0.02/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n134.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 06:06:54 CDT 2018 0.03/0.23 % CPUTime : 1.32/1.56 ============================== Prover9 =============================== 1.32/1.56 Prover9 (32) version 2009-11A, November 2009. 1.32/1.56 Process 60435 was started by sandbox2 on n134.star.cs.uiowa.edu, 1.32/1.56 Sat Jul 14 06:06:56 2018 1.32/1.56 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_60386_n134.star.cs.uiowa.edu". 1.32/1.56 ============================== end of head =========================== 1.32/1.56 1.32/1.56 ============================== INPUT ================================= 1.32/1.56 1.32/1.56 % Reading from file /tmp/Prover9_60386_n134.star.cs.uiowa.edu 1.32/1.56 1.32/1.56 set(prolog_style_variables). 1.32/1.56 set(auto2). 1.32/1.56 % set(auto2) -> set(auto). 1.32/1.56 % set(auto) -> set(auto_inference). 1.32/1.56 % set(auto) -> set(auto_setup). 1.32/1.56 % set(auto_setup) -> set(predicate_elim). 1.32/1.56 % set(auto_setup) -> assign(eq_defs, unfold). 1.32/1.56 % set(auto) -> set(auto_limits). 1.32/1.56 % set(auto_limits) -> assign(max_weight, "100.000"). 1.32/1.56 % set(auto_limits) -> assign(sos_limit, 20000). 1.32/1.56 % set(auto) -> set(auto_denials). 1.32/1.56 % set(auto) -> set(auto_process). 1.32/1.56 % set(auto2) -> assign(new_constants, 1). 1.32/1.56 % set(auto2) -> assign(fold_denial_max, 3). 1.32/1.56 % set(auto2) -> assign(max_weight, "200.000"). 1.32/1.56 % set(auto2) -> assign(max_hours, 1). 1.32/1.56 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.32/1.56 % set(auto2) -> assign(max_seconds, 0). 1.32/1.56 % set(auto2) -> assign(max_minutes, 5). 1.32/1.56 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.32/1.56 % set(auto2) -> set(sort_initial_sos). 1.32/1.56 % set(auto2) -> assign(sos_limit, -1). 1.32/1.56 % set(auto2) -> assign(lrs_ticks, 3000). 1.32/1.56 % set(auto2) -> assign(max_megs, 400). 1.32/1.56 % set(auto2) -> assign(stats, some). 1.32/1.56 % set(auto2) -> clear(echo_input). 1.32/1.56 % set(auto2) -> set(quiet). 1.32/1.56 % set(auto2) -> clear(print_initial_clauses). 1.32/1.56 % set(auto2) -> clear(print_given). 1.32/1.56 assign(lrs_ticks,-1). 1.32/1.56 assign(sos_limit,10000). 1.32/1.56 assign(order,kbo). 1.32/1.56 set(lex_order_vars). 1.32/1.56 clear(print_given). 1.32/1.56 1.32/1.56 % formulas(sos). % not echoed (1172 formulas) 1.32/1.56 1.32/1.56 ============================== end of input ========================== 1.32/1.56 1.32/1.56 % From the command line: assign(max_seconds, 300). 1.32/1.56 1.32/1.56 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.32/1.56 1.32/1.56 % Formulas that are not ordinary clauses: 1.32/1.56 1 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a)) # label(fact_mult__1__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 2 -(all B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) -> -(all B_w (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,v_z____))) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,v_z____)),B_d) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_w),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 3 (all V_y_2 ((exists B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)),V_y_2))) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2))) # label(fact_s1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 4 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))))) # label(fact_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 5 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 6 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 7 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) <-> (all B_d (V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) -> hBOOL(hAPP(V_P_2,B_d)))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) # label(fact_nat__diff__split) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 8 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_ab__diff__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 9 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 10 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 11 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls))) # label(fact_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 12 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 13 (all V_l c_Int_OBit1(V_l) != c_Int_OPls) # label(fact_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 14 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 15 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 16 (all V_a all V_b all T_a (class_RealVector_Oreal__normed__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))))) # label(fact_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 17 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 18 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_minus__mult__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 19 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 20 (all V_da_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2),V_da_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2))))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 21 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))))) # label(fact_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 22 (all V_w c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w)) # label(fact_real__le__refl) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 23 (all V_a_2 all V_wa_2 all V_b_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2) <-> (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)) & (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))))) # label(fact_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 24 (all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_b -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))))) # label(fact_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 25 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 26 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls))) # label(fact_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 27 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 28 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_norm__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 29 (all V_w all V_z2 all V_z1 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w)) # label(fact_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 30 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 31 (all V_a all T_a (class_Groups_Oabs__if(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> V_a = c_Groups_Oabs__class_Oabs(T_a,V_a)) & (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__if) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 32 (all V_n all V_m all V_k c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 33 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 34 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 35 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 36 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 37 (all V_S all V_R c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S)) # label(fact_real__divide__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 38 (all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_inverse__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 39 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 40 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 41 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_left__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 42 (all V_n all V_k all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 43 (all V_ra_2 all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2)))) # label(fact_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 44 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 45 (all V_n V_n != c_Nat_OSuc(V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 46 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 47 (all V_t all V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 48 (all V_c_2 all V_b_2 all V_wa_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Olinordered__field__inverse__zero(T_a) -> ((-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))))) # label(fact_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 49 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 50 (all V_n c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 51 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) <-> V_m_2 = V_n_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 52 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 53 (all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))))) # label(fact_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 54 (all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)))) # label(fact_le__imp__0__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 55 (all V_m all V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i)))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 56 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n_2)) # label(fact_less__Suc0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 57 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x))) # label(fact_norm__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 58 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a)) # label(fact_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 59 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))) # label(fact_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 60 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__mult__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 61 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 62 (all V_z3 all V_z2 all V_z1 c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 63 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 64 (all V_za_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 65 (all V_da_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_da_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 66 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 67 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 68 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 69 (all V_y all V_x (c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y) -> V_y = V_x)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 70 (all B_n exists B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))))) # label(fact_th) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 71 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))) # label(fact_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 72 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 73 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 74 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)))) # label(fact_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 75 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 76 (all V_r all V_q all V_r_H all V_q_H all V_b (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r)) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)))))) # label(fact_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 77 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_m = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 78 (all V_b all V_a all T_a (class_Rings_Oordered__ring__abs(T_a) -> ((c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))) & (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))) # label(fact_abs__eq__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 79 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 80 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 81 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 82 (all V_da_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,V_da_2) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 83 (all V_w all V_z c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 84 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 85 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__le__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 86 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 87 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 88 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls))) # label(fact_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 89 (all V_n_2 all V_m_2 all V_k_2 (V_n_2 = V_m_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 90 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) = c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 91 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 92 (all V_r_H all V_q_H all V_b_H (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H))))) # label(fact_q__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 93 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))))) # label(fact_one__less__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 94 (all V_za_2 (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = V_za_2 <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 95 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 96 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b)) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 97 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_nat__less__real__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 98 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k))) # label(fact_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 99 (all V_y all V_x all V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y))))) # label(fact_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 100 (all V_b_2 all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (V_a_2 = V_b_2 <-> c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)))) # label(fact_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 101 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)))) # label(fact_minus__less__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 102 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.56 103 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_a))) # label(fact_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 104 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 105 (all V_x c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x) # label(fact_real__sum__of__halves) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 106 (all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_a_2 <-> c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 107 (all V_v_H_2 all V_v_2 ((-c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)))) # label(fact_le__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 108 (all V_b all V_a all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (V_b = c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) -> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 109 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b)))) # label(fact_gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 110 (all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (V_a_2 = V_b_2 <-> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 111 (all V_w all T_b (class_Int_Onumber(T_b) & class_Rings_Odivision__ring(T_b) -> c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)) = c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)))) # label(fact_inverse__eq__divide__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 112 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)))) # label(fact_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 113 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 114 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)))) # label(fact_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 115 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)))))) # label(fact_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 116 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 117 (all V_za_2 all V_wa_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 118 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y))) # label(fact_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 119 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))) # label(fact_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 120 (all V_x all V_z all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 121 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 122 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 123 (all V_z all V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) # label(fact_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 124 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 125 (all V_q all V_r all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_q)) = V_a -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) # label(fact_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 126 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2))))) # label(fact_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 127 (all V_x all V_r all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x)) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_r)))))) # label(fact_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 128 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> V_a = c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__of__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 129 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)))) # label(fact_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 130 (all V_n V_n = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 131 (all V_n_2 (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_le__0__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 132 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 = V_n_2 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 133 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) -> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n)) # label(fact_less__2__cases) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 134 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))))) # label(fact_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 135 -(all B_N2 -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,B_N2))) # label(fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 136 (all V_x_2 all V_wa_2 all T_a (class_Int_Onumber(T_a) -> (V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) <-> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) # label(fact_number__of__reorient) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 137 (all V_w all V_z c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_w)) # label(fact_zmult__zminus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 138 (all V_r ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)) & (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r))) # label(fact_real__abs__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 139 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 140 (all V_b all V_a c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_real__average__minus__first) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 141 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 142 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 143 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 144 (exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____))) # label(fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 145 (all V_m all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 146 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a))))) # label(fact_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 147 (all V_n all V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 148 (all V_l all V_k c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l))) # label(fact_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 149 (all V_w all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 150 (all V_P_2 all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((V_n_2 = V_m_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 151 (all V_z all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),V_z) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z))) # label(fact_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 152 (all V_r c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)) # label(fact_real__norm__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 153 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_one__le__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 154 (all V_b_2 all V_a_2 all T_a (class_Rings_Oidom(T_a) -> (V_b_2 = V_a_2 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_a_2) = c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 155 (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,v_s____) <-> (exists B_x ((exists B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) & c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)))) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x))))) # label(fact_s) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 156 (all V_z all V_z_H all V_w all V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 157 (all V_s all V_r c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)) # label(fact_real__diff__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 158 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 != V_n_2)) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 159 (all V_y_2 all V_x_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 160 (all V_a_2 all V_wa_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> ((-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)) & (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)))) # label(fact_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 161 (all V_a_2 all V_b_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_b_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a) <-> V_a_2 = V_b_2)))) # label(fact_right__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 162 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 163 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)))) # label(fact_real__add__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 164 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 165 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 166 (all V_da_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_da_2) = V_c_2 <-> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 167 (all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k) = c_Int_OBit1(V_k)) # label(fact_Bit1__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 168 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 169 (all V_y_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))))) # label(fact_less__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 170 (all V_m all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)))) # label(fact_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 171 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 172 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))))) # label(fact_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 173 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_b) = c_Rings_Oinverse__class_Oinverse(T_a,V_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> V_b = V_a))))) # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 174 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__neg__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 175 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m))))) # label(fact_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 176 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 177 (all V_r_H all V_q_H all V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_q__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 178 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 179 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) = c_Groups_Otimes__class_Otimes(T_a,V_z,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_mult__2__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 180 (all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))) # label(fact_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 181 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 182 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_add__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 183 (all V_q all V_r all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_q)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q))))) # label(fact_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 184 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a) <-> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 185 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))))) # label(fact_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 186 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Oone__class_Oone(tc_Int_Oint) = V_x))) # label(fact_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 187 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 188 (all V_w all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))) # label(fact_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 189 (all V_x all V_u c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u,V_u)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x))) # label(fact_real__minus__mult__self__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 190 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2))) # label(fact_real__0__less__add__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 191 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 192 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 193 (all V_za_2 all V_y_2 all V_x_2 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x_2) <-> V_x_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_za_2)))) # label(fact_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 194 (all V_n all V_m all V_k c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) # label(fact_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 195 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) <-> V_b_2 = V_a_2))) # label(fact_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 196 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 197 (all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) | c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))))) # label(fact_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 198 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_a_2 <-> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 199 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2))) # label(fact_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 200 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 201 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 202 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 203 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v) -> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a)))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 204 (all V_x all V_y all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y)))) # label(fact_abs__div__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 205 (all V_nat_H c_Nat_OSuc(V_nat_H) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 206 (all V_l all V_k c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l))) # label(fact_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 207 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_real__less__half__sum) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 208 (all V_w all V_z c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) # label(fact_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 209 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 210 (all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) <-> c_Groups_Ozero__class_Ozero(T_a) = V_a_2))) # label(fact_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 211 (all V_n_2 all V_m_2 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n_2)) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 212 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 213 (all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z),v_r) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,V_z))))) # label(fact_s1m) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 214 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__zeroE) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 215 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 216 (all V_v_H all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) -> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) -> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)))))) # label(fact_add__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 217 (all V_c all V_b all V_v all T_b (class_Rings_Osemiring(T_b) & class_Int_Onumber(T_b) -> c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) = c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)))) # label(fact_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 218 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 219 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2))))) # label(fact_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 220 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))))) # label(fact_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 221 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)))) # label(fact_abs__le__D2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 222 (all V_n c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_mult__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 223 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 224 (all V_z all V_x all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_y -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)))) # label(fact_add__frac__num) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 225 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))) # label(fact_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 226 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_norm__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 227 (all V_z c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z)) # label(fact_nat__mult__2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 228 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)))) # label(fact_number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 229 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_field__divide__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 230 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2))))) # label(fact_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 231 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_abs__le__D1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 232 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 233 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> (c_Groups_Ozero__class_Ozero(T_a) != V_b -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 234 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x)))))) # label(fact_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 235 (all V_z all V_x all V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_d)),V_z))) # label(fact_decr__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 236 (all V_n_2 all V_m_2 (V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m_2 <-> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 237 (all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,V_a) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)))) # label(fact_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 238 (all V_wa_2 all V_za_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) & V_wa_2 != V_za_2 <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2))) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 239 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_x_2 <-> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(T_a,V_x_2)))) # label(fact_norm__eq__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 240 (all V_n_2 all V_m_2 ((exists B_k V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 241 (all V_wa_2 all V_b_2 all V_a_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber(T_a) -> ((c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = V_a_2) & (c_Groups_Ozero__class_Ozero(T_a) != c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) -> c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_b_2) <-> V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) # label(fact_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 242 (all V_x all T_a (class_Rings_Oring__1(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))))) # label(fact_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 243 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 244 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) <-> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 245 (all V_m all V_n V_m = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)) # label(fact_diff__add__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 246 (all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n_2)) # label(fact_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 247 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))) # label(fact_diff__diff__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 248 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(V_n)) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 249 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = V_a | V_b = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 250 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2) -> (c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m_2,V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 251 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_Suc__pred_H) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 252 (all V_h all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)),V_h) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h),V_d)))) # label(fact_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 253 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 254 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 255 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))))) # label(fact_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 256 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2)))) # label(fact_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 257 (all V_n c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)) # label(fact_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 258 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (V_m != