0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n003.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 14:58:32 EDT 2019 0.12/0.33 % CPUTime : 1.35/1.67 ============================== Prover9 =============================== 1.35/1.67 Prover9 (32) version 2009-11A, November 2009. 1.35/1.67 Process 2673 was started by sandbox2 on n003.cluster.edu, 1.35/1.67 Thu Aug 29 14:58:33 2019 1.35/1.67 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_2520_n003.cluster.edu". 1.35/1.67 ============================== end of head =========================== 1.35/1.67 1.35/1.67 ============================== INPUT ================================= 1.35/1.67 1.35/1.67 % Reading from file /tmp/Prover9_2520_n003.cluster.edu 1.35/1.67 1.35/1.67 set(prolog_style_variables). 1.35/1.67 set(auto2). 1.35/1.67 % set(auto2) -> set(auto). 1.35/1.67 % set(auto) -> set(auto_inference). 1.35/1.67 % set(auto) -> set(auto_setup). 1.35/1.67 % set(auto_setup) -> set(predicate_elim). 1.35/1.67 % set(auto_setup) -> assign(eq_defs, unfold). 1.35/1.67 % set(auto) -> set(auto_limits). 1.35/1.67 % set(auto_limits) -> assign(max_weight, "100.000"). 1.35/1.67 % set(auto_limits) -> assign(sos_limit, 20000). 1.35/1.67 % set(auto) -> set(auto_denials). 1.35/1.67 % set(auto) -> set(auto_process). 1.35/1.67 % set(auto2) -> assign(new_constants, 1). 1.35/1.67 % set(auto2) -> assign(fold_denial_max, 3). 1.35/1.67 % set(auto2) -> assign(max_weight, "200.000"). 1.35/1.67 % set(auto2) -> assign(max_hours, 1). 1.35/1.67 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.35/1.67 % set(auto2) -> assign(max_seconds, 0). 1.35/1.67 % set(auto2) -> assign(max_minutes, 5). 1.35/1.67 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.35/1.67 % set(auto2) -> set(sort_initial_sos). 1.35/1.67 % set(auto2) -> assign(sos_limit, -1). 1.35/1.67 % set(auto2) -> assign(lrs_ticks, 3000). 1.35/1.67 % set(auto2) -> assign(max_megs, 400). 1.35/1.67 % set(auto2) -> assign(stats, some). 1.35/1.67 % set(auto2) -> clear(echo_input). 1.35/1.67 % set(auto2) -> set(quiet). 1.35/1.67 % set(auto2) -> clear(print_initial_clauses). 1.35/1.67 % set(auto2) -> clear(print_given). 1.35/1.67 assign(lrs_ticks,-1). 1.35/1.67 assign(sos_limit,10000). 1.35/1.67 assign(order,kbo). 1.35/1.67 set(lex_order_vars). 1.35/1.67 clear(print_given). 1.35/1.67 1.35/1.67 % formulas(sos). % not echoed (1200 formulas) 1.35/1.67 1.35/1.67 ============================== end of input ========================== 1.35/1.67 1.35/1.67 % From the command line: assign(max_seconds, 180). 1.35/1.67 1.35/1.67 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.35/1.67 1.35/1.67 % Formulas that are not ordinary clauses: 1.35/1.67 1 (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,V_x,c_Transcendental_Opi) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x))))) # label(fact_sin__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 2 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_number__of__Pls) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 3 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 4 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_pos__mod__sign) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 5 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 6 (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]. 1.35/1.67 7 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> V_b = 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)))) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 8 (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]. 1.35/1.67 9 (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]. 1.35/1.67 10 (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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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_I25_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 11 (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]. 1.35/1.67 12 (all V_k_2 (c_Int_OBit0(V_k_2) = c_Int_OPls <-> V_k_2 = c_Int_OPls)) # label(fact_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 13 (all V_d_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_d_2) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_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_d_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 14 (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]. 1.35/1.67 15 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_neg__mod__sign) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 16 (all V_n_2 all V_m_2 (V_m_2 = V_n_2 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 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_Oone__class_Oone(T_a)))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 18 (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]. 1.35/1.67 19 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_k_2)))) # label(fact_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 20 (all V_z3 all V_z2 all V_z1 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3)) # label(fact_real__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 21 (all V_l_2 all V_k_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)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 22 (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]. 1.35/1.67 23 (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]. 1.35/1.67 24 (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,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_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 25 (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) -> (V_n_2 = V_m_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)))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 26 (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_one__neq__zero) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 27 (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(tc_RealDef_Oreal,V_x_2,V_y_2) | V_x_2 = V_y_2)) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 28 (all V_n_2 all V_k_2 all V_m_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_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 29 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 30 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarcsin(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_arcsin__ubound) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 31 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b))) # label(fact_mod__add__self1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 32 (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]. 1.35/1.67 33 (all V_x (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != V_x -> c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x),c_Transcendental_Opi),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(V_x)))) # label(fact_arctan__inverse) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 34 (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]. 1.35/1.67 35 (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]. 1.35/1.67 36 (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(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)))) # label(fact_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 37 (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]. 1.35/1.67 38 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_c = V_b -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 39 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> V_y_2 != V_x_2))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 40 (all V_y_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_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2)))) # label(fact_le__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 41 (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]. 1.35/1.67 42 (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]. 1.35/1.67 43 (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]. 1.35/1.67 44 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_y = V_x))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 45 (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]. 1.35/1.67 46 (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]. 1.35/1.67 47 (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]. 1.35/1.67 48 (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]. 1.35/1.67 49 (all V_x all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Transcendental_Opi) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y)))))) # label(fact_cos__monotone__0__pi_H) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 50 (all V_z all V_y all V_x all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> c_Orderings_Oord__class_Omin(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_z),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Orderings_Oord__class_Omin(T_a,V_x,V_y),V_z))) # label(fact_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 51 (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]. 