P4(x663,x662,x664)+~E(x661,x662)+~P4(x663,x661,x664) % 0.66/0.76 [67]P4(x673,x674,x672)+~E(x671,x672)+~P4(x673,x674,x671) % 0.66/0.76 [68]~P22(x681)+P22(x682)+~E(x681,x682) % 0.66/0.76 [69]~P45(x691)+P45(x692)+~E(x691,x692) % 0.66/0.76 [70]~P2(x701)+P2(x702)+~E(x701,x702) % 0.66/0.76 [71]P5(x712,x713,x714)+~E(x711,x712)+~P5(x711,x713,x714) % 0.66/0.76 [72]P5(x723,x722,x724)+~E(x721,x722)+~P5(x723,x721,x724) % 0.66/0.76 [73]P5(x733,x734,x732)+~E(x731,x732)+~P5(x733,x734,x731) % 0.66/0.76 [74]~P3(x741)+P3(x742)+~E(x741,x742) % 0.66/0.76 [75]~P44(x751)+P44(x752)+~E(x751,x752) % 0.66/0.76 [76]~P20(x761)+P20(x762)+~E(x761,x762) % 0.66/0.76 [77]~P6(x771)+P6(x772)+~E(x771,x772) % 0.66/0.76 [78]~P25(x781)+P25(x782)+~E(x781,x782) % 0.66/0.76 [79]~P8(x791)+P8(x792)+~E(x791,x792) % 0.66/0.76 [80]~P7(x801)+P7(x802)+~E(x801,x802) % 0.66/0.76 [81]~P46(x811)+P46(x812)+~E(x811,x812) % 0.66/0.76 [82]~P40(x821)+P40(x822)+~E(x821,x822) % 0.66/0.76 [83]~P17(x831)+P17(x832)+~E(x831,x832) % 0.66/0.76 [84]~P28(x841)+P28(x842)+~E(x841,x842) % 0.66/0.76 [85]~P18(x851)+P18(x852)+~E(x851,x852) % 0.66/0.76 [86]~P41(x861)+P41(x862)+~E(x861,x862) % 0.66/0.76 [87]~P26(x871)+P26(x872)+~E(x871,x872) % 0.66/0.76 [88]~P10(x881)+P10(x882)+~E(x881,x882) % 0.66/0.76 [89]~P39(x891)+P39(x892)+~E(x891,x892) % 0.66/0.76 [90]~P32(x901)+P32(x902)+~E(x901,x902) % 0.66/0.76 [91]~P12(x911)+P12(x912)+~E(x911,x912) % 0.66/0.76 [92]~P37(x921)+P37(x922)+~E(x921,x922) % 0.66/0.76 [93]~P42(x931)+P42(x932)+~E(x931,x932) % 0.66/0.76 [94]~P15(x941)+P15(x942)+~E(x941,x942) % 0.66/0.76 [95]~P14(x951)+P14(x952)+~E(x951,x952) % 0.66/0.76 [96]~P21(x961)+P21(x962)+~E(x961,x962) % 0.66/0.76 [97]~P27(x971)+P27(x972)+~E(x971,x972) % 0.66/0.76 [98]~P24(x981)+P24(x982)+~E(x981,x982) % 0.66/0.76 [99]~P13(x991)+P13(x992)+~E(x991,x992) % 0.66/0.76 [100]~P43(x1001)+P43(x1002)+~E(x1001,x1002) % 0.66/0.76 [101]~P31(x1011)+P31(x1012)+~E(x1011,x1012) % 0.66/0.76 [102]~P36(x1021)+P36(x1022)+~E(x1021,x1022) % 0.66/0.76 [103]~P30(x1031)+P30(x1032)+~E(x1031,x1032) % 0.66/0.76 [104]~P33(x1041)+P33(x1042)+~E(x1041,x1042) % 0.66/0.76 [105]~P23(x1051)+P23(x1052)+~E(x1051,x1052) % 0.66/0.76 [106]~P29(x1061)+P29(x1062)+~E(x1061,x1062) % 0.66/0.76 [107]~P34(x1071)+P34(x1072)+~E(x1071,x1072) % 0.66/0.76 [108]~P38(x1081)+P38(x1082)+~E(x1081,x1082) % 0.66/0.76 [109]~P47(x1091)+P47(x1092)+~E(x1091,x1092) % 0.66/0.76 [110]~P11(x1101)+P11(x1102)+~E(x1101,x1102) % 0.66/0.76 [111]~P16(x1111)+P16(x1112)+~E(x1111,x1112) % 0.66/0.76 [112]~P9(x1121)+P9(x1122)+~E(x1121,x1122) % 0.66/0.76 [113]~P35(x1131)+P35(x1132)+~E(x1131,x1132) % 0.66/0.76 [114]~P19(x1141)+P19(x1142)+~E(x1141,x1142) % 0.66/0.76 % 0.66/0.76 %------------------------------------------- % 0.66/0.76 cnf(609,plain, % 0.66/0.76 ($false), % 0.66/0.76 inference(scs_inference,[],[230,220,224,513]), % 0.66/0.76 ['proof']). % 0.66/0.76 % SZS output end Proof % 0.66/0.76 % Total time :0.020000s %------------------------------------------------------------------------------