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 259 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 260 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 261 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 262 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2))) # label(fact_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 263 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 264 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 265 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)))) # label(fact_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 266 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 267 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 268 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)))) # label(fact_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 269 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 270 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 271 (all V_y all V_x (V_y != V_x -> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 272 (all V_n (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n))) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n))))) # label(fact_number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 273 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 274 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v) -> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a)))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 275 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 276 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_not__less0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 277 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 278 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 279 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a)) # label(fact_minus__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 280 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 281 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 282 (all V_n all V_m all V_k c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 283 (all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 284 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 285 (all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 286 (all V_wa_2 all V_c_2 all V_b_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Ofield__inverse__zero(T_a) -> ((V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2)) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) <-> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))) # label(fact_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 287 (all V_i ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> V_i = c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)))) # label(fact_zabs__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 288 (all V_v_2 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls))) # label(fact_eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 289 (all V_n all V_m all V_l all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 290 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 291 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) <-> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))))) # label(fact_less__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 292 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 293 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 294 (all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_minus__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 295 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 296 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2))) # label(fact_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 297 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_y),V_x)))) # label(fact_abs__mult__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 298 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) & class_Int_Onumber__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))))) # label(fact_le__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 299 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j))) # label(fact_diff__diff__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 300 (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n)),v_r)) # label(fact_g_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 301 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_add__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 302 (all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) -> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_x | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x)) # label(fact_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 303 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 304 (all V_x (V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x),V_x))) # label(fact_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 305 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2))) # label(fact_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 306 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> V_a = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 307 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 308 (all V_z V_z = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zadd__0__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.57 309 (all V_nat_H_1 c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 310 (all V_c all V_b all V_v all T_b (class_Rings_Oring(T_b) & class_Int_Onumber(T_b) -> c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) = c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)))) # label(fact_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 311 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 312 (all V_n -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 313 (all V_n_2 all V_m_2 ((exists B_j (c_Nat_OSuc(B_j) = V_m_2 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2))) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_m_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)))) # label(fact_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 314 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 315 (all V_z3 all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_z3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_z2),V_z3)) # label(fact_zmult__assoc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 316 (all V_l all V_k c_Int_OBit1(V_k) != c_Int_OBit0(V_l)) # label(fact_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 317 (all V_w c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) # label(fact_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 318 (all V_y all V_x all V_c all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c,c_RealVector_Onorm__class_Onorm(T_a,V_y))) -> c_Groups_Ozero__class_Ozero(T_a) = V_x)))) # label(fact_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 319 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)))) # label(fact_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 320 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 321 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))))) # label(fact_less__half__sum) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 322 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a)) # label(fact_add__numeral__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 323 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)))) # label(fact_minus__le__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 324 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)))) # label(fact_zle__trans) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 325 (all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 326 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y))))) # label(fact_real__mult__order) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 327 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 328 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 329 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c))) # label(fact_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 330 (all V_w all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) & class_Int_Onumber__ring(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)))) # label(fact_norm__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 331 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))))) # label(fact_diff__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 332 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)))) # label(fact_norm__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 333 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 334 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 335 (all V_a_2 all V_c_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) <-> (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = V_a_2) & (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 336 (all V_n all V_m (c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n)) -> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 337 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 338 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 339 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 340 (all V_l all V_k c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l))) # label(fact_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 341 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 342 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b))))) # label(fact_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 343 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 344 (all V_z c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z) # label(fact_zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 345 (all V_v_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) <-> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))) # label(fact_eq__number__of__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 346 (all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 347 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)))) # label(fact_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 348 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 349 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 350 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 351 (all V_n_2 all V_fa_2 (c_SEQ_Osubseq(V_fa_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)))) # label(fact_seq__suble) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 352 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 353 (all B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))) # label(fact_g_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 354 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) <-> -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 355 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 356 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a))) # label(fact_inverse__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 357 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2))) # label(fact_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 358 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) <-> V_y_2 != V_x_2 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 359 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_a_2 <-> c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2))) # label(fact_neg__equal__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 360 (all V_fa_2 ((all B_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n)))) <-> c_SEQ_Osubseq(V_fa_2))) # label(fact_subseq__Suc__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 361 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 362 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)))) # label(fact_real__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 363 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 364 (all V_w all V_v c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))) # label(fact_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 365 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))) # label(fact_divide__zero__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 366 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__neg__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 367 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2)))) # label(fact_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 368 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 369 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_neq0__conv) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 370 (all V_w all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))) # label(fact_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 371 (all V_k V_k = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls)) # label(fact_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 372 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 373 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls))) # label(fact_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 374 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))) & (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))))))) # label(fact_less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 375 (all V_k all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 376 (all V_b all V_a all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 377 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))) # label(fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 378 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 379 (all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))) # label(fact_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 380 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls)))) # label(fact_le__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 381 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) | V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 382 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)))))) # label(fact_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 383 (all V_n -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n)) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 384 (all V_n_2 all V_m_2 all V_k_2 (V_n_2 = V_m_2 <-> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2))) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 385 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) <-> c_Groups_Ozero__class_Ozero(T_a) = V_a_2))) # label(fact_equal__neg__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 386 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 387 (all V_w all V_v c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))) # label(fact_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 388 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))))) # label(fact_le__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 389 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) & c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 390 (all V_y_2 all T_a (class_Rings_Olinordered__idom(T_a) & class_Int_Onumber__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2)))) # label(fact_less__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 391 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 392 (all V_y_2 all V_x_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_za_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_za_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 393 (all V_b_2 all V_a_2 all V_c_2 (V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (V_a_2 = V_b_2 <-> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 394 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 395 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 396 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 397 (all B_w (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,v_z____))) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,v_z____)),v_d____) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_w),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_d_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 398 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))) # label(fact_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 399 (all V_i_2 all V_k_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2))) # label(fact_le__diff__conv) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 400 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y))) # label(fact_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 401 (all V_a all T_a (class_Fields_Ofield(T_a) & class_Int_Onumber__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a)) # label(fact_divide__numeral__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 402 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 403 (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) & (all B_w (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,v_z____))) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,v_z____)),B_d) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_w),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 404 (all V_b all V_a all V_c all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_c -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))) # label(fact_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 405 (all V_n c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 406 (all V_nat_H_2 all V_nat_2 (V_nat_H_2 = V_nat_2 <-> c_Nat_OSuc(V_nat_H_2) = c_Nat_OSuc(V_nat_2))) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 407 (all V_d all V_b all V_c all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)))))) # label(fact_abs__mult__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 408 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z))) # label(fact_add__number__of__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 409 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 410 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n)) # label(fact_Suc__diff__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 411 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) # label(fact_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 412 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)))))))) # label(fact_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 413 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 414 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 415 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)))) # label(fact_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 416 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 417 (all V_a_2 all V_wa_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber(T_a) -> ((c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) -> c_Groups_Ozero__class_Ozero(T_a) = V_a_2) & (c_Groups_Ozero__class_Ozero(T_a) != c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) -> c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_b_2) <-> V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) # label(fact_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 418 (all V_m all V_n all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)))) # label(fact_le__add__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 419 (all V_k all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 420 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 421 (all V_k all V_v_H all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_v_H)),V_k)))) # label(fact_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 422 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 423 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 424 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))) # label(fact_mult__zero__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 425 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)) <-> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 426 (all V_n all V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = V_m -> c_Groups_Oone__class_Oone(tc_Nat_Onat) = V_n | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 427 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) <-> (exists B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))) # label(fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 428 (all V_l all V_k c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(V_k),V_l) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_l)),V_l)) # label(fact_mult__Bit1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 429 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_Deriv_Oinverse__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 430 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 431 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 432 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)))) # label(fact_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 433 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 434 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_abs__le__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 435 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_le0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 436 (all V_m_2 all V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> (V_n_2 = V_m_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 437 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 438 (all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Ofield(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))))) # label(fact_inverse__numeral__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 439 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)),V_a) = V_a)) # label(fact_mult__numeral__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 440 (all V_k c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k) # label(fact_number__of__is__id) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 441 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a))) # label(fact_abs__idempotent) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 442 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Groups_Ozero__class_Ozero(T_a) = V_y_2 & V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 443 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 444 (all V_m V_m = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 445 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) -> V_z = V_w))) # label(fact_zle__antisym) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 446 (all V_z2 all V_z1 all V_w c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 447 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> (c_Groups_Ozero__class_Ozero(T_a) != V_b -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_inverse__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 448 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))))) # label(fact_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 449 (all V_x_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_x_2 = c_Groups_Oone__class_Oone(T_a) <-> c_Groups_Oone__class_Oone(T_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)))) # label(fact_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 450 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)))) # label(fact_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 451 (all V_za_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 452 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) <-> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 453 (all V_n all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 454 (all V_n V_n = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)) # label(fact_nat__mult__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 455 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 456 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 457 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2)))) # label(fact_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 458 (all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))) # label(fact_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 459 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya))) # label(fact_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 460 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 461 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 462 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)))) # label(fact_number__of__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 463 (all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 464 (all V_n_2 all V_m_2 all V_k_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 465 (all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a))) # label(fact_ab__left__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 466 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 467 (all V_v_H all V_v ((-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_v_H))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 468 (all V_z c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z) = V_z) # label(fact_zmult__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 469 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 470 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__diff__assoc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 471 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oabs__class_Oabs(T_a,V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 472 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 473 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 474 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) -> V_w = V_z))) # label(fact_real__le__antisym) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 475 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> ((c_Groups_Ozero__class_Ozero(T_a) != V_c_2 -> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) <-> V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))) # label(fact_eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 476 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 477 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_nat__le__real__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 478 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_n_2 = V_m_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 479 (all V_l_2 all V_k_2 (V_k_2 = V_l_2 <-> c_Int_OBit1(V_l_2) = c_Int_OBit1(V_k_2))) # label(fact_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 480 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 481 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w) -> (c_Orderings_Oord__class_Oless(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__less2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 482 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2)))) # label(fact_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 483 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s)))))) # label(fact_norm__mult__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 484 (all V_w c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w)) # label(fact_zle__refl) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 485 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y))) # label(fact_real__gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 486 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 487 (all V_l_2 all V_k_2 (c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) <-> V_k_2 = V_l_2)) # label(fact_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 488 (all V_x_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_x_2 <-> c_Groups_Oone__class_Oone(T_a) = V_x_2))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 489 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 490 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a)) # label(fact_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 491 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__pos__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 492 (all V_m all V_l all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))))) # label(fact_abs__sum__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.58 493 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))) # label(fact_minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 494 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 495 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 496 (all V_wa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_wa_2,v_z____)),v_d____) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,V_wa_2),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_th1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 497 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 498 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) -> V_b = c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_minus__unique) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 499 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 500 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_less__add__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 501 (all V_y all V_x c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) # label(fact_divide__real__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 502 (all V_n all V_m (V_n = V_m | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 503 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 504 (all V_e all V_x all V_m (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_m,V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_m,V_e)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_m)),V_e)))) # label(fact_ath) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 505 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 506 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n) = c_Nat_OSuc(c_Nat_OSuc(V_n))) # label(fact_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 507 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))))) # label(fact_add__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 508 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__pos__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 509 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_x_2 | c_Groups_Ozero__class_Ozero(T_a) != V_y_2 <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)))))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 510 -(all B_N1 -(all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N1,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____)))) # label(fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 511 (all V_k c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))) # label(fact_minus__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 512 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))) # label(fact_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 513 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 514 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 515 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 516 (all V_l all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))) # label(fact_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 517 (all V_j all V_i -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)) # label(fact_not__add__less1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 518 (all V_i all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n))) # label(fact_diff__Suc__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 519 (all V_a ((-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> V_a = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)) & (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a)))) # label(fact_abs__real__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 520 (all V_y all V_x c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) # label(fact_minus__real__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 521 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2)))) # label(fact_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 522 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 523 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 524 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 525 (all V_da_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_da_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 526 (all V_x all V_z all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_y -> c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y)))) # label(fact_add__num__frac) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 527 (all V_n all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 528 (all V_l_2 (c_Int_OPls = c_Int_OBit0(V_l_2) <-> c_Int_OPls = V_l_2)) # label(fact_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 529 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 530 (all V_za_2 all V_wa_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 531 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 532 (all V_i_2 all V_j_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))))) # label(fact_le__diff__conv2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 533 (exists B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,B_n))) # label(fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 534 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 535 (exists B_z all B_x ((exists B_za (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_za)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_za),v_r))) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z))) # label(fact_mth2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 536 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) <-> V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 537 (all V_n all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) -> V_i = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)))) # label(fact_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 538 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))) # label(fact_le__minus__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 539 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 540 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 541 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_one__less__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 542 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 543 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) <-> V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 544 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) = c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)))) # label(fact_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 545 (all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_half) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 546 (all V_X_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> ((exists B_N all B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) <-> (exists B_K ((all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)))))) # label(fact_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 547 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 548 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 549 (all B_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) -> (exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),B_e))))) # label(fact_fz_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 550 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> V_m_2 = V_n_2 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 551 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z))) # label(fact_mult__number__of__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 552 (all V_x all T_a (class_Rings_Olinordered__idom(T_a) & class_Int_Onumber__ring(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Int_Onumber__class_Onumber__of(T_a,V_x)) & (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x))))) # label(fact_abs__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 553 (all V_y all V_x all V_c (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y))) -> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = V_x))) # label(fact_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 554 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 555 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 556 (all V_h all V_b all V_a all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),V_h) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_h)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))))) # label(fact_DERIV__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 557 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 558 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 559 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))))) # label(fact_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 560 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 561 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> c_Nat_OSuc(V_n_2) = V_m_2 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 562 (all V_m all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m)) -> V_n = V_m))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 563 (all V_x_2 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = V_x_2 <-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2)))) # label(fact_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 564 (all V_x -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) # label(fact_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 565 (all V_m all V_n c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))) # label(fact_diff__add__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 566 (all V_y_2 all V_x_2 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) <-> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))) # label(fact_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 567 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 568 (all V_ra_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2))) # label(fact_abs__le__interval__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 569 (all V_wa_2 all V_b_2 all V_a_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) <-> (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))) & (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))))) # label(fact_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 570 (all V_a_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)) & (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)))))) # label(fact_divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 571 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 572 (all V_v_H_2 all V_v_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)))) # label(fact_less__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 573 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 574 (all V_wa_2 all V_x_2 all V_za_2 all V_y_2 all T_a (class_Fields_Ofield(T_a) -> (V_y_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_za_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_y_2) = c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_za_2) <-> c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2) = c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 575 (all V_z2 all V_z1 all V_w c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))) # label(fact_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 576 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 577 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 578 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) -> (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> V_m = c_Nat_OSuc(V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 579 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 580 (all V_y_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) <-> (exists B_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)))),V_y_2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r))))) # label(fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 581 -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) -> (exists B_z all B_w (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),v_r) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_w))))) # label(fact_calculation) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 582 (all V_n all V_m all V_u all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n)))) # label(fact_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 583 (all V_b all V_a all V_c all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))) # label(fact_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 584 (all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_inverse__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 585 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 586 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__zero__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 587 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))))) # label(fact_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 588 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 589 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n)) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 590 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2) <-> V_b_2 = V_c_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 591 (all V_n c_Nat_OSuc(c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 592 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2) <-> V_m_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 593 (all V_b_2 all V_a_2 all V_c_2 (V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) <-> V_b_2 = V_a_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 594 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 595 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 596 (all V_y all V_x c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)))) # label(fact_abs__minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 597 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)))) # label(fact_norm__ge__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 598 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 599 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z))) # label(fact_mult__2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 600 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) # label(fact_minus__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 601 (all V_l all V_k c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k),V_l) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_l))) # label(fact_mult__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 602 (all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__Numeral0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 603 (all V_k c_Int_OBit1(V_k) != c_Int_OPls) # label(fact_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 604 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 605 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Nat_OSuc(V_m) != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 606 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 607 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (V_x_2 = c_Groups_Ozero__class_Ozero(T_a) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 608 (all V_k all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 609 (all V_l all V_k c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l))) # label(fact_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 610 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2) = V_n_2 <-> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)))) # label(fact_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 611 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a))))) # label(fact_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 612 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 613 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 614 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 615 (all V_l all V_k c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l))) # label(fact_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 616 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 617 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_a)))) # label(fact_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 618 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 619 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b))) # label(fact_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 620 (all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k) # label(fact_add__Pls) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 621 (all V_wa_2 all V_v_2 all T_a (class_Orderings_Olinorder(T_a) & class_Int_Onumber(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) # label(fact_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 622 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> ((c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))))) # label(fact_le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 623 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 624 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 625 (all V_x all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x)) # label(fact_divide__Numeral1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 626 (all V_r all V_q all V_r_H all V_q_H all V_b (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r)) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)))))) # label(fact_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 627 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) & V_m_2 != V_n_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 628 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 629 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))) # label(fact_minus__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 630 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 631 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))))) # label(fact_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 632 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_minus__divide__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 633 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 634 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 635 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 636 (all V_n_1 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(V_n_1))))) # label(fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 637 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) | c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 638 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)))) # label(fact_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 639 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 640 (all V_l c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l))) # label(fact_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 641 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divide__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 642 (all V_u all V_y all V_x1 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1,V_y),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_u)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x),V_y),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1),V_u)))))) # label(fact_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 643 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_divide__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 644 (all V_d all V_b all V_c all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)))) # label(fact_Deriv_Oadd__diff__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 645 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 646 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 647 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 648 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_add__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 649 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 650 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_z -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z) = c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))))) # label(fact_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 651 (all V_a_2 all V_b_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 652 (all V_x_2 all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) | V_x_2 = c_Groups_Oone__class_Oone(T_a) <-> c_Groups_Oone__class_Oone(T_a) = c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2)))) # label(fact_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 653 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 654 (all V_n all V_m all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 655 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)))))))) # label(fact_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 656 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__0__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 657 (all V_y_2 all T_a (class_Rings_Olinordered__idom(T_a) & class_Int_Onumber__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)))) # label(fact_le__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 658 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))))) # label(fact_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 659 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)) # label(fact_mult__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 660 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)))) # label(fact_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 661 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2) <-> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_k_2 | V_m_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 662 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_y != V_x -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 663 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 664 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 665 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 666 (all V_n all V_m ((c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != V_m -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) & (V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)))) # label(fact_mult__eq__if) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 667 (all V_x_2 all V_z_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r) -> (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,V_z_2)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 668 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b))))) # label(fact_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 669 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))))) # label(fact_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 670 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)))) # label(fact_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 671 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 672 (all V_n_2 all V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n_2 & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_m_2)) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 673 (all V_n_2 (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 674 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 675 (all V_n all V_m c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 676 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))))) # label(fact_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 677 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) <-> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2))) # label(fact_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 678 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 679 (all V_u all V_y all V_x1 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1,V_y),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_u)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))))))) # label(fact_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 680 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 681 (all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 682 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_z -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))))) # label(fact_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 683 (all V_k V_k = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls)) # label(fact_add__Pls__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 684 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 685 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 686 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2)) <-> c_Groups_Ozero__class_Ozero(T_a) != V_a_2))) # label(fact_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 687 (all V_n_2 all V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m_2 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 688 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_x_2 <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))))) # label(fact_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 689 (all V_w all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 690 (all V_c all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 691 (all V_x c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x)) # label(fact_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.59 692 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 693 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 694 (all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 695 (all V_a all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) & class_Rings_Odivision__ring__inverse__zero(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)))) # label(fact_norm__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 696 (all V_y_2 all V_x_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) <-> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)))) # label(fact_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 697 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))) # label(fact_diff__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 698 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 699 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_nonzero__abs__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 700 (all V_wa_2 all V_b_2 all V_a_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Olinordered__field__inverse__zero(T_a) -> ((-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))) & (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))))) # label(fact_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 701 (all V_n all V_m V_m = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)) # label(fact_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 702 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 703 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 704 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 705 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2))) # label(fact_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 706 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) # label(fact_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 707 (all V_z all V_x all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z))))) # label(fact_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 708 (all V_w all V_z c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 709 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a))) # label(fact_zero__neq__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 710 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 711 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 712 (all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_abs__one) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 713 (all V_m V_m = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 714 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 715 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 716 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))) # label(fact_mult__Suc__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 717 (all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))) # label(fact_number__of__Pls) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 718 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 719 (all V_x all V_z all V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_d))))) # label(fact_incr__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 720 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 721 (all V_wa_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> ((c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) # label(fact_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 722 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> (c_Groups_Ozero__class_Ozero(T_a) != V_b -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 723 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) # label(fact_norm__minus__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 724 (all V_c_2 all V_a_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (V_c_2 = V_b_2 <-> c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 725 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (V_m_2 = V_n_2 <-> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 726 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 727 (all V_a all V_b all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_b -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))))) # label(fact_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 728 (all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 729 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_x_2 <-> c_Groups_Ozero__class_Ozero(T_a) = V_x_2))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 730 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2)))) # label(fact_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 731 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))) # label(fact_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 732 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 733 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__pos__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 734 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 735 (all V_y_2 all T_a (class_Rings_Olinordered__idom(T_a) & class_Int_Onumber__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))))) # label(fact_le__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 736 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y))) # label(fact_divide_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 737 (all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_field__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 738 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)))) # label(fact_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 739 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2))) # label(fact_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 740 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 741 (all V_z V_z = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z)) # label(fact_real__mult__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 742 (all V_v_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2))) # label(fact_less__0__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 743 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 744 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 745 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) <-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) & -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_d (-hBOOL(hAPP(V_P_2,B_d)) & V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)))))) # label(fact_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 746 (all V_a_2 all V_x_2 (V_x_2 = V_a_2 <-> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)))) # label(fact_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 747 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) # label(fact_abs__minus__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 748 (all V_a all V_b c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a))) # label(fact_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 749 (all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_field__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 750 (all V_b_2 all V_a_2 all V_fa_2 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_b_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_a_2))) # label(fact_lemma__MVT) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 751 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_m = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 752 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)))) # label(fact_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 753 (all V_za_2 all V_wa_2 (V_wa_2 = V_za_2 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 754 (all V_n all V_k all V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k))) # label(fact_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 755 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_n = V_m))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 756 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 757 (all V_y_2 all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Int_Oring__char__0(T_a) -> (V_y_2 = V_x_2 <-> c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)))) # label(fact_eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 758 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 759 (all V_n all V_m (V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 760 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)))))) # label(fact_norm__add__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 761 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 762 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 763 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 764 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 765 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_abs__of__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 766 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 767 (all V_n all V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_m = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 768 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 769 (all V_a_2 all V_b_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))) # label(fact_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 770 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x)))))) # label(fact_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 771 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 772 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 773 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_c = V_b))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 774 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))) # label(fact_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 775 (all V_c all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c))) # label(fact_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 776 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oone__class_Oone(T_a) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)))) # label(fact_divide__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 777 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__add__abs) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 778 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a))) # label(fact_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 779 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 780 (all V_a all V_r c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_a),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r)) # label(fact_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 781 (all V_a all T_a (class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_a))) # label(fact_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 782 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 783 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 784 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__square__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 785 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 786 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 787 (all V_n_2 all V_m_2 (V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 788 (all V_a all V_b all T_a (class_Rings_Odivision__ring(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 789 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 790 (all V_z c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z) # label(fact_zmult__1__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 791 (all V_za_2 all V_wa_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2))) # label(fact_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 792 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 793 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_diff__Suc__1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 794 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 795 (all V_da_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oring(T_a) -> (V_da_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2) <-> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2)))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 796 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))))) # label(fact_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 797 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 798 (all V_z all V_x all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z))))) # label(fact_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 799 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 800 (all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)))) # label(fact_abs__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 801 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> (c_Groups_Ozero__class_Ozero(T_a) != V_b -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_no__zero__divisors) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 802 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) -> V_c = V_b))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 803 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) <-> (exists B_n V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 804 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 805 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 806 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_right__minus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 807 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 808 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)) & (V_a = c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divide__self__if) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 809 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))) # label(fact_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 810 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 811 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 812 (all V_c_2 all V_b_2 all V_wa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> ((-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))) & (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2)))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))))) # label(fact_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 813 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)))) # label(fact_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 814 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 815 (all V_a all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 816 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ominus__class_Ominus(T_a,V_a,V_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 817 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 818 (all V_r all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_half__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 819 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) <-> (exists B_m c_Nat_OSuc(B_m) = V_n_2))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 820 (all V_w all V_v c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))) # label(fact_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 821 (all V_w all V_z c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) # label(fact_diff__int__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 822 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 823 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))))) # label(fact_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 824 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)))))) # label(fact_diff__frac__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 825 (all V_n all V_m ((V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))) & (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_m -> V_n = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)))) # label(fact_add__eq__if) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 826 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2) <-> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2) = V_m_2))) # label(fact_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 827 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) <-> V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 828 (all V_y all V_x (V_y = V_x | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 829 (all V_z c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)) # label(fact_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 830 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 831 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 832 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 833 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b))))) # label(fact_abs__leI) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 834 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 835 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 836 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 837 (all V_w all V_c all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,V_c,c_Int_Onumber__class_Onumber__of(T_a,V_w))))) # label(fact_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 838 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> V_a = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 839 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a))) # label(fact_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 840 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)))) # label(fact_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 841 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) # label(fact_diff__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 842 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y))) # label(fact_divide_Ozero) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 843 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a)) # label(fact_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 844 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 845 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__ge__self) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 846 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)))) # label(fact_divide_Oadd) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 847 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)))) # label(fact_number__of__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 848 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> V_b = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))) # label(fact_minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 849 (all V_k_2 (V_k_2 = c_Int_OPls <-> c_Int_OPls = c_Int_OBit0(V_k_2))) # label(fact_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 850 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 851 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))) # label(fact_less__diff__conv) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 852 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) -> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_m = V_n))) # label(fact_less__SucE) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 853 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__neg__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 854 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 855 (all V_n_2 all V_m_2 (V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & c_Groups_Oone__class_Oone(tc_Nat_Onat) = V_m_2 <-> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 856 (all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),v_d____))) # label(fact_N1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 857 (all V_wa_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> ((c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) & (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2),V_b_2))) <-> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) # label(fact_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 858 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 859 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_abs__less__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 860 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 861 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2))))) # label(fact_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 862 (all V_x all V_z all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x) -> c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 863 (all V_n c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) # label(fact_fact__lemma) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 864 (all V_l all V_k c_Int_OBit1(V_l) != c_Int_OBit0(V_k)) # label(fact_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 865 (all V_y_2 all V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 866 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))))) # label(fact_less__minus__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 867 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_b_2 = V_a_2 <-> c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 868 (all V_n_2 all V_m_2 (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 869 (all V_n c_Nat_OSuc(V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 870 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 871 (all V_y_2 all V_x_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_za_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_za_2))))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 872 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 873 (all V_n_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_m_2)) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 874 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> c_Groups_Oone__class_Oone(T_a) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_right__inverse) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 875 (all V_fa_2 ((all B_m all B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)))) <-> c_SEQ_Osubseq(V_fa_2))) # label(fact_subseq__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 876 (all V_c_2 all V_b_2 all V_wa_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Ofield__inverse__zero(T_a) -> ((c_Groups_Ozero__class_Ozero(T_a) != V_c_2 -> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),V_c_2)) & (c_Groups_Ozero__class_Ozero(T_a) = V_c_2 -> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)) <-> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)))) # label(fact_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 877 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 878 (all V_k all V_j all V_u all V_i c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_u),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_k))) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 879 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult__1__right) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 880 (all V_i all V_j -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)) # label(fact_not__add__less2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 881 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_n) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_n)))) # label(fact_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 882 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Oone__class_Oone(T_a) -> V_b = c_Rings_Oinverse__class_Oinverse(T_a,V_a)))) # label(fact_inverse__unique) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 883 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2)))) # label(fact_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 884 (all V_X_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> ((exists B_N all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) <-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K))))))) # label(fact_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 885 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_add__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 886 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = V_m_2)) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 887 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 888 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 889 (all V_m all V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m)))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.60 890 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) | V_b_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 891 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 892 (all V_ra_2 all V_a_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)))) # label(fact_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 893 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 894 (all V_b all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b) -> V_b = V_a))) # label(fact_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 895 (all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__divide) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 896 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 897 (all V_y_2 all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2)))) # label(fact_less__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 898 (all V_n (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 899 (all V_m_2 all V_n_2 (V_n_2 = V_m_2 <-> c_RealDef_Oreal(tc_Nat_Onat,V_m_2) = c_RealDef_Oreal(tc_Nat_Onat,V_n_2))) # label(fact_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 900 (all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x)) = c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ouminus__class_Ouminus(T_a,V_x)))) # label(fact_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 901 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)))) # label(fact_divide_Odiff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 902 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 903 (all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 904 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 905 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 906 (all V_z all V_w c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))) # label(fact_complex__mod__triangle__sub) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 907 (all V_da_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2),V_da_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2))))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 908 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_z -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)))))) # label(fact_add__frac__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 909 (all V_n_2 exists B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n_2))))))) # label(fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 910 (all V_a all V_b all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_c -> (V_b = c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) -> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 911 (all V_v (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) -> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_expand__Suc) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 912 (all V_k c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k)) # label(fact_Bit0__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 913 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 914 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 915 (all V_m_2 all V_b_2 all V_e2_2 all V_a_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a_2,V_e2_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_m_2)),V_e2_2) -> -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_e2_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_m_2)),V_a_2))))) # label(fact_th0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 916 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 917 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 918 (all V_n_2 all V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 919 (all V_v all V_b all V_a all T_b (class_Rings_Oring(T_b) & class_Int_Onumber(T_b) -> c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) = c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)))) # label(fact_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 920 (all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) # label(fact_complex__diff__def) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 921 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 922 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 923 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 924 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 925 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) # label(fact_Suc__pred) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 926 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 927 (exists B_f all B_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_f,B_x)),v_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,hAPP(B_f,B_x))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_x))))))) # label(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 928 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2) -> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> c_Groups_Ozero__class_Ozero(T_a) = V_y_2 & c_Groups_Ozero__class_Ozero(T_a) = V_x_2))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 929 (all V_w c_Int_OPls = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,V_w)) # label(fact_mult__Pls) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 930 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 931 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 932 (all V_n all V_m all V_u all V_i all V_j (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_u),V_m),V_n))) # label(fact_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption]. 