1.35/1.67 52 (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]. 1.35/1.67 53 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 54 (all V_k_2 (c_Orderings_Oord__class_Oless(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_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 55 (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]. 1.35/1.67 56 (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]. 1.35/1.68 57 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 58 (all T_a (class_Rings_Osemiring__1(T_a) -> c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_iszero__0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 59 (all V_c_2 all V_b_2 all V_w_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,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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,c_Int_Onumber__class_Onumber__of(T_a,V_w_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,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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]. 1.35/1.68 60 (all V_v_2 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> 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]. 1.35/1.68 61 (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_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = 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)))) # label(fact_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 62 (all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 63 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 64 (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]. 1.35/1.68 65 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-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) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 66 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_z) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_z))) # label(fact_mult__minus1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 67 (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_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_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 68 (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]. 1.35/1.68 69 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) <-> V_x_2 = V_y_2))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 70 (all V_x c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_cos__arctan__not__zero) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 71 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z) # label(fact_zadd__0__right) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 72 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Orderings_Oord__class_Omin(T_a,V_y_2,V_z_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2)))) # label(fact_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 73 (all V_b all V_a all V_x all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Orderings_Oord__class_Omin(T_a,V_a,V_b)) -> -(c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b))))) # label(fact_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 74 (all V_w_2 all T_a (class_Int_Oring__char__0(T_a) & class_Int_Onumber__ring(T_a) -> (c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w_2))) <-> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))))) # label(fact_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 75 (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]. 1.35/1.68 76 (all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 77 (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]. 1.35/1.68 78 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarccos(V_y),c_Transcendental_Opi)))) # label(fact_arccos__ubound) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 79 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Orderings_Oord__class_Omin(T_a,V_y,V_z)))))) # label(fact_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 80 (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]. 1.35/1.68 81 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> 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)) = 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)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 82 (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,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = 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))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 83 (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),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,V_y_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_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)))) # label(fact_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 84 (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]. 1.35/1.68 85 (all V_w_2 all V_b_2 all V_a_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Ofield__inverse__zero(T_a) -> ((c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_b_2) & (c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = V_a_2) <-> V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))))) # label(fact_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 86 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2 <-> (c_Groups_Ozero__class_Ozero(T_a) = V_c_2 -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2)))) # label(fact_eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 87 (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_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = 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)))) # label(fact_number__of__mult) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 88 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_cos__le__one) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 89 (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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) = 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)))) # label(fact_add__number__of__left) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 90 (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) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_equal__neg__zero) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 91 (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_OBit1(V_k),c_Int_OBit0(V_l))) # label(fact_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 92 (all V_q all V_b all V_r all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (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,V_r,V_b) -> 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,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)))))) # label(fact_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 93 (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]. 1.35/1.68 94 (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]. 1.35/1.68 95 (all V_n_2 all V_m_2 (V_m_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) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 96 (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]. 1.35/1.68 97 (all V_z c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,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))))) # label(fact_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 98 (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]. 1.35/1.68 99 (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]. 1.35/1.68 100 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_b)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_a)))) # label(fact_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 101 (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_b_2 = c_Groups_Ozero__class_Ozero(T_a) | V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 102 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> V_a = c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mod__by__0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 103 (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]. 1.35/1.68 104 (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]. 1.35/1.68 105 (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]. 