1.32/1.61 933 (all V_z3 all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3))) # label(fact_real__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 934 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> V_a = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 935 (all V_da_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) -> (V_a_2 = V_b_2 <-> V_da_2 = V_c_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 936 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w))) # label(fact_real__le__linear) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 937 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__zero) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 938 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)))) # label(fact_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 939 (all V_a_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> ((-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))) & (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))) <-> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)))) # label(fact_divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 940 (all V_da_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_da_2))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 941 (all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 942 (all V_a all V_b c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) # label(fact_real__average__minus__second) # label(axiom) # label(non_clause). [assumption]. 1.44/1.66 1.44/1.66 ============================== end of process non-clausal formulas === 1.44/1.66 1.44/1.66 ============================== PROCESS INITIAL CLAUSES =============== 1.44/1.66 1.44/1.66 ============================== PREDICATE ELIMINATION ================= 1.44/1.66 943 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption]. 1.44/1.66 944 -class_Groups_Omonoid__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(1)]. 1.44/1.66 945 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption]. 1.51/1.77 946 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom). [assumption]. 1.51/1.77 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A) = A. [resolve(946,a,944,a)]. 1.51/1.77 947 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption]. 1.51/1.77 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) = A. [resolve(947,a,944,a)]. 1.51/1.77 948 -class_Groups_Omonoid__mult(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(879)]. 1.51/1.77 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(948,a,943,a)]. 1.51/1.77 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(948,a,945,a)]. 1.51/1.77 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(948,a,946,a)]. 1.51/1.77 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(948,a,947,a)]. 1.51/1.77 949 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__imp__less__right) # label(axiom). [clausify(386)]. 1.51/1.77 950 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 1.51/1.77 951 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 1.51/1.77 952 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 1.51/1.77 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(949,a,950,a)]. 1.51/1.77 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(949,a,951,a)]. 1.51/1.77 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(949,a,952,a)]. 1.51/1.77 953 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom). [clausify(430)]. 1.51/1.77 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(953,a,950,a)]. 1.51/1.77 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(953,a,951,a)]. 1.51/1.77 954 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom). [clausify(430)]. 1.51/1.77 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(954,a,950,a)]. 1.51/1.77 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(954,a,951,a)]. 1.61/1.80 955 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__cancel__left) # label(axiom). [clausify(539)]. 1.61/1.80 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(955,a,950,a)]. 1.61/1.80 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(955,a,951,a)]. 1.61/1.80 956 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__cancel__left) # label(axiom). [clausify(539)]. 1.61/1.80 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(956,a,950,a)]. 1.61/1.80 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(956,a,951,a)]. 1.61/1.80 957 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(630)]. 1.61/1.80 958 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(630)]. 1.61/1.80 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(958,a,950,a)]. 1.61/1.80 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(958,a,951,a)]. 1.61/1.80 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(958,a,952,a)]. 1.61/1.80 959 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__imp__le__right) # label(axiom). [clausify(634)]. 1.61/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(959,a,950,a)]. 1.61/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(959,a,951,a)]. 1.61/1.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(959,a,952,a)]. 1.61/1.80 960 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__imp__less__left) # label(axiom). [clausify(692)]. 1.64/1.89 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(960,a,952,a)]. 1.64/1.89 961 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__imp__le__left) # label(axiom). [clausify(743)]. 1.64/1.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(961,a,952,a)]. 1.64/1.89 962 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(870)]. 1.64/1.89 963 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(870)]. 1.64/1.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(963,a,950,a)]. 1.64/1.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(963,a,951,a)]. 1.64/1.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(963,a,952,a)]. 1.64/1.89 964 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 1.64/1.89 965 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,E)))) # label(fact_abs__diff__triangle__ineq) # label(axiom). [clausify(4)]. 1.64/1.89 966 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__ge__zero) # label(axiom). [clausify(49)]. 1.64/1.89 967 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_abs__triangle__ineq2) # label(axiom). [clausify(79)]. 1.64/1.89 968 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__of__pos) # label(axiom). [clausify(128)]. 1.64/1.89 969 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_abs__le__D2) # label(axiom). [clausify(221)]. 1.64/1.89 970 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_abs__le__D1) # label(axiom). [clausify(231)]. 1.64/1.89 971 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__minus__le__zero) # label(axiom). [clausify(259)]. 1.64/1.90 972 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_abs__triangle__ineq3) # label(axiom). [clausify(270)]. 1.64/1.90 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,D))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)))). [resolve(964,a,965,a)]. 1.64/1.90 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)). [resolve(964,a,966,a)]. 1.64/1.90 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))). [resolve(964,a,967,a)]. 1.64/1.90 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A. [resolve(964,a,968,a)]. 1.64/1.90 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B). [resolve(964,a,969,a)]. 1.64/1.90 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(964,a,971,a)]. 1.64/1.90 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))). [resolve(964,a,972,a)]. 1.64/1.90 973 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_abs__zero) # label(axiom). [clausify(325)]. 1.64/1.90 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(973,a,964,a)]. 1.64/1.90 974 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_abs__of__nonpos) # label(axiom). [clausify(409)]. 1.64/1.90 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A). [resolve(974,a,964,a)]. 1.64/1.90 975 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_abs__le__iff) # label(axiom). [clausify(434)]. 1.64/1.90 976 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_abs__le__iff) # label(axiom). [clausify(434)]. 1.64/1.90 977 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_abs__le__iff) # label(axiom). [clausify(434)]. 1.64/1.90 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(977,a,964,a)]. 1.73/1.95 978 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,B) # label(fact_abs__idempotent) # label(axiom). [clausify(441)]. 1.73/1.95 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A). [resolve(978,a,964,a)]. 1.73/1.95 979 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__eq__0) # label(axiom). [clausify(471)]. 1.73/1.95 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(979,a,964,a)]. 1.73/1.95 980 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__eq__0) # label(axiom). [clausify(471)]. 1.73/1.95 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(980,a,964,a)]. 1.73/1.95 981 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__not__less__zero) # label(axiom). [clausify(554)]. 1.73/1.95 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(981,a,964,a)]. 1.73/1.95 982 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B))) # label(fact_abs__triangle__ineq2__sym) # label(axiom). [clausify(658)]. 1.73/1.95 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A))). [resolve(982,a,964,a)]. 1.73/1.95 983 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(686)]. 1.73/1.95 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(983,a,964,a)]. 1.73/1.95 984 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(686)]. 1.73/1.95 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(984,a,964,a)]. 1.73/1.95 985 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__ge__minus__self) # label(axiom). [clausify(711)]. 1.73/1.95 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)). [resolve(985,a,964,a)]. 1.73/1.95 986 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)) # label(fact_abs__minus__commute) # label(axiom). [clausify(747)]. 1.73/1.97 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)). [resolve(986,a,964,a)]. 1.73/1.97 987 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_abs__of__neg) # label(axiom). [clausify(765)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A). [resolve(987,a,964,a)]. 1.73/1.97 988 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)) = c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))) # label(fact_abs__add__abs) # label(axiom). [clausify(777)]. 1.73/1.97 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))). [resolve(988,a,964,a)]. 1.73/1.97 989 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__of__nonneg) # label(axiom). [clausify(778)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A. [resolve(989,a,964,a)]. 1.73/1.97 990 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))) # label(fact_abs__triangle__ineq) # label(axiom). [clausify(789)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))). [resolve(990,a,964,a)]. 1.73/1.97 991 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) # label(fact_abs__leI) # label(axiom). [clausify(833)]. 1.73/1.97 992 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__ge__self) # label(axiom). [clausify(845)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)). [resolve(992,a,964,a)]. 1.73/1.97 993 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,D))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,D)))). [resolve(993,a,965,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)). [resolve(993,a,966,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B))). [resolve(993,a,967,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A. [resolve(993,a,968,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B). [resolve(993,a,969,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(993,a,970,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(993,a,971,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B))). [resolve(993,a,972,a)]. 1.73/1.97 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(993,a,973,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A). [resolve(993,a,974,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(993,a,977,a)]. 1.73/1.97 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,A). [resolve(993,a,978,a)]. 1.73/1.97 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(993,a,979,a)]. 1.73/1.97 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(993,a,980,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(993,a,981,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A))). [resolve(993,a,982,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(993,a,983,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(993,a,984,a)]. 1.73/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)). [resolve(993,a,985,a)]. 1.73/1.97 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A)). [resolve(993,a,986,a)]. 1.73/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A). [resolve(993,a,987,a)]. 1.73/1.97 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))). [resolve(993,a,988,a)]. 1.81/2.03 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A. [resolve(993,a,989,a)]. 1.81/2.03 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))). [resolve(993,a,990,a)]. 1.81/2.03 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)). [resolve(993,a,992,a)]. 1.81/2.03 994 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__le__zero__iff) # label(axiom). [clausify(913)]. 1.81/2.03 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(994,a,964,a)]. 1.81/2.03 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(994,a,993,a)]. 1.81/2.03 995 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__le__zero__iff) # label(axiom). [clausify(913)]. 1.81/2.03 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(995,a,964,a)]. 1.81/2.03 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(995,a,993,a)]. 1.81/2.03 996 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))) # label(fact_abs__triangle__ineq4) # label(axiom). [clausify(924)]. 1.81/2.03 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))). [resolve(996,a,964,a)]. 1.81/2.03 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))). [resolve(996,a,993,a)]. 1.81/2.03 997 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Oabs__class_Oabs(A,B) # label(fact_abs__minus__cancel) # label(axiom). [clausify(930)]. 1.81/2.03 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A). [resolve(997,a,964,a)]. 1.81/2.03 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,A). [resolve(997,a,993,a)]. 1.81/2.03 998 -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__commute) # label(axiom). [clausify(18)]. 1.81/2.03 999 class_Rings_Oring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring) # label(axiom). [assumption]. 1.81/2.03 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(998,a,999,a)]. 1.81/2.04 1000 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__right) # label(axiom). [clausify(66)]. 1.81/2.04 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1000,a,999,a)]. 1.81/2.04 1001 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E) != F | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E) # label(fact_eq__add__iff2) # label(axiom). [clausify(166)]. 1.81/2.04 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C),D) != E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C),E) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),D). [resolve(1001,a,999,a)]. 1.81/2.04 1002 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E) = F | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E) # label(fact_eq__add__iff2) # label(axiom). [clausify(166)]. 1.81/2.04 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C),D) = E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C),E) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),D). [resolve(1002,a,999,a)]. 1.81/2.04 1003 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)),c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),D)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,E,D)) # label(fact_mult__diff__mult) # label(axiom). [clausify(171)]. 1.81/2.04 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D),C)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,C)). [resolve(1003,a,999,a)]. 1.81/2.04 1004 class_Rings_Oring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring) # label(axiom). [assumption]. 1.81/2.04 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)). [resolve(1004,a,998,a)]. 1.81/2.04 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)). [resolve(1004,a,1000,a)]. 1.81/2.04 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D) != E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D). [resolve(1004,a,1001,a)]. 1.81/2.04 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D) = E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D). [resolve(1004,a,1002,a)]. 1.81/2.05 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D),C)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,C)). [resolve(1004,a,1003,a)]. 1.81/2.05 1005 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption]. 1.81/2.05 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1005,a,998,a)]. 1.81/2.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1005,a,1000,a)]. 1.81/2.05 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D) != E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D). [resolve(1005,a,1001,a)]. 1.81/2.05 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D) = E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D). [resolve(1005,a,1002,a)]. 1.81/2.05 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D),C)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,C)). [resolve(1005,a,1003,a)]. 1.81/2.05 1006 -class_Rings_Oring(A) | -class_Int_Onumber(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C),c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) = c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_right__diff__distrib__number__of) # label(axiom). [clausify(310)]. 1.81/2.05 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A),B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A),C)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C)). [resolve(1006,a,999,a)]. 1.81/2.05 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C)). [resolve(1006,a,1004,a)]. 1.81/2.05 1007 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_minus__mult__left) # label(axiom). [clausify(431)]. 1.81/2.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B). [resolve(1007,a,999,a)]. 1.91/2.10 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B). [resolve(1007,a,1004,a)]. 1.91/2.10 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B). [resolve(1007,a,1005,a)]. 1.91/2.10 1008 -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Otimes__class_Otimes(A,B,C) # label(fact_minus__mult__minus) # label(axiom). [clausify(680)]. 1.91/2.10 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B). [resolve(1008,a,999,a)]. 1.91/2.10 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B). [resolve(1008,a,1004,a)]. 1.91/2.10 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B). [resolve(1008,a,1005,a)]. 1.91/2.10 1009 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E) != F | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F) # label(fact_eq__add__iff1) # label(axiom). [clausify(795)]. 1.91/2.10 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C),D) != E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),D) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C),E). [resolve(1009,a,999,a)]. 1.91/2.10 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D) != E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E). [resolve(1009,a,1004,a)]. 1.91/2.10 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D) != E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E). [resolve(1009,a,1005,a)]. 1.91/2.10 1010 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E) = F | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F) # label(fact_eq__add__iff1) # label(axiom). [clausify(795)]. 1.91/2.10 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C),D) = E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),D) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C),E). [resolve(1010,a,999,a)]. 1.91/2.10 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D) = E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E). [resolve(1010,a,1004,a)]. 1.95/2.19 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D) = E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E). [resolve(1010,a,1005,a)]. 1.95/2.19 1011 -class_Rings_Oring(A) | -class_Int_Onumber(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)),c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_left__diff__distrib__number__of) # label(axiom). [clausify(919)]. 1.95/2.19 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B))) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)). [resolve(1011,a,999,a)]. 1.95/2.19 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1011,a,1004,a)]. 1.95/2.19 Derived: -class_Int_Onumber(tc_Int_Oint) | c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)). [resolve(1011,a,1005,a)]. 1.95/2.19 1012 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 1.95/2.19 1013 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__neg__neg) # label(axiom). [clausify(6)]. 1.95/2.19 1014 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(30)]. 1.95/2.19 1015 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(95)]. 1.95/2.19 1016 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(95)]. 1.95/2.19 1017 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(273)]. 1.95/2.19 1018 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(275)]. 1.95/2.19 1019 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(275)]. 1.95/2.19 1020 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(292)]. 1.95/2.19 1021 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(292)]. 1.95/2.19 1022 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__le__0__iff) # label(axiom). [clausify(311)]. 1.95/2.19 1023 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(311)]. 1.95/2.19 1024 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__le__0__iff) # label(axiom). [clausify(311)]. 1.95/2.19 1025 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(311)]. 1.95/2.19 1026 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(311)]. 1.95/2.19 1027 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(311)]. 1.95/2.19 1028 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(348)]. 1.95/2.19 1029 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(348)]. 1.95/2.19 1030 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,D,B) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(389)]. 1.95/2.19 1031 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,D,B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(389)]. 1.95/2.19 1032 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(389)]. 1.95/2.19 1033 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(389)]. 1.95/2.19 1034 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,D,B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(389)]. 1.95/2.19 1035 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,B,D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(389)]. 1.95/2.19 1036 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(442)]. 1.95/2.19 1037 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(442)]. 1.95/2.19 1038 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(442)]. 1.95/2.19 1039 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))) # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(509)]. 1.95/2.19 1040 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,C),c_Groups_Otimes__class_Otimes(A,B,B))) # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(509)]. 1.95/2.19 1041 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))) # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(509)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1012,a,1013,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1012,a,1014,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1012,a,1015,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1012,a,1016,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)). [resolve(1012,a,1017,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B). [resolve(1012,a,1018,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B). [resolve(1012,a,1019,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1012,a,1021,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1012,a,1022,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1012,a,1025,a)]. 1.95/2.19 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1012,a,1026,a)]. 1.95/2.19 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1012,a,1027,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1012,a,1028,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1012,a,1029,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1012,a,1030,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1012,a,1031,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1012,a,1032,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1012,a,1033,a)]. 1.95/2.19 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1012,a,1035,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1012,a,1036,a)]. 1.95/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1012,a,1037,a)]. 1.95/2.19 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1012,a,1038,a)]. 1.95/2.21 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B))). [resolve(1012,a,1039,a)]. 1.95/2.21 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A))). [resolve(1012,a,1040,a)]. 1.95/2.21 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B))). [resolve(1012,a,1041,a)]. 1.95/2.21 1042 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(637)]. 1.95/2.21 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1042,a,1012,a)]. 1.95/2.21 1043 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(637)]. 1.95/2.21 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1043,a,1012,a)]. 1.95/2.21 1044 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,D,C) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(637)]. 1.95/2.21 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1044,a,1012,a)]. 1.95/2.21 1045 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,D,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(637)]. 1.95/2.21 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1045,a,1012,a)]. 1.95/2.21 1046 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(637)]. 2.04/2.23 1047 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,C,D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(637)]. 2.04/2.23 1048 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(698)]. 2.04/2.23 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1048,a,1012,a)]. 2.04/2.23 1049 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(698)]. 2.04/2.23 1050 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(698)]. 2.04/2.23 1051 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(698)]. 2.04/2.23 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1051,a,1012,a)]. 2.04/2.23 1052 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(698)]. 2.04/2.23 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1052,a,1012,a)]. 2.04/2.23 1053 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(698)]. 2.04/2.23 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1053,a,1012,a)]. 2.04/2.27 1054 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(783)]. 2.04/2.27 1055 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(783)]. 2.04/2.27 1056 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(783)]. 2.04/2.27 1057 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1057,a,1013,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1057,a,1014,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1057,a,1015,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1057,a,1016,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,A)). [resolve(1057,a,1017,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B). [resolve(1057,a,1018,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B). [resolve(1057,a,1019,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1057,a,1021,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1022,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1057,a,1023,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1024,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1057,a,1025,a)]. 2.04/2.27 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1057,a,1026,a)]. 2.04/2.27 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1057,a,1027,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1057,a,1028,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1057,a,1029,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1057,a,1030,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1057,a,1031,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1057,a,1032,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1057,a,1033,a)]. 2.04/2.27 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1057,a,1035,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1057,a,1036,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1057,a,1037,a)]. 2.04/2.27 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1057,a,1038,a)]. 2.04/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B))). [resolve(1057,a,1039,a)]. 2.04/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A))). [resolve(1057,a,1040,a)]. 2.04/2.27 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B))). [resolve(1057,a,1041,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1057,a,1042,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1043,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1057,a,1044,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1045,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1057,a,1048,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1049,a)]. 2.04/2.27 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1057,a,1050,a)]. 2.12/2.36 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1051,a)]. 2.12/2.36 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1057,a,1052,a)]. 2.12/2.36 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1057,a,1053,a)]. 2.12/2.36 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1057,a,1054,a)]. 2.12/2.36 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1057,a,1055,a)]. 2.12/2.36 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1057,a,1056,a)]. 2.12/2.36 1058 class_Groups_Oab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__group__add) # label(axiom). [assumption]. 2.12/2.36 1059 -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Ominus__class_Ominus(A,B,C) # label(fact_ab__diff__minus) # label(axiom). [clausify(8)]. 2.12/2.36 1060 -class_Groups_Oab__group__add(A) | B != C | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_eq__iff__diff__eq__0) # label(axiom). [clausify(110)]. 2.12/2.36 Derived: A != B | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1060,a,1058,a)]. 2.12/2.36 1061 -class_Groups_Oab__group__add(A) | B = C | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_eq__iff__diff__eq__0) # label(axiom). [clausify(110)]. 2.12/2.36 Derived: A = B | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1061,a,1058,a)]. 2.12/2.36 1062 class_Groups_Oab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__group__add) # label(axiom). [assumption]. 2.12/2.36 Derived: A != B | c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1062,a,1060,a)]. 2.12/2.36 Derived: A = B | c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1062,a,1061,a)]. 2.12/2.36 1063 -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_ab__left__minus) # label(axiom). [clausify(465)]. 2.12/2.36 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1063,a,1058,a)]. 2.12/2.36 1064 -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_Groups_Ominus__class_Ominus(A,C,B) # label(fact_minus__diff__eq) # label(axiom). [clausify(600)]. 2.12/2.36 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A). [resolve(1064,a,1058,a)]. 2.23/2.41 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A). [resolve(1064,a,1062,a)]. 2.23/2.41 1065 -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,E)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_Deriv_Oadd__diff__add) # label(axiom). [clausify(644)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1065,a,1058,a)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1065,a,1062,a)]. 2.23/2.41 1066 -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_minus__add__distrib) # label(axiom). [clausify(810)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)). [resolve(1066,a,1058,a)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). [resolve(1066,a,1062,a)]. 2.23/2.41 1067 class_Groups_Oab__group__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__group__add) # label(axiom). [assumption]. 2.23/2.41 Derived: A != B | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1067,a,1060,a)]. 2.23/2.41 Derived: A = B | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1067,a,1061,a)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1067,a,1063,a)]. 2.23/2.41 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,A). [resolve(1067,a,1064,a)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,D)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,D)). [resolve(1067,a,1065,a)]. 2.23/2.41 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)). [resolve(1067,a,1066,a)]. 2.23/2.41 1068 -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | D != E | B = C # label(fact_diff__eq__diff__eq) # label(axiom). [clausify(935)]. 2.23/2.41 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | C != D | A = B. [resolve(1068,a,1058,a)]. 2.23/2.41 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | C != D | A = B. [resolve(1068,a,1062,a)]. 2.23/2.41 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) != c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,D) | C != D | A = B. [resolve(1068,a,1067,a)]. 2.25/2.47 1069 -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | D = E | B != C # label(fact_diff__eq__diff__eq) # label(axiom). [clausify(935)]. 2.25/2.47 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | C = D | A != B. [resolve(1069,a,1058,a)]. 2.25/2.47 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | C = D | A != B. [resolve(1069,a,1062,a)]. 2.25/2.47 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) != c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,D) | C = D | A != B. [resolve(1069,a,1067,a)]. 2.25/2.47 1070 class_Rings_Ocomm__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.25/2.47 1071 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) = c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(9)]. 2.25/2.47 1072 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,C,B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(12)]. 2.25/2.47 1073 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)) = c_Groups_Otimes__class_Otimes(A,C,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(15)]. 2.25/2.47 1074 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(40)]. 2.25/2.47 1075 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(87)]. 2.25/2.47 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1070,a,1073,a)]. 2.25/2.47 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,D)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1070,a,1075,a)]. 2.25/2.47 1076 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(327)]. 2.25/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),B). [resolve(1076,a,1070,a)]. 2.25/2.47 1077 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,c_Groups_Otimes__class_Otimes(A,D,E))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(339)]. 2.25/2.47 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,D)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,D))). [resolve(1077,a,1070,a)]. 2.25/2.49 1078 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(372)]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1078,a,1070,a)]. 2.25/2.49 1079 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(466)]. 2.25/2.49 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),B). [resolve(1079,a,1070,a)]. 2.25/2.49 1080 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.25/2.49 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)). [resolve(1080,a,1073,a)]. 2.25/2.49 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,D)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1080,a,1075,a)]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). [resolve(1080,a,1076,a)]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1080,a,1078,a)]. 2.25/2.49 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),B). [resolve(1080,a,1079,a)]. 2.25/2.49 1081 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1081,a,1071,a)]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,A). [resolve(1081,a,1072,a)]. 2.25/2.49 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1081,a,1073,a)]. 2.25/2.49 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,D)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1081,a,1075,a)]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),B). [resolve(1081,a,1076,a)]. 2.25/2.49 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1081,a,1078,a)]. 2.35/2.53 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),B). [resolve(1081,a,1079,a)]. 2.35/2.53 1082 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C)). [resolve(1082,a,1071,a)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A). [resolve(1082,a,1072,a)]. 2.35/2.53 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)). [resolve(1082,a,1073,a)]. 2.35/2.53 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C)). [resolve(1082,a,1074,a)]. 2.35/2.53 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,D)). [resolve(1082,a,1075,a)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),B). [resolve(1082,a,1076,a)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,D)). [resolve(1082,a,1078,a)]. 2.35/2.53 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),B). [resolve(1082,a,1079,a)]. 2.35/2.53 1083 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(734)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)). [resolve(1083,a,1070,a)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(1083,a,1080,a)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)). [resolve(1083,a,1081,a)]. 2.35/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)). [resolve(1083,a,1082,a)]. 2.35/2.53 1084 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Otimes__class_Otimes(A,C,B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(764)]. 2.43/2.62 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A). [resolve(1084,a,1070,a)]. 2.43/2.62 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A). [resolve(1084,a,1080,a)]. 2.43/2.62 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A). [resolve(1084,a,1081,a)]. 2.43/2.62 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,A). [resolve(1084,a,1082,a)]. 2.43/2.62 1085 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Otimes__class_Otimes(A,D,c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(768)]. 2.43/2.62 1086 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(831)]. 2.43/2.62 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(1086,a,1070,a)]. 2.43/2.62 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1086,a,1080,a)]. 2.43/2.62 1087 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(872)]. 2.43/2.62 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1087,a,1070,a)]. 2.43/2.62 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). [resolve(1087,a,1080,a)]. 2.43/2.62 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1087,a,1081,a)]. 2.43/2.62 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A). [resolve(1087,a,1082,a)]. 2.43/2.62 1088 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(891)]. 2.43/2.62 1089 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 2.43/2.62 1090 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing2) # label(axiom). [clausify(10)]. 2.43/2.62 1091 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__nonneg) # label(axiom). [clausify(36)]. 2.43/2.62 1092 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,D,B)) # label(fact_add__increasing2) # label(axiom). [clausify(122)]. 2.43/2.62 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1089,a,1090,a)]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,A)). [resolve(1089,a,1092,a)]. 2.43/2.64 1093 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__neg) # label(axiom). [clausify(196)]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1093,a,1089,a)]. 2.43/2.64 1094 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__neg) # label(axiom). [clausify(223)]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1094,a,1089,a)]. 2.43/2.64 1095 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__pos) # label(axiom). [clausify(267)]. 2.43/2.64 1096 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A)). [resolve(1096,a,1092,a)]. 2.43/2.64 1097 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing) # label(axiom). [clausify(505)]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1097,a,1089,a)]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1097,a,1096,a)]. 2.43/2.64 1098 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__increasing) # label(axiom). [clausify(513)]. 2.43/2.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1098,a,1089,a)]. 2.51/2.67 1099 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__pos__nonneg) # label(axiom). [clausify(515)]. 2.51/2.67 1100 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1100,a,1090,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)). [resolve(1100,a,1091,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A)). [resolve(1100,a,1092,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1100,a,1093,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1100,a,1094,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1100,a,1097,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1100,a,1098,a)]. 2.51/2.67 1101 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__nonpos) # label(axiom). [clausify(720)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1101,a,1089,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1101,a,1096,a)]. 2.51/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1101,a,1100,a)]. 2.54/2.71 1102 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__pos__pos) # label(axiom). [clausify(758)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). [resolve(1102,a,1089,a)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)). [resolve(1102,a,1100,a)]. 2.54/2.71 1103 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__nonpos) # label(axiom). [clausify(792)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1103,a,1089,a)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1103,a,1100,a)]. 2.54/2.71 1104 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(928)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1104,a,1089,a)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1104,a,1096,a)]. 2.54/2.71 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1104,a,1100,a)]. 2.54/2.71 1105 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(928)]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1105,a,1089,a)]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1105,a,1096,a)]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1105,a,1100,a)]. 2.66/2.83 1106 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(928)]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1106,a,1089,a)]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A. [resolve(1106,a,1096,a)]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1106,a,1100,a)]. 2.66/2.83 1107 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 2.66/2.83 1108 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__left__mono) # label(axiom). [clausify(14)]. 2.66/2.83 1109 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 2.66/2.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). [resolve(1109,a,1108,a)]. 2.66/2.83 1110 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__mono) # label(axiom). [clausify(836)]. 2.73/2.93 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1110,a,1107,a)]. 2.73/2.93 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1110,a,1109,a)]. 2.73/2.93 1111 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 2.73/2.93 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1111,a,1110,a)]. 2.73/2.93 1112 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__right__mono) # label(axiom). [clausify(854)]. 2.73/2.93 1113 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption]. 2.73/2.93 1114 -class_RealVector_Oreal__normed__field(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C),c_RealVector_Onorm__class_Onorm(A,B)) = c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_nonzero__norm__divide) # label(axiom). [clausify(16)]. 2.73/2.93 1115 -class_Fields_Ofield__inverse__zero(A) | -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)) = c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_norm__divide) # label(axiom). [clausify(226)]. 2.73/2.93 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1113,a,1114,a)]. 2.73/2.93 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1113,a,1115,b)]. 2.73/2.93 1116 -class_RealVector_Oreal__normed__field(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)),D) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D)),c_Rings_Oinverse__class_Oinverse(A,C))) # label(fact_DERIV__inverse__lemma) # label(axiom). [clausify(556)]. 2.73/2.93 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),C) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))). [resolve(1116,a,1113,a)]. 2.80/2.99 1117 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide_Ominus) # label(axiom). [clausify(736)]. 2.80/2.99 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1117,a,1113,a)]. 2.80/2.99 1118 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide_Ozero) # label(axiom). [clausify(842)]. 2.80/2.99 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1118,a,1113,a)]. 2.80/2.99 1119 -class_RealVector_Oreal__normed__field(A) | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Rings_Oinverse__class_Odivide(A,D,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_divide_Oadd) # label(axiom). [clausify(846)]. 2.80/2.99 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),B). [resolve(1119,a,1113,a)]. 2.80/2.99 1120 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide_Odiff) # label(axiom). [clausify(901)]. 2.80/2.99 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1120,a,1113,a)]. 2.80/2.99 1121 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption]. 2.80/2.99 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A)). [resolve(1121,a,1114,a)]. 2.80/2.99 Derived: -class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)). [resolve(1121,a,1115,b)]. 2.80/2.99 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)),C) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B))). [resolve(1121,a,1116,a)]. 2.80/2.99 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)). [resolve(1121,a,1117,a)]. 2.80/2.99 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1121,a,1118,a)]. 2.86/3.09 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),B). [resolve(1121,a,1119,a)]. 2.86/3.09 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)). [resolve(1121,a,1120,a)]. 2.86/3.09 1122 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption]. 2.86/3.09 1123 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))) # label(fact_zero__less__two) # label(axiom). [clausify(17)]. 2.86/3.09 1124 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_pos__add__strict) # label(axiom). [clausify(63)]. 2.86/3.09 1125 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__le__one) # label(axiom). [clausify(85)]. 2.86/3.09 1126 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__less__zero) # label(axiom). [clausify(284)]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1122,a,1123,a)]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1122,a,1125,a)]. 2.86/3.09 1127 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_less__add__one) # label(axiom). [clausify(500)]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1127,a,1122,a)]. 2.86/3.09 1128 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1128,a,1123,a)]. 2.86/3.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)). [resolve(1128,a,1124,a)]. 2.86/3.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1128,a,1126,a)]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1128,a,1127,a)]. 2.86/3.09 1129 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__less__one) # label(axiom). [clausify(646)]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1129,a,1122,a)]. 2.86/3.09 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1129,a,1128,a)]. 3.03/3.20 1130 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__le__zero) # label(axiom). [clausify(710)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1130,a,1122,a)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1130,a,1128,a)]. 3.03/3.20 1131 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption]. 3.03/3.20 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1131,a,1123,a)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(1131,a,1124,a)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1131,a,1126,a)]. 3.03/3.20 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1131,a,1127,a)]. 3.03/3.20 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1131,a,1129,a)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1131,a,1130,a)]. 3.03/3.20 1132 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_less__1__mult) # label(axiom). [clausify(887)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1132,a,1122,a)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1132,a,1128,a)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1132,a,1131,a)]. 3.03/3.20 1133 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom). [assumption]. 3.03/3.20 1134 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E),F) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(20)]. 3.03/3.20 1135 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E),F) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(20)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E)). [resolve(1133,a,1134,a)]. 3.03/3.20 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D),E) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E)). [resolve(1133,a,1135,a)]. 3.03/3.20 1136 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,C,D),E),F)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,E),B),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,E),F)) # label(fact_le__add__iff2) # label(axiom). [clausify(65)]. 3.03/3.20 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C),D),E)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,D),A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D),E)). [resolve(1136,a,1133,a)]. 3.03/3.20 1137 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,C,D),E),F)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,E),B),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,E),F)) # label(fact_le__add__iff2) # label(axiom). [clausify(65)]. 3.03/3.20 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C),D),E)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,D),A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D),E)). [resolve(1137,a,1133,a)]. 3.03/3.20 1138 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(165)]. 3.03/3.20 1139 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,C,B)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(165)]. 3.03/3.20 1140 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__nonpos__nonpos) # label(axiom). [clausify(176)]. 3.11/3.28 1141 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__right__mono__neg) # label(axiom). [clausify(215)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1141,a,1133,a)]. 3.11/3.28 1142 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D),E) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E)). [resolve(1142,a,1134,a)]. 3.11/3.28 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D),E) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E)). [resolve(1142,a,1135,a)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C),D),E)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,D),A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D),E)). [resolve(1142,a,1136,a)]. 3.11/3.28 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C),D),E)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,D),A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D),E)). [resolve(1142,a,1137,a)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1142,a,1141,a)]. 3.11/3.28 1143 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_mult__left__mono__neg) # label(axiom). [clausify(797)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)). [resolve(1143,a,1133,a)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,A)). [resolve(1143,a,1142,a)]. 3.11/3.28 1144 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E),F) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(907)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D),E) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E)). [resolve(1144,a,1133,a)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D),E) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E)). [resolve(1144,a,1142,a)]. 3.11/3.28 1145 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D),E),F) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),E),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(907)]. 3.11/3.28 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C),D),E) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),D),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),E)). [resolve(1145,a,1133,a)]. 3.11/3.28 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C),D),E) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),D),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),E)). [resolve(1145,a,1142,a)]. 3.11/3.28 1146 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)) # label(fact_less__add__iff2) # label(axiom). [clausify(940)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,B),E)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A),B),E)). [resolve(1146,a,1133,a)]. 3.11/3.28 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,B),E)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A),B),E)). [resolve(1146,a,1142,a)]. 3.11/3.28 1147 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)) # label(fact_less__add__iff2) # label(axiom). [clausify(940)]. 3.32/3.49 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,B),E)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A),B),E)). [resolve(1147,a,1133,a)]. 3.32/3.49 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,B),E)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A),B),E)). [resolve(1147,a,1142,a)]. 3.32/3.49 1148 -class_Rings_Oordered__comm__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_comm__mult__left__mono) # label(axiom). [clausify(678)]. 3.32/3.49 1149 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 3.32/3.49 1150 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 3.32/3.49 1151 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 3.32/3.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)). [resolve(1148,a,1150,a)]. 3.32/3.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)). [resolve(1148,a,1151,a)]. 3.32/3.49 1152 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption]. 3.32/3.49 1153 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))) # label(fact_norm__triangle__ineq4) # label(axiom). [clausify(21)]. 3.32/3.49 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))). [resolve(1152,a,1153,a)]. 3.32/3.49 1154 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,E)))) # label(fact_norm__diff__triangle__ineq) # label(axiom). [clausify(53)]. 3.32/3.49 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,D))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D)))). [resolve(1154,a,1152,a)]. 3.32/3.50 1155 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_RealVector_Onorm__class_Onorm(A,B) # label(fact_norm__minus__cancel) # label(axiom). [clausify(57)]. 3.32/3.50 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A). [resolve(1155,a,1152,a)]. 3.32/3.50 1156 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C))) # label(fact_norm__diff__ineq) # label(axiom). [clausify(59)]. 3.32/3.50 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B))). [resolve(1156,a,1152,a)]. 3.32/3.50 1157 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_norm__triangle__ineq3) # label(axiom). [clausify(84)]. 3.32/3.50 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B))). [resolve(1157,a,1152,a)]. 3.32/3.50 1158 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_norm__triangle__ineq2) # label(axiom). [clausify(202)]. 3.32/3.50 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B))). [resolve(1158,a,1152,a)]. 3.32/3.50 1159 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)) = c_RealVector_Onorm__class_Onorm(A,B) # label(fact_abs__norm__cancel) # label(axiom). [clausify(237)]. 3.32/3.50 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A). [resolve(1159,a,1152,a)]. 3.32/3.50 1160 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) != B | c_RealVector_Onorm__class_Onorm(A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) # label(fact_norm__eq__zero) # label(axiom). [clausify(239)]. 3.32/3.50 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1160,a,1152,a)]. 3.32/3.50 1161 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) = B | c_RealVector_Onorm__class_Onorm(A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) # label(fact_norm__eq__zero) # label(axiom). [clausify(239)]. 3.32/3.52 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1161,a,1152,a)]. 3.32/3.52 1162 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_norm__not__less__zero) # label(axiom). [clausify(277)]. 3.32/3.52 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1162,a,1152,a)]. 3.32/3.52 1163 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A,D))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_norm__ratiotest__lemma) # label(axiom). [clausify(318)]. 3.32/3.52 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1163,a,1152,a)]. 3.32/3.52 1164 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f10(B,A,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,D)),f11(B,A)) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(546)]. 3.32/3.52 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f10(A,tc_Complex_Ocomplex,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,C)),f11(A,tc_Complex_Ocomplex)). [resolve(1164,a,1152,a)]. 3.32/3.52 1165 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f10(B,A,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f11(B,A)) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(546)]. 3.32/3.52 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f10(A,tc_Complex_Ocomplex,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f11(A,tc_Complex_Ocomplex)). [resolve(1165,a,1152,a)]. 3.32/3.52 1166 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f12(B,A)))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f13(B,A,D))),D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(546)]. 3.32/3.52 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f12(A,tc_Complex_Ocomplex)))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f13(A,tc_Complex_Ocomplex,C))),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1166,a,1152,a)]. 3.32/3.52 1167 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)) # label(fact_norm__ge__zero) # label(axiom). [clausify(597)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)). [resolve(1167,a,1152,a)]. 3.32/3.55 1168 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_norm__le__zero__iff) # label(axiom). [clausify(607)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1168,a,1152,a)]. 3.32/3.55 1169 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_norm__le__zero__iff) # label(axiom). [clausify(607)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1169,a,1152,a)]. 3.32/3.55 1170 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)) # label(fact_zero__less__norm__iff) # label(axiom). [clausify(688)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)). [resolve(1170,a,1152,a)]. 3.32/3.55 1171 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)) # label(fact_zero__less__norm__iff) # label(axiom). [clausify(688)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)). [resolve(1171,a,1152,a)]. 3.32/3.55 1172 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,B)) # label(fact_norm__minus__commute) # label(axiom). [clausify(723)]. 3.32/3.55 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,A)). [resolve(1172,a,1152,a)]. 3.32/3.55 1173 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))). [resolve(1173,a,1153,a)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,D))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)))). [resolve(1173,a,1154,a)]. 3.32/3.55 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A). [resolve(1173,a,1155,a)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))). [resolve(1173,a,1156,a)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))). [resolve(1173,a,1157,a)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))). [resolve(1173,a,1158,a)]. 3.32/3.55 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A). [resolve(1173,a,1159,a)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1173,a,1160,a)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1173,a,1161,a)]. 3.32/3.55 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1173,a,1162,a)]. 3.32/3.55 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1173,a,1163,a)]. 3.32/3.55 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f10(A,tc_RealDef_Oreal,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,C)),f11(A,tc_RealDef_Oreal)). [resolve(1173,a,1164,a)]. 3.32/3.55 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f10(A,tc_RealDef_Oreal,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f11(A,tc_RealDef_Oreal)). [resolve(1173,a,1165,a)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f12(A,tc_RealDef_Oreal)))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f13(A,tc_RealDef_Oreal,C))),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1173,a,1166,a)]. 3.32/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)). [resolve(1173,a,1167,a)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1173,a,1168,a)]. 3.32/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1173,a,1169,a)]. 3.40/3.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)). [resolve(1173,a,1170,a)]. 3.40/3.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)). [resolve(1173,a,1171,a)]. 3.40/3.57 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)). [resolve(1173,a,1172,a)]. 3.40/3.57 1174 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,E)) # label(fact_norm__add__less) # label(axiom). [clausify(760)]. 3.40/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1174,a,1152,a)]. 3.40/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1174,a,1173,a)]. 3.40/3.57 1175 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))) # label(fact_norm__triangle__ineq) # label(axiom). [clausify(823)]. 3.40/3.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))). [resolve(1175,a,1152,a)]. 3.40/3.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))). [resolve(1175,a,1173,a)]. 3.40/3.57 1176 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f21(B,A,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f22(B,A)) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(884)]. 3.40/3.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f21(A,tc_Complex_Ocomplex,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f22(A,tc_Complex_Ocomplex)). [resolve(1176,a,1152,a)]. 3.40/3.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f21(A,tc_RealDef_Oreal,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f22(A,tc_RealDef_Oreal)). [resolve(1176,a,1173,a)]. 3.47/3.65 1177 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f21(B,A,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,D)),f22(B,A)) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(884)]. 3.47/3.65 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f21(A,tc_Complex_Ocomplex,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,C)),f22(A,tc_Complex_Ocomplex)). [resolve(1177,a,1152,a)]. 3.47/3.65 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f21(A,tc_RealDef_Oreal,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,C)),f22(A,tc_RealDef_Oreal)). [resolve(1177,a,1173,a)]. 3.47/3.65 1178 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f23(B,A)))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f24(B,A,D))),D) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(884)]. 3.47/3.65 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f23(A,tc_Complex_Ocomplex)))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f24(A,tc_Complex_Ocomplex,C))),C). [resolve(1178,a,1152,a)]. 3.47/3.65 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f23(A,tc_RealDef_Oreal)))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f24(A,tc_RealDef_Oreal,C))),C). [resolve(1178,a,1173,a)]. 3.47/3.65 1179 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) # label(fact_norm__zero) # label(axiom). [clausify(937)]. 3.47/3.65 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1179,a,1152,a)]. 3.47/3.65 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1179,a,1173,a)]. 3.47/3.65 1180 -class_Rings_Olinordered__semiring__1__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oplus__class_Oplus(A,E,F) != c_Groups_Oone__class_Oone(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C) # label(fact_convex__bound__lt) # label(axiom). [clausify(274)]. 3.47/3.65 1181 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 3.47/3.65 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,D,E) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,E,C)),B). [resolve(1180,a,1181,a)]. 3.62/3.85 1182 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 3.62/3.85 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,E) != c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,E,C)),B). [resolve(1182,a,1180,a)]. 3.62/3.85 1183 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption]. 3.62/3.85 1184 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1185 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1186 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1187 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1188 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1189 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1190 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1191 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1192 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1193 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(23)]. 3.62/3.85 1194 -class_Int_Onumber__ring(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_half__gt__zero__iff) # label(axiom). [clausify(43)]. 3.62/3.85 1195 -class_Int_Onumber__ring(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_half__gt__zero__iff) # label(axiom). [clausify(43)]. 3.62/3.85 1196 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1197 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1198 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1199 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1200 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),B) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1201 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1202 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),B) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1203 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1204 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1205 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(48)]. 3.62/3.85 1206 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,B))) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1207 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)),C) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1208 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B))) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)),C) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1209 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1210 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C))) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1211 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1212 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C))) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1213 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)),C) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1214 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)),C) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1215 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,B))) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(160)]. 3.62/3.85 1216 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_inverse__positive__iff__positive) # label(axiom). [clausify(185)]. 3.62/3.85 1217 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_inverse__positive__iff__positive) # label(axiom). [clausify(185)]. 3.62/3.85 1218 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(197)]. 3.62/3.85 1219 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(197)]. 3.62/3.85 1220 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(197)]. 3.62/3.85 1221 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(197)]. 3.62/3.85 1222 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(197)]. 3.62/3.85 1223 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(197)]. 3.62/3.85 1224 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),B) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_abs__div__pos) # label(axiom). [clausify(204)]. 3.62/3.85 1225 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(255)]. 3.62/3.85 1226 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(255)]. 3.62/3.85 1227 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(255)]. 3.62/3.85 1228 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom). [clausify(346)]. 3.62/3.85 1229 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom). [clausify(346)]. 3.62/3.85 1230 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom). [clausify(346)]. 3.62/3.85 1231 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom). [clausify(346)]. 3.62/3.85 1232 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom). [clausify(346)]. 3.62/3.85 1233 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom). [clausify(346)]. 3.62/3.85 1234 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__negative__iff__negative) # label(axiom). [clausify(361)]. 3.62/3.85 1235 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__negative__iff__negative) # label(axiom). [clausify(361)]. 3.62/3.85 1236 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1237 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1238 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1239 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1240 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1241 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1242 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1243 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1244 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),C) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1245 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),C) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_less__divide__eq) # label(axiom). [clausify(374)]. 3.62/3.85 1246 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,D),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_divide__right__mono__neg) # label(axiom). [clausify(382)]. 3.62/3.85 1247 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(422)]. 3.62/3.85 1248 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oone__class_Oone(A)) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(422)]. 3.62/3.85 1249 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oone__class_Oone(A)) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(422)]. 3.62/3.85 1250 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_divide__left__mono__neg) # label(axiom). [clausify(437)]. 3.62/3.85 1251 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(463)]. 3.62/3.85 1252 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(463)]. 3.62/3.85 1253 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(463)]. 3.62/3.85 1254 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(463)]. 3.62/3.85 1255 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(463)]. 3.62/3.85 1256 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(463)]. 3.62/3.85 1257 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide__right__mono) # label(axiom). [clausify(473)]. 3.62/3.85 1258 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(499)]. 3.62/3.85 1259 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(499)]. 3.62/3.85 1260 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_half) # label(axiom). [clausify(545)]. 3.62/3.85 1261 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1262 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1263 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1264 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1265 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1266 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1267 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1268 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1269 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1270 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(569)]. 3.62/3.85 1271 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1272 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1273 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1274 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1275 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1276 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1277 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1278 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1279 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1280 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(570)]. 3.62/3.85 1281 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1282 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1283 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1284 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1285 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1286 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1287 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1288 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1289 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1290 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_le__divide__eq) # label(axiom). [clausify(622)]. 3.62/3.85 1291 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(669)]. 3.62/3.85 1292 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(669)]. 3.62/3.86 1293 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(669)]. 3.62/3.86 1294 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(694)]. 3.62/3.86 1295 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(694)]. 3.62/3.86 1296 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(694)]. 3.62/3.86 1297 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(694)]. 3.62/3.86 1298 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(694)]. 3.62/3.86 1299 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(694)]. 3.62/3.86 1300 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) | c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1301 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,B))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(A,D,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1302 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,B))) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,B)),C) | c_Orderings_Oord__class_Oless(A,D,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1303 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1304 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1305 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1306 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1307 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1308 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,B))) | -c_Orderings_Oord__class_Oless(A,D,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1309 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B)),D) | -c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(700)]. 3.62/3.86 1310 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1311 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1312 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1313 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1314 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1315 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),B) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1316 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1317 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1318 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1319 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(721)]. 3.62/3.86 1320 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(766)]. 3.62/3.86 1321 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(766)]. 3.62/3.86 1322 -class_Fields_Olinordered__field__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_abs__inverse) # label(axiom). [clausify(800)]. 