1.35/1.68 106 (all V_v_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) <-> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_eq__number__of__0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 107 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) <-> -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 108 (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) <-> c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2)))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 109 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 110 (all V_z V_z = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) # label(fact_zmult__1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 111 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_n != V_m)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 112 (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]. 1.35/1.68 113 (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]. 1.35/1.68 114 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin))) # label(fact_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 115 (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]. 1.35/1.68 116 (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]. 1.35/1.68 117 (all V_y all V_x c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Transcendental_Osin(V_y)))) # label(fact_cos__diff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 118 (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__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]. 1.35/1.68 119 (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]. 1.35/1.68 120 (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]. 1.35/1.68 121 (all V_l c_Int_OPls != c_Int_OBit1(V_l)) # label(fact_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 122 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.35/1.68 123 (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]. 1.35/1.68 124 (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]. 1.35/1.68 125 (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]. 1.47/1.68 126 (all V_b all V_x all V_a all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless(T_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b),V_x)))) # label(fact_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 127 (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]. 1.47/1.68 128 (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]. 1.47/1.68 129 (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]. 1.47/1.68 130 (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) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2)))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 131 (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]. 1.47/1.68 132 (all V_b all V_a all T_a (class_Groups_Ogroup__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_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_minus__add) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 133 (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]. 1.47/1.68 134 (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]. 1.47/1.68 135 (all V_b_2 all V_a_2 all V_f_2 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_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_f_2,V_b_2),hAPP(V_f_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_f_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_f_2,V_b_2),hAPP(V_f_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]. 1.47/1.68 136 (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,V_m_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)))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 137 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 138 (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]. 1.47/1.68 139 (all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_a,V_b) = c_Orderings_Oord__class_Omin(T_a,V_b,V_a))) # label(fact_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 140 (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]. 1.47/1.68 141 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Opi),V_x) -> c_Transcendental_Oarccos(c_Transcendental_Ocos(V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)))) # label(fact_arccos__cos2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 142 (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]. 1.47/1.68 143 (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]. 1.47/1.68 144 (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]. 1.47/1.68 145 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (V_x_2 != c_Groups_Ozero__class_Ozero(T_a) | 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]. 1.47/1.68 146 (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]. 1.47/1.68 147 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 148 (all T_a (class_Int_Onumber__ring(T_a) -> -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))))) # label(fact_not__iszero__Numeral1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 149 (all V_x c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Otan(V_x)) = c_Transcendental_Otan(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) # label(fact_tan__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 150 (all V_y all V_x (c_Transcendental_Ocos(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Transcendental_Ocos(V_y) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Otan(V_x),c_Transcendental_Otan(V_y))))) # label(fact_add__tan__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 151 (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_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]. 1.47/1.68 152 (all V_n c_Orderings_Oord__class_Omin(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_min__0L) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 153 (all V_y c_Transcendental_Otan(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(V_y))) # label(fact_tan__inverse) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 154 (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]. 1.47/1.68 155 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 156 (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]. 1.47/1.68 157 (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]. 1.47/1.68 158 (all V_y exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),B_x) & c_Transcendental_Otan(B_x) = V_y & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_lemma__tan__total1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 159 (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]. 1.47/1.68 160 (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]. 1.47/1.68 161 (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]. 1.47/1.68 162 (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,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 163 (all V_q all V_r all V_b all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_c),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)))))) # label(fact_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 164 (all V_l all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))) # label(fact_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 165 (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]. 1.47/1.68 166 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 167 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 168 (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,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__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 169 (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]. 1.47/1.68 170 (all V_x c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_minus__sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 171 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 172 (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]. 1.47/1.68 173 (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_lx,c_Groups_Otimes__class_Otimes(T_a,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]. 1.47/1.68 174 (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_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) <-> V_n_2 = V_m_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 175 (all V_x (c_Transcendental_Ocos(V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) -> c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 176 (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]. 1.47/1.68 177 (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]. 1.47/1.68 178 (all V_y_2 all V_x_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_y_2) = c_Int_Onumber__class_Onumber__of(T_a,V_x_2) <-> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))))) # label(fact_eq__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 179 (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]. 1.47/1.68 180 (all V_w_2 all V_z_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) & V_z_2 != V_w_2 <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2))) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 181 (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]. 