3.62/3.86 1323 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1324 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,D),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1325 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B),C) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,D),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1326 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1327 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C),D) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1328 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1329 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D),C) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1330 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1331 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,D),c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 1332 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(812)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1183,a,1184,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1183,a,1185,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1183,a,1186,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1183,a,1187,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1183,a,1188,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1183,a,1189,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1183,a,1190,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1183,a,1191,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1183,a,1192,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1183,a,1193,b)]. 3.62/3.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1194,b)]. 3.62/3.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1195,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1196,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1197,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1198,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1199,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1200,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1201,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1202,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1203,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1204,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1205,b)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C). [resolve(1183,a,1206,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),B). [resolve(1183,a,1207,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),B). [resolve(1183,a,1208,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1183,a,1209,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1183,a,1210,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1183,a,1211,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1183,a,1212,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),B). [resolve(1183,a,1213,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),B). [resolve(1183,a,1214,a)]. 3.62/3.86 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C). [resolve(1183,a,1215,a)]. 3.62/3.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1183,a,1216,a)]. 3.62/3.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1183,a,1217,a)]. 3.62/3.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1218,a)]. 3.62/3.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1183,a,1219,a)]. 3.62/3.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1220,a)]. 3.62/3.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1221,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1183,a,1222,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1183,a,1223,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B),A) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1224,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1183,a,1225,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1183,a,1226,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1183,a,1227,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1183,a,1229,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1230,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1232,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1183,a,1233,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1234,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1235,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),B). [resolve(1183,a,1236,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1237,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1238,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1239,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1240,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1241,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1183,a,1242,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1243,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1244,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1245,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1183,a,1246,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1247,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1183,a,1248,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1183,a,1249,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1183,a,1250,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1183,a,1251,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1254,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1255,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1256,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1183,a,1257,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1258,a)]. 3.70/3.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1183,a,1259,a)]. 3.70/3.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(1183,a,1260,a)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1261,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))). [resolve(1183,a,1262,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B). [resolve(1183,a,1263,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B). [resolve(1183,a,1264,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1183,a,1265,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B). [resolve(1183,a,1266,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1183,a,1267,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B). [resolve(1183,a,1268,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1183,a,1269,b)]. 3.70/3.87 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B). [resolve(1183,a,1270,b)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)). [resolve(1183,a,1271,a)]. 3.70/3.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1183,a,1272,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),A). [resolve(1183,a,1273,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),A). [resolve(1183,a,1274,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1275,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),A). [resolve(1183,a,1276,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1183,a,1277,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),A). [resolve(1183,a,1278,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1279,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),A). [resolve(1183,a,1280,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1281,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1282,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1283,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1183,a,1284,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1183,a,1285,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1183,a,1286,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1183,a,1287,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1288,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1183,a,1289,a)]. 3.71/3.88 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1183,a,1290,a)]. 3.71/3.88 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1183,a,1291,a)]. 3.71/3.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1183,a,1292,a)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1183,a,1293,a)]. 3.71/3.89 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1294,a)]. 3.71/3.89 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1295,a)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1296,a)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1297,a)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1298,a)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1299,a)]. 3.71/3.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1320,a)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1183,a,1321,a)]. 3.71/3.89 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1183,a,1322,a)]. 3.71/3.89 1333 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(813)]. 3.71/3.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1333,a,1183,a)]. 3.71/3.89 1334 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(813)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1334,a,1183,a)]. 3.71/3.89 1335 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(813)]. 3.71/3.89 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1335,a,1183,a)]. 3.71/3.89 1336 -class_Int_Onumber__ring(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_half__gt__zero) # label(axiom). [clausify(818)]. 3.71/3.89 1337 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.89 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1337,a,1183,a)]. 3.71/3.89 1338 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.89 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1338,a,1183,a)]. 3.71/3.89 1339 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.89 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1339,a,1183,a)]. 3.71/3.89 1340 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.89 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1340,a,1183,a)]. 3.71/3.89 1341 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),B) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.89 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1341,a,1183,a)]. 3.71/3.89 1342 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.89 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1342,a,1183,a)]. 3.71/3.90 1343 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),B) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.90 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1343,a,1183,a)]. 3.71/3.90 1344 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),B)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.90 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1344,a,1183,a)]. 3.71/3.90 1345 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.90 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1345,a,1183,a)]. 3.71/3.90 1346 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B),D) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(857)]. 3.71/3.91 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1346,a,1183,a)]. 3.71/3.91 1347 -class_Fields_Olinordered__field__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_abs__divide) # label(axiom). [clausify(895)]. 3.71/3.91 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1347,a,1183,a)]. 3.71/3.91 1348 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C). [resolve(1348,a,1183,a)]. 3.71/3.91 1349 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),C) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),B). [resolve(1349,a,1183,a)]. 3.71/3.91 1350 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Otimes__class_Otimes(A,C,B)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),C) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),B). [resolve(1350,a,1183,a)]. 3.71/3.91 1351 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,C),B) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),A). [resolve(1351,a,1183,a)]. 3.71/3.91 1352 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,C),B) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),A). [resolve(1352,a,1183,a)]. 3.71/3.91 1353 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,C),B) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),A). [resolve(1353,a,1183,a)]. 3.71/3.91 1354 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,C),B) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),A). [resolve(1354,a,1183,a)]. 3.71/3.91 1355 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),C) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.71/3.91 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),B). [resolve(1355,a,1183,a)]. 3.71/3.91 1356 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),C) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.85/4.04 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),B). [resolve(1356,a,1183,a)]. 3.85/4.04 1357 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_divide__less__eq) # label(axiom). [clausify(939)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C). [resolve(1357,a,1183,a)]. 3.85/4.04 1358 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption]. 3.85/4.04 1359 -class_Fields_Olinordered__field(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_nonzero__abs__divide) # label(axiom). [clausify(24)]. 3.85/4.04 1360 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,C,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_divide__left__mono) # label(axiom). [clausify(25)]. 3.85/4.04 1361 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_negative__imp__inverse__negative) # label(axiom). [clausify(34)]. 3.85/4.04 1362 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,D),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_divide__strict__right__mono__neg) # label(axiom). [clausify(39)]. 3.85/4.04 1363 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(46)]. 3.85/4.04 1364 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(46)]. 3.85/4.04 1365 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))),C) # label(fact_gt__half__sum) # label(axiom). [clausify(109)]. 3.85/4.04 1366 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,C,B)) # label(fact_neg__le__divide__eq) # label(axiom). [clausify(115)]. 3.85/4.04 1367 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Otimes__class_Otimes(A,C,B)) # label(fact_neg__le__divide__eq) # label(axiom). [clausify(115)]. 3.85/4.04 1368 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_mult__imp__le__div__pos) # label(axiom). [clausify(120)]. 3.85/4.04 1369 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_pos__divide__less__eq) # label(axiom). [clausify(126)]. 3.85/4.04 1370 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_pos__divide__less__eq) # label(axiom). [clausify(126)]. 3.85/4.04 1371 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_inverse__le__imp__le) # label(axiom). [clausify(146)]. 3.85/4.04 1372 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__le__inverse) # label(axiom). [clausify(153)]. 3.85/4.04 1373 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__neg__pos) # label(axiom). [clausify(174)]. 3.85/4.04 1374 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__nonpos__pos) # label(axiom). [clausify(209)]. 3.85/4.04 1375 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,B),C) # label(fact_neg__divide__le__eq) # label(axiom). [clausify(230)]. 3.85/4.04 1376 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,B),C) # label(fact_neg__divide__le__eq) # label(axiom). [clausify(230)]. 3.85/4.04 1377 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(264)]. 3.85/4.04 1378 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(264)]. 3.85/4.04 1379 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_positive__imp__inverse__positive) # label(axiom). [clausify(278)]. 3.85/4.04 1380 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A)))) # label(fact_less__half__sum) # label(axiom). [clausify(321)]. 3.85/4.04 1381 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_frac__le) # label(axiom). [clausify(333)]. 3.85/4.04 1382 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide__strict__right__mono) # label(axiom). [clausify(338)]. 3.85/4.04 1383 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_divide__strict__left__mono__neg) # label(axiom). [clausify(352)]. 3.85/4.04 1384 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide__nonpos__neg) # label(axiom). [clausify(396)]. 3.85/4.04 1385 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide__nonneg__pos) # label(axiom). [clausify(423)]. 3.85/4.04 1386 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_inverse__less__imp__less__neg) # label(axiom). [clausify(461)]. 3.85/4.04 1387 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_frac__less2) # label(axiom). [clausify(481)]. 3.85/4.04 1388 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_le__imp__inverse__le) # label(axiom). [clausify(486)]. 3.85/4.04 1389 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_le__imp__inverse__le__neg) # label(axiom). [clausify(489)]. 3.85/4.04 1390 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__pos__neg) # label(axiom). [clausify(508)]. 3.85/4.04 1391 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_frac__less) # label(axiom). [clausify(523)]. 3.85/4.04 1392 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__less__inverse) # label(axiom). [clausify(541)]. 3.85/4.04 1393 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_less__imp__inverse__less) # label(axiom). [clausify(547)]. 3.85/4.04 1394 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__positive__imp__positive) # label(axiom). [clausify(559)]. 3.85/4.04 1395 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,C,B)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_divide__strict__left__mono) # label(axiom). [clausify(576)]. 3.85/4.04 1396 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | c_Orderings_Oord__class_Oless(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_neg__less__divide__eq) # label(axiom). [clausify(587)]. 3.85/4.04 1397 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_neg__less__divide__eq) # label(axiom). [clausify(587)]. 3.85/4.04 1398 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__negative__imp__negative) # label(axiom). [clausify(588)]. 3.85/4.04 1399 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_inverse__le__imp__le__neg) # label(axiom). [clausify(611)]. 3.85/4.04 1400 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(693)]. 3.85/4.04 1401 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | -c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(693)]. 3.85/4.04 1402 -class_Fields_Olinordered__field(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_nonzero__abs__inverse) # label(axiom). [clausify(699)]. 3.85/4.04 1403 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_mult__imp__div__pos__le) # label(axiom). [clausify(707)]. 3.85/4.04 1404 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_inverse__less__imp__less) # label(axiom). [clausify(715)]. 3.85/4.04 1405 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide__pos__pos) # label(axiom). [clausify(733)]. 3.85/4.04 1406 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_mult__imp__div__pos__less) # label(axiom). [clausify(798)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1358,a,1360,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1358,a,1362,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),B). [resolve(1358,a,1365,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)). [resolve(1358,a,1366,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)). [resolve(1358,a,1367,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1358,a,1371,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1358,a,1374,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),B). [resolve(1358,a,1375,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),B). [resolve(1358,a,1376,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),B). [resolve(1358,a,1377,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),B). [resolve(1358,a,1378,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). [resolve(1358,a,1380,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,D),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1358,a,1381,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1358,a,1382,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1358,a,1383,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1358,a,1384,a)]. 3.85/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(1358,a,1385,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1358,a,1386,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,D),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1358,a,1387,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1358,a,1388,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1358,a,1389,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,D),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1358,a,1391,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1358,a,1393,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1358,a,1395,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1358,a,1396,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1358,a,1397,a)]. 3.85/4.05 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1358,a,1399,a)]. 3.91/4.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1358,a,1404,a)]. 3.91/4.16 1407 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide__neg__neg) # label(axiom). [clausify(853)]. 3.91/4.16 1408 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(861)]. 3.91/4.16 1409 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(861)]. 3.91/4.16 1410 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),D) | c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_mult__imp__less__div__pos) # label(axiom). [clausify(862)]. 3.91/4.16 1411 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__nonneg__neg) # label(axiom). [clausify(905)]. 3.91/4.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1411,a,1358,a)]. 3.91/4.16 1412 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_less__imp__inverse__less__neg) # label(axiom). [clausify(917)]. 3.91/4.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1412,a,1358,a)]. 3.91/4.16 1413 -class_Groups_Ocomm__monoid__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_mult__1) # label(axiom). [clausify(253)]. 3.91/4.16 1414 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 3.91/4.16 1415 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 3.91/4.16 1416 -class_Groups_Ocomm__monoid__mult(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom). [clausify(261)]. 3.91/4.16 1417 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 4.32/4.48 1418 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 4.32/4.48 1419 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption]. 4.32/4.48 1420 -class_RealVector_Oreal__normed__algebra__1(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) # label(fact_norm__one) # label(axiom). [clausify(28)]. 4.32/4.48 1421 -class_RealVector_Oreal__normed__algebra__1(A) | -class_Int_Onumber__ring(A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = c_RealVector_Onorm__class_Onorm(A,c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_norm__number__of) # label(axiom). [clausify(330)]. 4.32/4.48 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1419,a,1420,a)]. 4.32/4.48 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1419,a,1421,a)]. 4.32/4.48 1422 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption]. 4.32/4.48 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1422,a,1420,a)]. 4.32/4.48 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)). [resolve(1422,a,1421,a)]. 4.32/4.48 1423 class_Groups_Oabs__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oabs__if) # label(axiom). [assumption]. 4.32/4.48 1424 -class_Groups_Oabs__if(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__if) # label(axiom). [clausify(31)]. 4.32/4.48 1425 -class_Groups_Oabs__if(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_abs__if) # label(axiom). [clausify(31)]. 4.32/4.48 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A. [resolve(1423,a,1424,a)]. 4.32/4.48 1426 class_Groups_Oabs__if(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oabs__if) # label(axiom). [assumption]. 4.32/4.48 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A. [resolve(1426,a,1424,a)]. 4.32/4.48 1427 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom). [assumption]. 4.32/4.48 1428 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_inverse__1) # label(axiom). [clausify(38)]. 4.32/4.48 1429 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),B) = c_Groups_Oone__class_Oone(A) # label(fact_left__inverse) # label(axiom). [clausify(41)]. 4.32/4.48 1430 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_nonzero__inverse__minus__eq) # label(axiom). [clausify(75)]. 4.32/4.48 1431 -class_Rings_Odivision__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Rings_Oinverse__class_Odivide(A,D,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_add__divide__distrib) # label(axiom). [clausify(80)]. 4.32/4.49 1432 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__eq__divide) # label(axiom). [clausify(103)]. 4.32/4.49 1433 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_eq__divide__imp) # label(axiom). [clausify(108)]. 4.32/4.49 1434 -class_Int_Onumber(A) | -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,c_Int_Onumber__class_Onumber__of(A,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_inverse__eq__divide__number__of) # label(axiom). [clausify(111)]. 4.32/4.49 1435 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != c_Groups_Oone__class_Oone(A) | C = B # label(fact_right__inverse__eq) # label(axiom). [clausify(161)]. 4.32/4.49 1436 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = c_Groups_Oone__class_Oone(A) | C != B # label(fact_right__inverse__eq) # label(axiom). [clausify(161)]. 4.32/4.49 1437 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ozero__class_Ozero(A) = B | B = C # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(173)]. 4.32/4.49 1438 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_divide__1) # label(axiom). [clausify(187)]. 4.32/4.49 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1427,a,1428,a)]. 4.32/4.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1427,a,1429,a)]. 4.32/4.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1427,a,1430,a)]. 4.32/4.49 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A). [resolve(1427,a,1432,a)]. 4.32/4.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,A) != C | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A) = B. [resolve(1427,a,1433,a)]. 4.32/4.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | B = A. [resolve(1427,a,1435,a)]. 4.32/4.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | B != A. [resolve(1427,a,1436,a)]. 4.32/4.49 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | A = B. [resolve(1427,a,1437,a)]. 4.32/4.49 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1427,a,1438,a)]. 4.32/4.49 1439 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ominus__class_Ominus(A,C,B)),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__diff) # label(axiom). [clausify(233)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,A)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1439,a,1427,a)]. 4.32/4.50 1440 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom). [assumption]. 4.32/4.50 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1440,a,1428,a)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1440,a,1430,a)]. 4.32/4.50 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1440,a,1432,a)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A) != C | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A) = B. [resolve(1440,a,1433,a)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | B = A. [resolve(1440,a,1435,a)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | B != A. [resolve(1440,a,1436,a)]. 4.32/4.50 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | A = B. [resolve(1440,a,1437,a)]. 4.32/4.50 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1440,a,1438,a)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1440,a,1439,a)]. 4.32/4.50 1441 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_diff__divide__distrib) # label(axiom). [clausify(329)]. 4.32/4.50 1442 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__zero__left) # label(axiom). [clausify(365)]. 4.32/4.50 1443 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ominus__class_Ominus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,C))) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_Deriv_Oinverse__diff__inverse) # label(axiom). [clausify(429)]. 4.32/4.50 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1443,a,1427,a)]. 4.35/4.52 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1443,a,1440,a)]. 4.35/4.52 1444 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(536)]. 4.35/4.52 1445 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) = D | c_Rings_Oinverse__class_Odivide(A,D,B) != C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(536)]. 4.35/4.52 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,A) = C | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A) != B. [resolve(1445,a,1427,a)]. 4.35/4.52 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A) = C | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A) != B. [resolve(1445,a,1440,a)]. 4.35/4.52 1446 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(543)]. 4.35/4.52 1447 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) = D | c_Rings_Oinverse__class_Odivide(A,D,B) != C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(543)]. 4.35/4.52 1448 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom). [clausify(585)]. 4.35/4.52 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1448,a,1427,a)]. 4.35/4.52 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1448,a,1440,a)]. 4.35/4.52 1449 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_nonzero__inverse__eq__divide) # label(axiom). [clausify(617)]. 4.35/4.52 1450 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__zero__imp__zero) # label(axiom). [clausify(628)]. 4.35/4.52 1451 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_minus__divide__left) # label(axiom). [clausify(632)]. 4.35/4.52 1452 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_divide__inverse) # label(axiom). [clausify(643)]. 4.36/4.53 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1452,a,1427,a)]. 4.36/4.53 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1452,a,1440,a)]. 4.36/4.53 1453 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_nonzero__inverse__mult__distrib) # label(axiom). [clausify(722)]. 4.36/4.53 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1453,a,1427,a)]. 4.36/4.53 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1453,a,1440,a)]. 4.36/4.53 1454 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_nonzero__minus__divide__right) # label(axiom). [clausify(727)]. 4.36/4.53 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A)). [resolve(1454,a,1427,a)]. 4.36/4.53 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1454,a,1440,a)]. 4.36/4.53 1455 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_times__divide__eq__right) # label(axiom). [clausify(774)]. 4.36/4.53 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)). [resolve(1455,a,1427,a)]. 4.36/4.53 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1455,a,1440,a)]. 4.36/4.53 1456 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_divide__self) # label(axiom). [clausify(776)]. 4.36/4.53 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1456,a,1427,a)]. 4.36/4.53 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1456,a,1440,a)]. 4.36/4.53 1457 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) = c_Rings_Oinverse__class_Odivide(A,C,B) # label(fact_nonzero__minus__divide__divide) # label(axiom). [clausify(788)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A). [resolve(1457,a,1427,a)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A). [resolve(1457,a,1440,a)]. 4.36/4.55 1458 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B)) = B # label(fact_nonzero__inverse__inverse__eq) # label(axiom). [clausify(839)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1458,a,1427,a)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = A. [resolve(1458,a,1440,a)]. 4.36/4.55 1459 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Oinverse(A,B)) = c_Groups_Oone__class_Oone(A) # label(fact_right__inverse) # label(axiom). [clausify(874)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1459,a,1427,a)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1459,a,1440,a)]. 4.36/4.55 1460 -class_Rings_Odivision__ring(A) | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Oone__class_Oone(A) | c_Rings_Oinverse__class_Oinverse(A,B) = C # label(fact_inverse__unique) # label(axiom). [clausify(882)]. 4.36/4.55 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = B. [resolve(1460,a,1427,a)]. 4.36/4.55 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = B. [resolve(1460,a,1440,a)]. 4.36/4.55 1461 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oplus__class_Oplus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__add) # label(axiom). [clausify(902)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1461,a,1427,a)]. 4.36/4.55 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1461,a,1440,a)]. 4.52/4.76 1462 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_divide__eq__imp) # label(axiom). [clausify(910)]. 4.52/4.76 1463 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B) = B # label(fact_add__0__left) # label(axiom). [clausify(104)]. 4.52/4.76 1464 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption]. 4.52/4.76 1465 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = A. [resolve(1465,a,1463,a)]. 4.52/4.76 1466 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = A. [resolve(1466,a,1463,a)]. 4.52/4.76 1467 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom). [assumption]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = A. [resolve(1467,a,1463,a)]. 4.52/4.76 1468 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(934)]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1468,a,1464,a)]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1468,a,1465,a)]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1468,a,1466,a)]. 4.52/4.76 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1468,a,1467,a)]. 4.52/4.76 1469 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__number__of__eq__not__less) # label(axiom). [clausify(621)]. 4.52/4.76 1470 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption]. 4.52/4.76 1471 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption]. 4.52/4.76 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1469,a,1470,a)]. 4.52/4.76 Derived: -class_Int_Onumber(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1469,a,1471,a)]. 4.52/4.76 1472 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__number__of__eq__not__less) # label(axiom). [clausify(621)]. 4.52/4.76 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1472,a,1470,a)]. 4.67/4.86 Derived: -class_Int_Onumber(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1472,a,1471,a)]. 4.67/4.86 1473 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption]. 4.67/4.86 Derived: -class_Int_Onumber(tc_Nat_Onat) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)). [resolve(1473,a,1469,a)]. 4.67/4.86 Derived: -class_Int_Onumber(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)). [resolve(1473,a,1472,a)]. 4.67/4.86 1474 -class_Rings_Olinordered__idom(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Otimes__class_Otimes(A,B,B) # label(fact_abs__mult__self) # label(axiom). [clausify(60)]. 4.67/4.86 1475 class_Rings_Olinordered__idom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__idom) # label(axiom). [assumption]. 4.67/4.86 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A). [resolve(1474,a,1475,a)]. 4.67/4.86 1476 class_Rings_Olinordered__idom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__idom) # label(axiom). [assumption]. 4.67/4.86 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A). [resolve(1476,a,1474,a)]. 4.67/4.86 1477 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_less__special_I2_J) # label(axiom). [clausify(169)]. 4.67/4.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1477,b,1475,a)]. 4.67/4.86 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1477,b,1476,a)]. 4.67/4.86 1478 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_less__special_I2_J) # label(axiom). [clausify(169)]. 4.67/4.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1478,b,1475,a)]. 4.67/4.86 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1478,b,1476,a)]. 4.67/4.87 1479 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),B) # label(fact_mult__right__le__one__le) # label(axiom). [clausify(234)]. 4.67/4.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),A). [resolve(1479,a,1475,a)]. 4.67/4.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),A). [resolve(1479,a,1476,a)]. 4.67/4.87 1480 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_less__special_I4_J) # label(axiom). [clausify(291)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1480,b,1475,a)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1480,b,1476,a)]. 4.67/4.87 1481 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_less__special_I4_J) # label(axiom). [clausify(291)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1481,b,1475,a)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1481,b,1476,a)]. 4.67/4.87 1482 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,c_Groups_Otimes__class_Otimes(A,C,B)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,C),B) # label(fact_abs__mult__pos) # label(axiom). [clausify(297)]. 4.67/4.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B),A). [resolve(1482,a,1475,a)]. 4.67/4.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,B),A). [resolve(1482,a,1476,a)]. 4.67/4.87 1483 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_le__number__of) # label(axiom). [clausify(298)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1483,a,1475,a)]. 4.67/4.87 1484 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_le__number__of) # label(axiom). [clausify(298)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1484,a,1475,a)]. 4.67/4.87 1485 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OPls) # label(fact_le__special_I3_J) # label(axiom). [clausify(380)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1485,b,1475,a)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1485,b,1476,a)]. 4.67/4.87 1486 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OPls) # label(fact_le__special_I3_J) # label(axiom). [clausify(380)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1486,b,1475,a)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1486,b,1476,a)]. 4.67/4.87 1487 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_le__special_I4_J) # label(axiom). [clausify(388)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1487,b,1475,a)]. 4.67/4.87 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1487,b,1476,a)]. 4.67/4.87 1488 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) # label(fact_le__special_I4_J) # label(axiom). [clausify(388)]. 4.67/4.88 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1488,b,1475,a)]. 4.67/4.88 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1488,b,1476,a)]. 4.67/4.88 1489 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B) # label(fact_less__special_I1_J) # label(axiom). [clausify(390)]. 4.67/4.88 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1489,a,1475,a)]. 4.67/4.88 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1489,a,1476,a)]. 4.67/4.88 1490 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B) # label(fact_less__special_I1_J) # label(axiom). [clausify(390)]. 4.67/4.88 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1490,a,1475,a)]. 4.67/4.88 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1490,a,1476,a)]. 4.67/4.88 1491 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_less__minus__self__iff) # label(axiom). [clausify(398)]. 4.67/4.88 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1491,a,1475,a)]. 4.67/4.88 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1491,a,1476,a)]. 4.67/4.88 1492 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_less__minus__self__iff) # label(axiom). [clausify(398)]. 4.67/4.88 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1492,a,1475,a)]. 4.67/4.88 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1492,a,1476,a)]. 4.67/4.88 1493 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,D),E) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,D)),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_abs__mult__less) # label(axiom). [clausify(407)]. 4.67/4.89 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1493,a,1475,a)]. 4.67/4.89 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,C),D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,C)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1493,a,1476,a)]. 4.67/4.89 1494 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__special_I3_J) # label(axiom). [clausify(452)]. 4.67/4.89 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1494,b,1475,a)]. 4.67/4.89 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1494,b,1476,a)]. 4.67/4.89 1495 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__special_I3_J) # label(axiom). [clausify(452)]. 4.67/4.89 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1495,b,1475,a)]. 4.67/4.89 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1495,b,1476,a)]. 4.67/4.89 1496 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_even__less__0__iff) # label(axiom). [clausify(503)]. 4.67/4.89 1497 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_even__less__0__iff) # label(axiom). [clausify(503)]. 4.67/4.89 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1497,a,1475,a)]. 4.67/4.89 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1497,a,1476,a)]. 4.67/4.89 1498 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Int_Onumber__class_Onumber__of(A,B) = c_Groups_Oabs__class_Oabs(A,c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_abs__number__of) # label(axiom). [clausify(552)]. 4.67/4.89 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1498,a,1475,a)]. 4.67/4.90 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1498,a,1476,a)]. 4.67/4.90 1499 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,c_Int_Onumber__class_Onumber__of(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_abs__number__of) # label(axiom). [clausify(552)]. 4.67/4.90 1500 -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__mult) # label(axiom). [clausify(624)]. 4.67/4.90 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1500,a,1475,a)]. 4.67/4.90 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1500,a,1476,a)]. 4.67/4.90 1501 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) # label(fact_le__special_I2_J) # label(axiom). [clausify(657)]. 4.67/4.90 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1501,a,1475,a)]. 4.67/4.90 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1501,a,1476,a)]. 4.67/4.90 1502 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) # label(fact_le__special_I2_J) # label(axiom). [clausify(657)]. 4.67/4.90 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1502,a,1475,a)]. 4.67/4.90 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1502,a,1476,a)]. 4.67/4.90 1503 -class_Rings_Olinordered__idom(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neqE__linordered__idom) # label(axiom). [clausify(662)]. 4.67/4.90 Derived: A = B | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1503,a,1475,a)]. 4.67/4.90 1504 -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_abs__one) # label(axiom). [clausify(712)]. 4.67/4.91 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1504,a,1475,a)]. 4.67/4.91 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1504,a,1476,a)]. 4.67/4.91 1505 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__special_I1_J) # label(axiom). [clausify(735)]. 4.67/4.91 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1505,a,1475,a)]. 4.67/4.91 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1505,a,1476,a)]. 4.67/4.91 1506 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__special_I1_J) # label(axiom). [clausify(735)]. 4.67/4.91 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1506,a,1475,a)]. 4.67/4.91 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(1506,a,1476,a)]. 4.67/4.91 1507 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),B) # label(fact_mult__left__le__one__le) # label(axiom). [clausify(770)]. 4.67/4.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),A). [resolve(1507,a,1475,a)]. 4.67/4.91 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A),A). [resolve(1507,a,1476,a)]. 4.67/4.91 1508 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_abs__less__iff) # label(axiom). [clausify(859)]. 4.67/4.91 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B). [resolve(1508,a,1475,a)]. 4.67/4.91 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B). [resolve(1508,a,1476,a)]. 4.76/4.92 1509 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_abs__less__iff) # label(axiom). [clausify(859)]. 4.76/4.92 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1509,a,1475,a)]. 4.76/4.92 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1509,a,1476,a)]. 4.76/4.92 1510 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_abs__less__iff) # label(axiom). [clausify(859)]. 4.76/4.92 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1510,a,1475,a)]. 4.76/4.92 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1510,a,1476,a)]. 4.76/4.92 1511 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,B,C)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,D,B)),C) # label(fact_abs__diff__less__iff) # label(axiom). [clausify(892)]. 4.76/4.92 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,A)),B). [resolve(1511,a,1475,a)]. 4.76/4.92 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,A)),B). [resolve(1511,a,1476,a)]. 4.76/4.92 1512 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,D,B)),C) # label(fact_abs__diff__less__iff) # label(axiom). [clausify(892)]. 4.76/4.92 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,A)),B). [resolve(1512,a,1475,a)]. 4.76/4.92 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,A)),B). [resolve(1512,a,1476,a)]. 4.76/4.92 1513 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D) # label(fact_abs__diff__less__iff) # label(axiom). [clausify(892)]. 4.76/4.92 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),C). [resolve(1513,a,1475,a)]. 4.76/4.92 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),C). [resolve(1513,a,1476,a)]. 4.83/5.01 1514 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) # label(fact_less__number__of) # label(axiom). [clausify(897)]. 4.83/5.01 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1514,b,1475,a)]. 4.83/5.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1514,b,1476,a)]. 4.83/5.01 1515 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) # label(fact_less__number__of) # label(axiom). [clausify(897)]. 4.83/5.01 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1515,b,1475,a)]. 4.83/5.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1515,b,1476,a)]. 4.83/5.01 1516 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),C)) = C # label(fact_add__minus__cancel) # label(axiom). [clausify(96)]. 4.83/5.01 1517 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption]. 4.83/5.01 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B)) = B. [resolve(1516,a,1517,a)]. 4.83/5.01 1518 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(106)]. 4.83/5.01 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1518,a,1517,a)]. 4.83/5.01 1519 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(106)]. 4.83/5.01 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1519,a,1517,a)]. 4.83/5.01 1520 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(141)]. 4.83/5.01 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),B) = A. [resolve(1520,a,1517,a)]. 4.83/5.01 1521 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ouminus__class_Ouminus(A,C) | B = C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(195)]. 4.83/5.01 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) | A = B. [resolve(1521,a,1517,a)]. 4.83/5.01 1522 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ouminus__class_Ouminus(A,C) | B != C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(195)]. 4.83/5.01 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) | A != B. [resolve(1522,a,1517,a)]. 4.83/5.02 1523 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(210)]. 4.83/5.02 1524 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(210)]. 4.83/5.02 1525 class_Groups_Ogroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ogroup__add) # label(axiom). [assumption]. 4.83/5.02 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B)) = B. [resolve(1525,a,1516,a)]. 4.83/5.02 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1525,a,1518,a)]. 4.83/5.02 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1525,a,1519,a)]. 4.83/5.02 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),B) = A. [resolve(1525,a,1520,a)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) | A = B. [resolve(1525,a,1521,a)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) | A != B. [resolve(1525,a,1522,a)]. 4.83/5.02 1526 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_equation__minus__iff) # label(axiom). [clausify(244)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A. [resolve(1526,a,1517,a)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) = A. [resolve(1526,a,1525,a)]. 4.83/5.02 1527 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_equation__minus__iff) # label(axiom). [clausify(244)]. 4.83/5.02 1528 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B)) = B # label(fact_minus__minus) # label(axiom). [clausify(279)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = A. [resolve(1528,a,1525,a)]. 4.83/5.02 1529 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_minus__zero) # label(axiom). [clausify(294)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1529,a,1525,a)]. 4.83/5.02 1530 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom). [assumption]. 4.83/5.02 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B)) = B. [resolve(1530,a,1516,a)]. 4.83/5.02 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1530,a,1518,a)]. 4.83/5.02 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1530,a,1519,a)]. 4.83/5.02 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),B) = A. [resolve(1530,a,1520,a)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) | A = B. [resolve(1530,a,1521,a)]. 4.83/5.02 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) | A != B. [resolve(1530,a,1522,a)]. 4.83/5.04 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) = A. [resolve(1530,a,1526,a)]. 4.83/5.04 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = A. [resolve(1530,a,1528,a)]. 4.83/5.04 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1530,a,1529,a)]. 4.83/5.04 1531 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_diff__minus__eq__add) # label(axiom). [clausify(411)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1531,a,1517,a)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1531,a,1525,a)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)). [resolve(1531,a,1530,a)]. 4.83/5.04 1532 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_left__minus) # label(axiom). [clausify(472)]. 4.83/5.04 1533 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C # label(fact_minus__unique) # label(axiom). [clausify(498)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = B. [resolve(1533,a,1517,a)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = B. [resolve(1533,a,1525,a)]. 4.83/5.04 1534 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(614)]. 4.83/5.04 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1534,a,1517,a)]. 4.83/5.04 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1534,a,1525,a)]. 4.83/5.04 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1534,a,1530,a)]. 4.83/5.04 1535 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,C,B)) # label(fact_minus__add) # label(axiom). [clausify(629)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A)). [resolve(1535,a,1517,a)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A)). [resolve(1535,a,1525,a)]. 4.83/5.04 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,A)). [resolve(1535,a,1530,a)]. 4.83/5.04 1536 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = B # label(fact_add__diff__cancel) # label(axiom). [clausify(648)]. 4.83/5.04 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),B) = A. [resolve(1536,a,1517,a)]. 4.83/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),B) = A. [resolve(1536,a,1525,a)]. 4.83/5.05 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),B) = A. [resolve(1536,a,1530,a)]. 4.83/5.05 1537 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_add__eq__0__iff) # label(axiom). [clausify(696)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1537,a,1517,a)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1537,a,1525,a)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1537,a,1530,a)]. 4.83/5.05 1538 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_add__eq__0__iff) # label(axiom). [clausify(696)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1538,a,1530,a)]. 4.83/5.05 1539 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ominus__class_Ominus(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_diff__0) # label(axiom). [clausify(697)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1539,a,1517,a)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A). [resolve(1539,a,1525,a)]. 4.83/5.05 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1539,a,1530,a)]. 4.83/5.05 1540 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(739)]. 4.83/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A. [resolve(1540,a,1517,a)]. 4.83/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) = A. [resolve(1540,a,1525,a)]. 4.83/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) = A. [resolve(1540,a,1530,a)]. 4.83/5.05 1541 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(739)]. 4.83/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) != A. [resolve(1541,a,1517,a)]. 4.83/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) != A. [resolve(1541,a,1525,a)]. 4.83/5.05 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) != A. [resolve(1541,a,1530,a)]. 4.83/5.05 1542 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ozero__class_Ozero(A) # label(fact_right__minus) # label(axiom). [clausify(806)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1542,a,1517,a)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1542,a,1525,a)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1542,a,1530,a)]. 4.97/5.16 1543 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_diff__self) # label(axiom). [clausify(816)]. 4.97/5.16 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1543,a,1517,a)]. 4.97/5.16 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1543,a,1525,a)]. 4.97/5.16 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1543,a,1530,a)]. 4.97/5.16 1544 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_minus__equation__iff) # label(axiom). [clausify(827)]. 4.97/5.16 1545 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_minus__equation__iff) # label(axiom). [clausify(827)]. 4.97/5.16 1546 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Ominus__class_Ominus(A,B,C) # label(fact_diff__def) # label(axiom). [clausify(841)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B). [resolve(1546,a,1517,a)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B). [resolve(1546,a,1530,a)]. 4.97/5.16 1547 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oplus__class_Oplus(A,B,C)) = C # label(fact_minus__add__cancel) # label(axiom). [clausify(848)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)) = B. [resolve(1547,a,1517,a)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = B. [resolve(1547,a,1525,a)]. 4.97/5.16 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)) = B. [resolve(1547,a,1530,a)]. 4.97/5.16 1548 -class_Groups_Ogroup__add(A) | B != C | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_right__minus__eq) # label(axiom). [clausify(867)]. 4.97/5.16 1549 -class_Groups_Ogroup__add(A) | B = C | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_right__minus__eq) # label(axiom). [clausify(867)]. 4.97/5.16 1550 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.97/5.16 1551 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(61)]. 4.97/5.16 1552 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(91)]. 4.97/5.16 1553 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__less__le__imp__less) # label(axiom). [clausify(192)]. 4.97/5.16 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1550,a,1553,a)]. 4.97/5.16 1554 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__pos__pos) # label(axiom). [clausify(307)]. 4.97/5.16 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1554,a,1550,a)]. 4.97/5.16 1555 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__left__le__imp__le) # label(axiom). [clausify(342)]. 4.97/5.16 1556 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg2) # label(axiom). [clausify(343)]. 4.97/5.16 1557 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__neg__pos) # label(axiom). [clausify(366)]. 4.97/5.16 1558 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__le__less__imp__less) # label(axiom). [clausify(416)]. 4.97/5.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1558,a,1550,a)]. 4.97/5.16 1559 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.97/5.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1559,a,1553,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1559,a,1554,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1559,a,1556,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1559,a,1558,a)]. 4.97/5.17 1560 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg) # label(axiom). [clausify(491)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1560,a,1559,a)]. 4.97/5.17 1561 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1561,a,1553,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1561,a,1554,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1561,a,1556,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1561,a,1558,a)]. 4.97/5.17 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1561,a,1560,a)]. 4.97/5.18 1562 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__strict__mono_H) # label(axiom). [clausify(540)]. 4.97/5.18 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1562,a,1550,a)]. 4.97/5.18 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1562,a,1559,a)]. 4.97/5.18 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1562,a,1561,a)]. 4.97/5.18 1563 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__strict__mono) # label(axiom). [clausify(555)]. 4.97/5.18 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1563,a,1550,a)]. 4.97/5.18 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1563,a,1559,a)]. 4.97/5.18 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1563,a,1561,a)]. 4.97/5.18 1564 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__less__imp__less__right) # label(axiom). [clausify(635)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1564,a,1550,a)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1564,a,1559,a)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1564,a,1561,a)]. 4.97/5.19 1565 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__less__mult__pos) # label(axiom). [clausify(664)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). [resolve(1565,a,1550,a)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1565,a,1559,a)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1565,a,1561,a)]. 4.97/5.19 1566 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_mult__right__le__imp__le) # label(axiom). [clausify(668)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1566,a,1550,a)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1566,a,1561,a)]. 4.97/5.19 1567 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__mult__pos2) # label(axiom). [clausify(703)]. 4.97/5.19 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). [resolve(1567,a,1550,a)]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1567,a,1559,a)]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1567,a,1561,a)]. 5.14/5.31 1568 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__imp__less__left) # label(axiom). [clausify(811)]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1568,a,1550,a)]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1568,a,1559,a)]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1568,a,1561,a)]. 5.14/5.31 1569 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 5.14/5.31 1570 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__strict__left__mono) # label(axiom). [clausify(68)]. 5.14/5.31 1571 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 5.14/5.31 1572 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__strict__mono) # label(axiom). [clausify(254)]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1572,a,1569,a)]. 5.14/5.31 1573 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 5.14/5.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1573,a,1572,a)]. 5.14/5.31 1574 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__strict__right__mono) # label(axiom). [clausify(822)]. 5.26/5.41 1575 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__le__less__mono) # label(axiom). [clausify(834)]. 5.26/5.41 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1575,a,1569,a)]. 5.26/5.41 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1575,a,1571,a)]. 5.26/5.41 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1575,a,1573,a)]. 5.26/5.41 1576 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__less__le__mono) # label(axiom). [clausify(877)]. 5.26/5.41 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1576,a,1569,a)]. 5.26/5.41 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1576,a,1571,a)]. 5.26/5.41 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)). [resolve(1576,a,1573,a)]. 5.26/5.41 1577 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 5.26/5.41 1578 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(72)]. 5.26/5.41 1579 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(72)]. 5.26/5.41 1580 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(82)]. 5.26/5.41 1581 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(82)]. 5.26/5.41 1582 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__less__iff) # label(axiom). [clausify(101)]. 5.26/5.41 1583 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__less__iff) # label(axiom). [clausify(101)]. 5.26/5.42 1584 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__imp__neg__le) # label(axiom). [clausify(134)]. 5.26/5.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1577,a,1578,a)]. 5.26/5.42 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1577,a,1579,a)]. 5.26/5.42 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D). [resolve(1577,a,1580,a)]. 5.26/5.42 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D). [resolve(1577,a,1581,a)]. 5.26/5.42 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B),A). [resolve(1577,a,1582,a)]. 5.26/5.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1577,a,1584,a)]. 5.26/5.42 1585 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__le__iff) # label(axiom). [clausify(323)]. 5.26/5.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B),A). [resolve(1585,a,1577,a)]. 5.26/5.42 1586 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__le__iff) # label(axiom). [clausify(323)]. 5.26/5.42 1587 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(402)]. 5.26/5.42 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1587,a,1577,a)]. 5.26/5.42 1588 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(402)]. 5.26/5.42 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1588,a,1577,a)]. 5.26/5.42 1589 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(525)]. 5.26/5.42 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1589,a,1577,a)]. 5.28/5.43 1590 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(525)]. 5.28/5.43 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1590,a,1577,a)]. 5.28/5.43 1591 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__minus__iff) # label(axiom). [clausify(538)]. 5.28/5.43 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1591,a,1577,a)]. 5.28/5.43 1592 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__minus__iff) # label(axiom). [clausify(538)]. 5.28/5.43 1593 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 5.28/5.43 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1593,a,1578,a)]. 5.28/5.43 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1593,a,1579,a)]. 5.28/5.43 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D). [resolve(1593,a,1580,a)]. 5.28/5.43 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D). [resolve(1593,a,1581,a)]. 5.28/5.43 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),A). [resolve(1593,a,1582,a)]. 5.28/5.43 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1593,a,1584,a)]. 5.28/5.43 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),A). [resolve(1593,a,1585,a)]. 5.28/5.43 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1593,a,1587,a)]. 5.28/5.43 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1593,a,1588,a)]. 5.28/5.43 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1593,a,1589,a)]. 5.28/5.44 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1593,a,1590,a)]. 5.28/5.44 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1593,a,1591,a)]. 5.28/5.44 1594 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_neg__less__iff__less) # label(axiom). [clausify(651)]. 5.28/5.44 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1594,a,1577,a)]. 5.28/5.44 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1594,a,1593,a)]. 5.28/5.44 1595 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_neg__less__iff__less) # label(axiom). [clausify(651)]. 5.28/5.44 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1595,a,1577,a)]. 5.28/5.44 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1595,a,1593,a)]. 5.28/5.44 1596 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(665)]. 5.28/5.44 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1596,a,1577,a)]. 5.28/5.44 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1596,a,1593,a)]. 5.28/5.44 1597 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(665)]. 5.28/5.44 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1597,a,1577,a)]. 5.28/5.44 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1597,a,1593,a)]. 5.28/5.44 1598 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(702)]. 5.28/5.44 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1598,a,1577,a)]. 5.28/5.45 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1598,a,1593,a)]. 5.28/5.45 1599 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(702)]. 5.28/5.45 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1599,a,1577,a)]. 5.28/5.45 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1599,a,1593,a)]. 5.28/5.45 1600 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(731)]. 5.28/5.45 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1600,a,1577,a)]. 5.28/5.45 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1600,a,1593,a)]. 5.28/5.45 1601 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(731)]. 5.28/5.45 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1601,a,1577,a)]. 5.28/5.45 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1601,a,1593,a)]. 5.28/5.45 1602 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_neg__le__iff__le) # label(axiom). [clausify(769)]. 5.28/5.45 1603 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_neg__le__iff__le) # label(axiom). [clausify(769)]. 5.28/5.45 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1603,a,1577,a)]. 5.28/5.45 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1603,a,1593,a)]. 5.28/5.45 1604 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_less__minus__iff) # label(axiom). [clausify(866)]. 5.37/5.55 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1604,a,1577,a)]. 5.37/5.55 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1604,a,1593,a)]. 5.37/5.55 1605 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_less__minus__iff) # label(axiom). [clausify(866)]. 5.37/5.55 1606 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(922)]. 5.37/5.55 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1606,a,1577,a)]. 5.37/5.55 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1606,a,1593,a)]. 5.37/5.55 1607 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(922)]. 5.37/5.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1607,a,1577,a)]. 5.37/5.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1607,a,1593,a)]. 5.37/5.55 1608 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 5.37/5.55 1609 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__nonneg) # label(axiom). [clausify(73)]. 5.37/5.55 1610 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__nonneg) # label(axiom). [clausify(73)]. 5.37/5.55 1611 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(102)]. 5.37/5.55 1612 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(102)]. 5.37/5.55 1613 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__minus__self__iff) # label(axiom). [clausify(119)]. 5.37/5.55 1614 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__minus__self__iff) # label(axiom). [clausify(119)]. 5.37/5.55 1615 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_double__zero__sym) # label(axiom). [clausify(184)]. 5.37/5.56 1616 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_double__zero__sym) # label(axiom). [clausify(184)]. 5.37/5.56 1617 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_double__eq__0__iff) # label(axiom). [clausify(198)]. 5.37/5.56 1618 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_double__eq__0__iff) # label(axiom). [clausify(198)]. 5.37/5.56 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1608,a,1609,a)]. 5.37/5.56 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1608,a,1610,a)]. 5.37/5.56 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1608,a,1613,a)]. 5.37/5.56 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1608,a,1614,a)]. 5.37/5.56 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1608,a,1615,a)]. 5.37/5.56 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1608,a,1616,a)]. 5.37/5.56 1619 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(290)]. 5.37/5.56 1620 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(290)]. 5.37/5.56 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A)). [resolve(1620,a,1608,a)]. 5.37/5.56 1621 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ouminus__class_Ouminus(A,B) = B # label(fact_neg__equal__zero) # label(axiom). [clausify(359)]. 5.37/5.56 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = A. [resolve(1621,a,1608,a)]. 5.37/5.56 1622 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ouminus__class_Ouminus(A,B) != B # label(fact_neg__equal__zero) # label(axiom). [clausify(359)]. 5.37/5.56 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != A. [resolve(1622,a,1608,a)]. 5.37/5.56 1623 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_equal__neg__zero) # label(axiom). [clausify(385)]. 5.37/5.56 1624 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_equal__neg__zero) # label(axiom). [clausify(385)]. 5.37/5.58 1625 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_minus__le__self__iff) # label(axiom). [clausify(579)]. 5.37/5.58 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1625,a,1608,a)]. 5.37/5.58 1626 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_minus__le__self__iff) # label(axiom). [clausify(579)]. 5.37/5.58 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1626,a,1608,a)]. 5.37/5.58 1627 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(649)]. 5.37/5.58 1628 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(649)]. 5.37/5.58 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1628,a,1608,a)]. 5.37/5.58 1629 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 5.37/5.58 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1629,a,1609,a)]. 5.37/5.58 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1629,a,1610,a)]. 5.37/5.58 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1629,a,1613,a)]. 5.37/5.58 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1629,a,1614,a)]. 5.37/5.58 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1629,a,1615,a)]. 5.37/5.58 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1629,a,1616,a)]. 5.37/5.58 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)). [resolve(1629,a,1620,a)]. 5.37/5.58 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = A. [resolve(1629,a,1621,a)]. 5.37/5.58 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != A. [resolve(1629,a,1622,a)]. 5.37/5.58 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1629,a,1625,a)]. 5.57/5.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1629,a,1626,a)]. 5.57/5.81 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1629,a,1628,a)]. 5.57/5.81 1630 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(804)]. 5.57/5.81 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1630,a,1608,a)]. 5.57/5.81 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1630,a,1629,a)]. 5.57/5.81 1631 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(804)]. 5.57/5.81 1632 -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B) = B # label(fact_add__0) # label(axiom). [clausify(306)]. 5.57/5.81 1633 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 5.57/5.81 1634 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 5.57/5.81 1635 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 5.57/5.81 1636 class_Groups_Ocomm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 5.57/5.81 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = A. [resolve(1636,a,1632,a)]. 5.57/5.81 1637 -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add_Ocomm__neutral) # label(axiom). [clausify(838)]. 5.57/5.81 1638 class_Rings_Oordered__ring__abs(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring__abs) # label(axiom). [assumption]. 5.57/5.81 1639 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,c_Groups_Otimes__class_Otimes(A,C,B)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__eq__mult) # label(axiom). [clausify(78)]. 5.57/5.81 1640 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oabs__class_Oabs(A,c_Groups_Otimes__class_Otimes(A,C,B)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__eq__mult) # label(axiom). [clausify(78)]. 5.57/5.81 1641 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,c_Groups_Otimes__class_Otimes(A,C,B)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__eq__mult) # label(axiom). [clausify(78)]. 5.74/5.93 1642 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oabs__class_Oabs(A,c_Groups_Otimes__class_Otimes(A,C,B)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__eq__mult) # label(axiom). [clausify(78)]. 5.74/5.93 1643 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring__abs) # label(axiom). [assumption]. 5.74/5.93 1644 -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_field__divide__inverse) # label(axiom). [clausify(229)]. 5.74/5.93 1645 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom). [assumption]. 5.74/5.93 1646 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,C,c_Groups_Otimes__class_Otimes(A,B,D)),B) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_divide__diff__eq__iff) # label(axiom). [clausify(265)]. 5.74/5.93 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)),A) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C). [resolve(1646,a,1645,a)]. 5.74/5.93 1647 -class_Fields_Ofield(A) | -class_Int_Onumber__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) = B # label(fact_divide__numeral__1) # label(axiom). [clausify(401)]. 5.74/5.93 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(c_Int_OPls))) = A. [resolve(1647,a,1645,a)]. 5.74/5.94 1648 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,B,D)),B) # label(fact_divide__add__eq__iff) # label(axiom). [clausify(415)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)),A). [resolve(1648,a,1645,a)]. 5.74/5.94 1649 -class_Int_Onumber__ring(A) | -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Oinverse(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)) # label(fact_inverse__numeral__1) # label(axiom). [clausify(438)]. 5.74/5.94 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(c_Int_OPls)). [resolve(1649,b,1645,a)]. 5.74/5.94 1650 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_inverse__add) # label(axiom). [clausify(447)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1650,a,1645,a)]. 5.74/5.94 1651 class_Fields_Ofield(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield) # label(axiom). [assumption]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)),A) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C). [resolve(1651,a,1646,a)]. 5.74/5.94 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls))) = A. [resolve(1651,a,1647,a)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)),A). [resolve(1651,a,1648,a)]. 5.74/5.94 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls)). [resolve(1651,a,1649,b)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1651,a,1650,a)]. 5.74/5.94 1652 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,D,C) != c_Groups_Otimes__class_Otimes(A,E,B) | c_Rings_Oinverse__class_Odivide(A,D,B) = c_Rings_Oinverse__class_Odivide(A,E,C) # label(fact_frac__eq__eq) # label(axiom). [clausify(574)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B) != c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,A) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B). [resolve(1652,a,1645,a)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B). [resolve(1652,a,1651,a)]. 5.74/5.94 1653 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,D,C) = c_Groups_Otimes__class_Otimes(A,E,B) | c_Rings_Oinverse__class_Odivide(A,D,B) != c_Rings_Oinverse__class_Odivide(A,E,C) # label(fact_frac__eq__eq) # label(axiom). [clausify(574)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,A) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B). [resolve(1653,a,1645,a)]. 5.74/5.94 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B). [resolve(1653,a,1651,a)]. 5.74/5.96 1654 -class_Int_Onumber__ring(A) | -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) = B # label(fact_divide__Numeral1) # label(axiom). [clausify(625)]. 5.74/5.96 1655 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),B) = c_Groups_Ominus__class_Ominus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_diff__divide__eq__iff) # label(axiom). [clausify(650)]. 5.74/5.96 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C),A) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)). [resolve(1655,a,1645,a)]. 5.74/5.96 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C),A) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1655,a,1651,a)]. 5.74/5.96 1656 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),B) # label(fact_add__divide__eq__iff) # label(axiom). [clausify(682)]. 5.74/5.96 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C),A). [resolve(1656,a,1645,a)]. 5.74/5.96 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),C),A). [resolve(1656,a,1651,a)]. 5.74/5.96 1657 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),B) = c_Groups_Oone__class_Oone(A) # label(fact_field__inverse) # label(axiom). [clausify(737)]. 5.74/5.96 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1657,a,1651,a)]. 5.74/5.96 1658 -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_field__class_Onormalizing__field__rules_I2_J) # label(axiom). [clausify(781)]. 5.74/5.96 1659 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)),c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)) # label(fact_diff__frac__eq) # label(axiom). [clausify(824)]. 5.74/5.96 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,A)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)). [resolve(1659,a,1645,a)]. 5.88/6.07 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B)). [resolve(1659,a,1651,a)]. 5.88/6.07 1660 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_add__frac__eq) # label(axiom). [clausify(908)]. 5.88/6.07 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,A)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)). [resolve(1660,a,1645,a)]. 5.88/6.07 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1660,a,1651,a)]. 5.88/6.07 1661 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption]. 5.88/6.07 1662 -class_Rings_Ocomm__semiring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(86)]. 5.88/6.07 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),B). [resolve(1661,a,1662,a)]. 5.88/6.07 1663 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom). [assumption]. 5.88/6.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),B). [resolve(1663,a,1662,a)]. 5.88/6.07 1664 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption]. 5.88/6.07 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). [resolve(1664,a,1662,a)]. 5.88/6.07 1665 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption]. 5.88/6.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),B). [resolve(1665,a,1662,a)]. 5.97/6.19 1666 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 5.97/6.19 1667 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_mult__right_Oadd) # label(axiom). [clausify(90)]. 5.97/6.19 1668 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__left_Ozero) # label(axiom). [clausify(118)]. 5.97/6.19 1669 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_mult_Ominus__left) # label(axiom). [clausify(139)]. 5.97/6.19 1670 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,E)),c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),E)),c_Groups_Otimes__class_Otimes(A,C,c_Groups_Ominus__class_Ominus(A,D,E))) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult_Oprod__diff__prod) # label(axiom). [clausify(376)]. 5.97/6.19 1671 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_mult__left_Ominus) # label(axiom). [clausify(400)]. 5.97/6.19 1672 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__right_Ozero) # label(axiom). [clausify(414)]. 5.97/6.19 1673 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mult__left_Odiff) # label(axiom). [clausify(459)]. 5.97/6.19 1674 -class_RealVector_Oreal__normed__algebra(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Otimes__class_Otimes(A,B,D)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,E)) # label(fact_norm__mult__less) # label(axiom). [clausify(483)]. 5.97/6.19 1675 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_mult_Oadd__right) # label(axiom). [clausify(534)]. 5.97/6.19 1676 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult_Ozero__right) # label(axiom). [clausify(616)]. 5.97/6.19 1677 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mult_Odiff__left) # label(axiom). [clausify(619)]. 5.97/6.19 1678 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_mult_Ominus__right) # label(axiom). [clausify(740)]. 5.97/6.19 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)). [resolve(1666,a,1667,a)]. 6.04/6.20 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,D)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),D)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,D))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,D)). [resolve(1666,a,1670,a)]. 6.04/6.20 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1666,a,1672,a)]. 6.04/6.20 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),B). [resolve(1666,a,1673,a)]. 6.04/6.20 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1666,a,1674,a)]. 6.04/6.20 1679 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult__right_Odiff) # label(axiom). [clausify(752)]. 6.04/6.20 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C)). [resolve(1679,a,1666,a)]. 6.04/6.20 1680 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult_Ozero__left) # label(axiom). [clausify(756)]. 6.04/6.20 1681 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mult__left_Oadd) # label(axiom). [clausify(761)]. 6.04/6.20 1682 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult_Odiff__right) # label(axiom). [clausify(794)]. 6.04/6.20 1683 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Otimes__class_Otimes(A,B,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))) # label(fact_norm__mult__ineq) # label(axiom). [clausify(796)]. 6.04/6.20 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))). [resolve(1683,a,1666,a)]. 6.04/6.20 1684 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mult_Oadd__left) # label(axiom). [clausify(805)]. 6.15/6.31 1685 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 6.15/6.31 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)). [resolve(1685,a,1667,a)]. 6.15/6.31 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),D)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1685,a,1670,a)]. 6.15/6.31 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1685,a,1672,a)]. 6.15/6.31 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C),B). [resolve(1685,a,1673,a)]. 6.15/6.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1685,a,1674,a)]. 6.15/6.31 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C)). [resolve(1685,a,1679,a)]. 6.15/6.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))). [resolve(1685,a,1683,a)]. 6.15/6.31 1686 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_mult__right_Ominus) # label(axiom). [clausify(900)]. 6.15/6.31 1687 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption]. 6.15/6.31 1688 -class_Rings_Odivision__ring__inverse__zero(A) | B != C | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Oinverse(A,C) # label(fact_inverse__eq__iff__eq) # label(axiom). [clausify(100)]. 6.15/6.31 1689 -class_Rings_Odivision__ring__inverse__zero(A) | B = C | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) # label(fact_inverse__eq__iff__eq) # label(axiom). [clausify(100)]. 6.15/6.31 Derived: A != B | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B). [resolve(1687,a,1688,a)]. 6.15/6.31 Derived: A = B | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B). [resolve(1687,a,1689,a)]. 6.15/6.31 1690 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_inverse__zero) # label(axiom). [clausify(584)]. 6.15/6.32 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1690,a,1687,a)]. 6.15/6.32 1691 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption]. 6.15/6.32 Derived: A != B | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B). [resolve(1691,a,1688,a)]. 6.15/6.32 Derived: A = B | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B). [resolve(1691,a,1689,a)]. 6.15/6.32 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1691,a,1690,a)]. 6.15/6.32 1692 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__zero) # label(axiom). [clausify(641)]. 6.15/6.32 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1692,a,1687,a)]. 6.15/6.32 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1692,a,1691,a)]. 6.15/6.32 1693 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(681)]. 6.15/6.32 1694 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(681)]. 6.15/6.32 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1694,a,1687,a)]. 6.15/6.32 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1694,a,1691,a)]. 6.15/6.32 1695 -class_RealVector_Oreal__normed__div__algebra(A) | -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)) = c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_norm__inverse) # label(axiom). [clausify(695)]. 6.15/6.32 Derived: -class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1695,b,1687,a)]. 6.15/6.32 Derived: -class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1695,b,1691,a)]. 6.15/6.32 1696 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_divide__self__if) # label(axiom). [clausify(808)]. 6.15/6.32 1697 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__self__if) # label(axiom). [clausify(808)]. 6.15/6.32 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1697,a,1687,a)]. 6.15/6.32 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1697,a,1691,a)]. 6.34/6.54 1698 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B)) = B # label(fact_inverse__inverse__eq) # label(axiom). [clausify(843)]. 6.34/6.54 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = A. [resolve(1698,a,1687,a)]. 6.34/6.54 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1698,a,1691,a)]. 6.34/6.54 1699 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | B = C # label(fact_inverse__eq__imp__eq) # label(axiom). [clausify(894)]. 6.34/6.54 1700 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_inverse__minus__eq) # label(axiom). [clausify(923)]. 6.34/6.54 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1700,a,1687,a)]. 6.34/6.54 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1700,a,1691,a)]. 6.34/6.54 1701 -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oone__class_Oone(A) # label(fact_one__neq__zero) # label(axiom). [clausify(191)]. 6.34/6.54 1702 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom). [assumption]. 6.34/6.54 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1701,a,1702,a)]. 6.34/6.54 1703 class_Rings_Ozero__neq__one(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ozero__neq__one) # label(axiom). [assumption]. 6.34/6.54 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1703,a,1701,a)]. 6.34/6.54 1704 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ozero__neq__one) # label(axiom). [assumption]. 6.34/6.54 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1704,a,1701,a)]. 6.34/6.54 1705 -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oone__class_Oone(A) # label(fact_zero__neq__one) # label(axiom). [clausify(709)]. 6.34/6.54 1706 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ozero__neq__one) # label(axiom). [assumption]. 6.34/6.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1706,a,1701,a)]. 6.34/6.54 1707 -class_Rings_Olinordered__semiring__1(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oplus__class_Oplus(A,E,F) != c_Groups_Oone__class_Oone(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C) # label(fact_convex__bound__le) # label(axiom). [clausify(203)]. 6.34/6.54 1708 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom). [assumption]. 6.34/6.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,D,E) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,E,C)),B). [resolve(1707,a,1708,a)]. 6.57/6.77 1709 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption]. 6.57/6.77 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,E) != c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,E,C)),B). [resolve(1709,a,1707,a)]. 6.57/6.77 1710 -class_Rings_Oring__1(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Oone__class_Oone(A)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A)),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(242)]. 6.57/6.77 1711 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom). [assumption]. 6.57/6.77 1712 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption]. 6.57/6.77 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))). [resolve(1710,a,1711,a)]. 6.57/6.77 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1710,a,1712,a)]. 6.57/6.77 1713 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption]. 6.57/6.77 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1713,a,1710,a)]. 6.57/6.77 1714 class_Rings_Oidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oidom) # label(axiom). [assumption]. 6.57/6.77 1715 -class_Rings_Oidom(A) | B != C | c_Groups_Otimes__class_Otimes(A,B,B) = c_Groups_Otimes__class_Otimes(A,C,C) # label(fact_square__eq__iff) # label(axiom). [clausify(154)]. 6.57/6.77 1716 -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Otimes__class_Otimes(A,C,C) = c_Groups_Otimes__class_Otimes(A,B,B) # label(fact_square__eq__iff) # label(axiom). [clausify(154)]. 6.57/6.77 1717 -class_Rings_Oidom(A) | B = C | c_Groups_Ouminus__class_Ouminus(A,C) = B | c_Groups_Otimes__class_Otimes(A,B,B) != c_Groups_Otimes__class_Otimes(A,C,C) # label(fact_square__eq__iff) # label(axiom). [clausify(154)]. 6.57/6.77 Derived: A != B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B). [resolve(1714,a,1715,a)]. 6.57/6.77 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A). [resolve(1714,a,1716,a)]. 6.57/6.77 Derived: A = B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) = A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B). [resolve(1714,a,1717,a)]. 6.78/7.00 1718 class_Rings_Oidom(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oidom) # label(axiom). [assumption]. 6.78/7.00 Derived: A != B | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,B). [resolve(1718,a,1715,a)]. 6.78/7.00 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A). [resolve(1718,a,1716,a)]. 6.78/7.00 Derived: A = B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) != c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,B). [resolve(1718,a,1717,a)]. 6.78/7.00 1719 class_Rings_Oidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oidom) # label(axiom). [assumption]. 6.78/7.00 Derived: A != B | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B). [resolve(1719,a,1715,a)]. 6.78/7.00 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A). [resolve(1719,a,1716,a)]. 6.78/7.00 Derived: A = B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) != c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B). [resolve(1719,a,1717,a)]. 6.78/7.00 1720 -class_RealVector_Oreal__field(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,C,D),E)),c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,F),E),D)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,F,D)),E) # label(fact_DERIV__mult__lemma) # label(axiom). [clausify(252)]. 6.78/7.00 1721 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption]. 6.78/7.00 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C),D)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,E),D),C)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,E,C)),D). [resolve(1720,a,1721,a)]. 6.78/7.00 1722 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption]. 6.78/7.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C),D)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,E),D),C)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,E,C)),D). [resolve(1722,a,1720,a)]. 6.78/7.00 1723 -class_Rings_Osemiring(A) | -class_Int_Onumber(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C),c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) = c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_right__distrib__number__of) # label(axiom). [clausify(217)]. 6.78/7.00 1724 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom). [assumption]. 6.78/7.00 1725 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption]. 6.94/7.14 1726 -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D),E) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),E)) # label(fact_combine__common__factor) # label(axiom). [clausify(378)]. 6.94/7.14 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C),D) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C),D)). [resolve(1726,a,1724,a)]. 6.94/7.14 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C),D) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),D)). [resolve(1726,a,1725,a)]. 6.94/7.14 1727 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)),c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_left__distrib__number__of) # label(axiom). [clausify(544)]. 6.94/7.14 1728 class_Rings_Osemiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring) # label(axiom). [assumption]. 6.94/7.14 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C),D) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),D)). [resolve(1728,a,1726,a)]. 6.94/7.14 1729 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption]. 6.94/7.14 Derived: -class_Int_Onumber(tc_Nat_Onat) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(1729,a,1723,a)]. 6.94/7.14 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C),D) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D)). [resolve(1729,a,1726,a)]. 6.94/7.14 1730 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | B != C | c_Int_Onumber__class_Onumber__of(A,B) = c_Int_Onumber__class_Onumber__of(A,C) # label(fact_eq__number__of) # label(axiom). [clausify(757)]. 6.94/7.14 1731 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption]. 6.94/7.14 1732 class_Int_Oring__char__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Oring__char__0) # label(axiom). [assumption]. 6.94/7.14 1733 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption]. 6.94/7.14 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != B | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B). [resolve(1730,b,1731,a)]. 6.94/7.14 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A != B | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B). [resolve(1730,b,1732,a)]. 6.94/7.14 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != B | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B). [resolve(1730,b,1733,a)]. 7.38/7.59 1734 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | B = C | c_Int_Onumber__class_Onumber__of(A,B) != c_Int_Onumber__class_Onumber__of(A,C) # label(fact_eq__number__of) # label(axiom). [clausify(757)]. 7.38/7.59 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = B | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B). [resolve(1734,b,1731,a)]. 7.38/7.59 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A = B | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B). [resolve(1734,b,1732,a)]. 7.38/7.59 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = B | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B). [resolve(1734,b,1733,a)]. 7.38/7.59 1735 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_mult__zero__left) # label(axiom). [clausify(424)]. 7.38/7.59 1736 class_Rings_Omult__zero(tc_Int_Oint) # label(arity_Int__Oint__Rings_Omult__zero) # label(axiom). [assumption]. 7.38/7.59 1737 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom). [assumption]. 7.38/7.59 1738 class_Rings_Omult__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Omult__zero) # label(axiom). [assumption]. 7.38/7.59 1739 class_Rings_Omult__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Omult__zero) # label(axiom). [assumption]. 7.38/7.59 1740 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__zero__right) # label(axiom). [clausify(586)]. 7.38/7.59 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1740,a,1736,a)]. 7.38/7.59 1741 -class_Groups_Oab__semigroup__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(714)]. 7.38/7.59 1742 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.38/7.59 1743 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.38/7.59 1744 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.38/7.59 1745 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.38/7.59 1746 -class_Rings_Olinordered__comm__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(860)]. 7.38/7.59 1747 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 7.38/7.59 1748 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 7.38/7.59 1749 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 7.38/7.59 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)). [resolve(1746,a,1748,a)]. 7.38/7.59 1750 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__right__less__imp__less) # label(axiom). [clausify(567)]. 7.66/7.81 1751 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption]. 7.66/7.81 1752 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom). [assumption]. 7.66/7.81 1753 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption]. 7.66/7.81 1754 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__left__less__imp__less) # label(axiom). [clausify(926)]. 7.66/7.81 1755 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 7.66/7.81 1756 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Otimes__class_Otimes(A,B,C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divisors__zero) # label(axiom). [clausify(249)]. 7.66/7.81 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1755,a,1756,a)]. 7.66/7.81 1757 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 7.66/7.81 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1757,a,1756,a)]. 7.66/7.81 1758 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ozero__class_Ozero(A) != c_Groups_Otimes__class_Otimes(A,B,C) # label(fact_no__zero__divisors) # label(axiom). [clausify(801)]. 7.66/7.81 1759 class_Rings_Ono__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 7.66/7.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1759,a,1756,a)]. 7.66/7.81 1760 class_Rings_Ono__zero__divisors(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 7.66/7.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1760,a,1756,a)]. 7.66/7.81 1761 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.66/7.81 1762 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonpos__nonneg) # label(axiom). [clausify(314)]. 7.66/7.81 1763 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__nonneg__nonneg) # label(axiom). [clausify(355)]. 7.66/7.81 1764 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.66/7.81 1765 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos2) # label(axiom). [clausify(524)]. 7.98/8.15 1766 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(653)]. 7.98/8.15 1767 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(653)]. 7.98/8.15 1768 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.98/8.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1768,a,1762,a)]. 7.98/8.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1768,a,1763,a)]. 7.98/8.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1768,a,1766,a)]. 7.98/8.15 1769 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos) # label(axiom). [clausify(893)]. 7.98/8.15 1770 -class_Groups_Oab__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(606)]. 7.98/8.15 1771 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 7.98/8.15 1772 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 7.98/8.15 1773 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 7.98/8.15 1774 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 7.98/8.15 1775 -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f9(A)),hAPP(A,c_Nat_OSuc(f9(A)))) | c_SEQ_Osubseq(A) # label(fact_subseq__Suc__iff) # label(axiom). [clausify(360)]. 7.98/8.15 1776 -c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)) # label(fact_seq__suble) # label(axiom). [clausify(351)]. 7.98/8.15 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f9(A)),hAPP(A,c_Nat_OSuc(f9(A)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1775,b,1776,a)]. 7.98/8.15 1777 c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))) | -c_SEQ_Osubseq(A) # label(fact_subseq__Suc__iff) # label(axiom). [clausify(360)]. 8.22/8.37 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f9(A)),hAPP(A,c_Nat_OSuc(f9(A)))). [resolve(1777,b,1775,b)]. 8.22/8.37 1778 c_SEQ_Osubseq(v_f____) # label(fact_fz_I1_J) # label(axiom). [assumption]. 8.22/8.37 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(v_f____,A)). [resolve(1778,a,1776,a)]. 8.22/8.37 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A),hAPP(v_f____,c_Nat_OSuc(A))). [resolve(1778,a,1777,b)]. 8.22/8.37 1779 c_Orderings_Oord__class_Oless(tc_Nat_Onat,f19(A),f20(A)) | c_SEQ_Osubseq(A) # label(fact_subseq__def) # label(axiom). [clausify(875)]. 8.22/8.37 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,f19(A),f20(A)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1779,b,1776,a)]. 8.22/8.37 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,f19(A),f20(A)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))). [resolve(1779,b,1777,b)]. 8.22/8.37 1780 -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f19(A)),hAPP(A,f20(A))) | c_SEQ_Osubseq(A) # label(fact_subseq__def) # label(axiom). [clausify(875)]. 8.22/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f19(A)),hAPP(A,f20(A))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1780,b,1776,a)]. 8.22/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f19(A)),hAPP(A,f20(A))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))). [resolve(1780,b,1777,b)]. 8.22/8.37 1781 -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,A),hAPP(C,B)) | -c_SEQ_Osubseq(C) # label(fact_subseq__def) # label(axiom). [clausify(875)]. 8.22/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,A),hAPP(C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,f9(C)),hAPP(C,c_Nat_OSuc(f9(C)))). [resolve(1781,c,1775,b)]. 8.22/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A),hAPP(v_f____,B)). [resolve(1781,c,1778,a)]. 8.22/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,A),hAPP(C,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f19(C),f20(C)). [resolve(1781,c,1779,b)]. 8.22/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,A),hAPP(C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,f19(C)),hAPP(C,f20(C))). [resolve(1781,c,1780,b)]. 8.22/8.37 1782 -class_Groups_Ocancel__ab__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__imp__eq) # label(axiom). [clausify(618)]. 8.22/8.37 1783 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 8.22/8.37 1784 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 8.22/8.37 1785 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 8.22/8.37 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B = C. [resolve(1782,a,1783,a)]. 8.22/8.37 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B = C. [resolve(1782,a,1784,a)]. 8.22/8.37 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B = C. [resolve(1782,a,1785,a)]. 8.22/8.37 1786 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 8.22/8.37 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B = C. [resolve(1786,a,1782,a)]. 8.22/8.37 1787 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption]. 8.22/8.37 1788 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__sum__squares__lt__zero) # label(axiom). [clausify(456)]. 8.27/8.49 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1787,a,1788,a)]. 8.27/8.49 1789 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,B)) # label(fact_zero__le__square) # label(axiom). [clausify(557)]. 8.27/8.49 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A)). [resolve(1789,a,1787,a)]. 8.27/8.49 1790 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom). [assumption]. 8.27/8.49 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1790,a,1788,a)]. 8.27/8.49 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A)). [resolve(1790,a,1789,a)]. 8.27/8.49 1791 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))) # label(fact_sum__squares__ge__zero) # label(axiom). [clausify(613)]. 8.27/8.49 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B))). [resolve(1791,a,1787,a)]. 8.27/8.49 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B))). [resolve(1791,a,1790,a)]. 8.27/8.49 1792 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__square__less__zero) # label(axiom). [clausify(784)]. 8.27/8.49 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1792,a,1787,a)]. 8.27/8.49 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1792,a,1790,a)]. 8.27/8.49 1793 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_mult__left__mono) # label(axiom). [clausify(529)]. 8.27/8.49 1794 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption]. 8.27/8.49 1795 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__right__mono) # label(axiom). [clausify(558)]. 8.27/8.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(1795,a,1794,a)]. 8.27/8.49 1796 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1796,a,1795,a)]. 8.27/8.50 1797 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__mono_H) # label(axiom). [clausify(782)]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1797,a,1794,a)]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1797,a,1796,a)]. 8.27/8.50 1798 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__mono) # label(axiom). [clausify(844)]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D)). [resolve(1798,a,1794,a)]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1798,a,1796,a)]. 8.27/8.50 1799 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom). [assumption]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)). [resolve(1799,a,1795,a)]. 8.27/8.50 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1799,a,1797,a)]. 8.44/8.62 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D)). [resolve(1799,a,1798,a)]. 8.44/8.62 1800 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(590)]. 8.44/8.62 1801 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 8.44/8.62 1802 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,B,D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(590)]. 8.44/8.62 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B != C. [resolve(1802,a,1801,a)]. 8.44/8.62 1803 -class_Groups_Ocancel__semigroup__add(A) | B != C | c_Groups_Oplus__class_Oplus(A,B,D) = c_Groups_Oplus__class_Oplus(A,C,D) # label(fact_add__right__cancel) # label(axiom). [clausify(724)]. 8.44/8.62 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C). [resolve(1803,a,1801,a)]. 8.44/8.62 1804 -class_Groups_Ocancel__semigroup__add(A) | B = C | c_Groups_Oplus__class_Oplus(A,B,D) != c_Groups_Oplus__class_Oplus(A,C,D) # label(fact_add__right__cancel) # label(axiom). [clausify(724)]. 8.44/8.62 Derived: A = B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C). [resolve(1804,a,1801,a)]. 8.44/8.62 1805 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 8.44/8.62 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B != C. [resolve(1805,a,1802,a)]. 8.44/8.62 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C). [resolve(1805,a,1803,a)]. 8.44/8.62 Derived: A = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C). [resolve(1805,a,1804,a)]. 8.44/8.62 1806 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__imp__eq) # label(axiom). [clausify(773)]. 8.44/8.62 1807 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 8.44/8.62 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B != C. [resolve(1807,a,1802,a)]. 8.44/8.62 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C). [resolve(1807,a,1803,a)]. 8.44/8.62 Derived: A = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C). [resolve(1807,a,1804,a)]. 8.44/8.62 1808 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__imp__eq) # label(axiom). [clausify(802)]. 8.44/8.62 1809 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 8.44/8.62 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B != C. [resolve(1809,a,1802,a)]. 8.44/8.62 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C). [resolve(1809,a,1803,a)]. 8.44/8.62 Derived: A = B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C). [resolve(1809,a,1804,a)]. 8.67/8.84 1810 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B | c_Groups_Otimes__class_Otimes(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_square__eq__1__iff) # label(axiom). [clausify(652)]. 8.67/8.84 1811 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption]. 8.67/8.84 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) != A | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1810,a,1811,a)]. 8.67/8.84 1812 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) != B | c_Groups_Otimes__class_Otimes(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_square__eq__1__iff) # label(axiom). [clausify(652)]. 8.67/8.84 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != A | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1812,a,1811,a)]. 8.67/8.84 1813 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B | c_Groups_Oone__class_Oone(A) = B | c_Groups_Otimes__class_Otimes(A,B,B) != c_Groups_Oone__class_Oone(A) # label(fact_square__eq__1__iff) # label(axiom). [clausify(652)]. 8.67/8.84 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A | c_Groups_Oone__class_Oone(tc_Int_Oint) = A | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) != c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1813,a,1811,a)]. 8.67/8.84 1814 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption]. 8.67/8.84 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1814,a,1810,a)]. 8.67/8.84 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1814,a,1812,a)]. 8.67/8.84 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = A | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1814,a,1813,a)]. 8.67/8.84 1815 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption]. 8.67/8.84 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) != A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1815,a,1810,a)]. 8.67/8.84 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1815,a,1812,a)]. 8.67/8.84 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1815,a,1813,a)]. 8.67/8.84 1816 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Otimes__class_Otimes(A,B,C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(890)]. 8.67/8.84 1817 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption]. 8.67/8.84 1818 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption]. 8.67/8.84 1819 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom). [assumption]. 13.38/13.58 1820 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,B,C) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(890)]. 13.38/13.58 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1820,a,1817,a)]. 13.38/13.58 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1820,a,1818,a)]. 13.38/13.58 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1820,a,1819,a)]. 13.38/13.58 1821 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Otimes__class_Otimes(A,B,C) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(890)]. 13.38/13.58 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1821,a,1817,a)]. 13.38/13.58 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1821,a,1818,a)]. 13.38/13.58 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1821,a,1819,a)]. 13.38/13.58 13.38/13.58 ============================== end predicate elimination ============= 13.38/13.58 13.38/13.58 Auto_denials: (non-Horn, no changes). 13.38/13.58 13.38/13.58 Term ordering decisions: 13.38/13.58 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Int_Oint=1. tc_Nat_Onat=1. tc_Complex_Ocomplex=1. c_Int_OPls=1. v_p=1. v_s____=1. v_z____=1. v_N1____=1. v_N2____=1. v_r=1. v_f____=1. v_d____=1. v_w____=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c_Int_Onumber__class_Onumber__of=1. c_Groups_Ouminus__class_Ouminus=1. c_RealVector_Onorm__class_Onorm=1. c_Groups_Oabs__class_Oabs=1. c_Rings_Oinverse__class_Oinverse=1. hAPP=1. c_RealDef_Oreal=1. f6=1. f7=1. f8=1. f11=1. f12=1. f17=1. f22=1. f23=1. c_Groups_Ozero__class_Ozero=1. c_Groups_Oone__class_Oone=1. c_Nat_OSuc=1. c_Int_OBit1=1. c_Int_OBit0=1. v_g____=1. f1=1. f3=1. f4=1. f5=1. f9=1. f14=1. f15=1. f18=1. f19=1. f20=1. f25=1. c_Groups_Otimes__class_Otimes=1. c_Groups_Oplus__class_Oplus=1. c_Groups_Ominus__class_Ominus=1. c_Rings_Oinverse__class_Odivide=1. c_Polynomial_Opoly=1. f2=1. f10=1. f13=1. f16=1. f21=1. f24=1. 13.38/13.58 13.38/13.58 ============================== end of process initial clauses ======== 13.38/13.58 13.38/13.58 ============================== CLAUSES FOR SEARCH ==================== 13.38/13.58 13.38/13.58 ============================== end of clauses for search ============= 13.38/13.58 13.38/13.58 ============================== SEARCH ================================ 13.38/13.58 13.38/13.58 % Starting search at 7.80 seconds. 13.38/13.58 13.38/13.58 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 8.18 sec). 13.38/13.58 13.38/13.58 Low Water (keep): wt=53.000, iters=3649 13.38/13.58 13.38/13.58 Low Water (keep): wt=31.000, iters=3392 13.38/13.58 13.38/13.58 Low Water (keep): wt=30.000, iters=3360 13.38/13.58 13.38/13.58 Low Water (keep): wt=29.000, iters=3399 13.38/13.58 13.38/13.58 Low Water (keep): wt=28.000, iters=3379 13.38/13.58 13.38/13.58 Low Water (keep): wt=27.000, iters=3345 13.38/13.58 13.38/13.58 Low Water (keep): wt=26.000, iters=3360 13.38/13.58 13.38/13.58 Low Water (keep): wt=25.000, iters=3393 13.38/13.58 13.38/13.58 Low Water (keep): wt=24.000, iters=3344 13.38/13.58 13.38/13.58 Low Water (keep): wt=23.000, iters=3335 13.38/13.58 13.38/13.58 Low Water (keep): wt=22.000, iters=3342 13.38/13.58 13.38/13.58 Low Water (keep): wt=21.000, iters=3346 13.38/13.58 13.38/13.58 Low Water (keep): wt=20.000, iters=3335 13.38/13.58 13.38/13.58 Low Water (keep): wt=19.000, iters=3340 13.38/13.58 13.38/13.58 Low Water (keep): wt=18.000, iters=3336 13.38/13.58 13.38/13.58 Low Water (keep): wt=17.000, iters=3337 13.38/13.58 13.38/13.58 Low Water (keep): wt=16.000, iters=3334 13.38/13.58 13.38/13.58 Low Water (keep): wt=15.000, iters=3336 13.38/13.58 13.38/13.58 Low Water (keep): wt=14.000, iters=3333 13.38/13.58 13.38/13.58 Low Water (keep): wt=13.000, iters=3335 13.38/13.58 13.38/13.58 Low Water (keep): wt=12.000, iters=3360 13.38/13.58 13.38/13.58 Low Water (displace): id=5552, wt=153.000 13.38/13.58 13.38/13.58 Low Water (displace): id=6554, wt=95.000 13.38/13.58 13.38/13.58 Low Water (displace): id=7009, wt=81.000 13.38/13.58 13.38/13.58 Low Water (displace): id=6497, wt=79.000 13.38/13.58 13.38/13.58 Low Water (displace):Cputime limit exceeded (core dumped) 300.01/300.19 EOF