1.47/1.68 182 (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]. 1.47/1.68 183 (all V_a c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin))) # label(fact_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 184 (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) -> (V_y_2 = c_Groups_Ozero__class_Ozero(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) = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 185 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_y_2 = V_x_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 186 (all V_y_2 all V_x_2 all T_a (class_Lattices_Oboolean__algebra(T_a) -> (V_x_2 = V_y_2 <-> c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)))) # label(fact_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 187 (all V_x_2 all V_A_2 all T_b all T_a (class_Groups_Ouminus(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)))) # label(fact_uminus__apply) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 188 (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]. 1.47/1.68 189 (all V_y c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(V_y))) # label(fact_arctan__lbound) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 190 (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]. 1.47/1.68 191 (all V_n_2 all V_k_2 all V_m_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_n_2,V_k_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 192 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 193 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 194 (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]. 1.47/1.68 195 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 196 (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_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = 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__frac__num) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 197 (all V_x c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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))),c_Transcendental_Opi))) = c_Transcendental_Ocos(V_x)) # label(fact_cos__periodic) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 198 (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) <-> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) = V_y_2)) # label(fact_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 199 (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]. 1.47/1.68 200 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> V_x = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)))) # label(fact_double__compl) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 201 (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_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 202 (all V_v_H all V_v ((-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)))) & (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)))) # label(fact_add__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 203 (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_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) -> V_c = V_b))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 204 (all V_k V_k = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k)) # label(fact_add__Pls) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 205 (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]. 1.47/1.68 206 (all V_z all V_y all V_x all T_a (class_Groups_Oordered__ab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Orderings_Oord__class_Omin(T_a,V_x,V_y),V_z) = c_Orderings_Oord__class_Omin(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_z),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)))) # label(fact_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 207 (all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 208 (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_OPls,V_y_2) <-> 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))))) # label(fact_less__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 209 (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,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]. 1.47/1.68 210 (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]. 1.47/1.68 211 (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_k,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 212 (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)))) -> c_Groups_Oone__class_Oone(tc_Int_Oint) = V_x | V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 213 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_divide__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 214 (all V_b all V_a all T_a (class_Groups_Oab__group__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_ab__diff__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 215 (all V_x all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) = c_Groups_Ouminus__class_Ouminus(T_a,V_x))) # label(fact_divide__minus1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 216 (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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,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))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 217 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,c_Orderings_Oord__class_Omin(T_a,V_x,V_y),V_z) = c_Orderings_Oord__class_Omin(T_a,V_x,c_Orderings_Oord__class_Omin(T_a,V_y,V_z)))) # label(fact_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 218 (all V_w all V_z c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = 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))) # label(fact_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 219 (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]. 1.47/1.68 220 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 221 (all V_x c_Groups_Otimes__class_Otimes(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))),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_x)) = c_Transcendental_Osin(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))) # label(fact_sin__double) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 222 (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(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]. 1.47/1.68 223 (all V_x all V_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_y) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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_Transcendental_Otan(V_y),c_Transcendental_Otan(V_x)))))) # label(fact_tan__monotone) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 224 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.68 225 (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]. 1.47/1.68 226 (all V_w_2 all V_c_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__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_w_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,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_2))))))) # label(fact_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 227 (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,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_a_2,V_b_2))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 228 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 229 (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]. 1.47/1.69 230 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 231 (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]. 1.47/1.69 232 (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]. 1.47/1.69 233 (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]. 1.47/1.69 234 (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]. 1.47/1.69 235 (all V_k_2 all V_n_2 all V_P_2 ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) & c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,B_i),B_j) = V_n_2 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> hBOOL(hAPP(V_P_2,B_j))))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,B_i),B_j) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) -> hBOOL(hAPP(V_P_2,B_j))))) & (c_Groups_Ozero__class_Ozero(tc_Int_Oint) = V_k_2 -> hBOOL(hAPP(V_P_2,V_n_2))) <-> hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))))) # label(fact_split__zmod) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 236 (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]. 1.47/1.69 237 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 238 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)))) # label(fact_iszero__Numeral0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 239 (all V_y all V_x (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(V_x) -> (c_Transcendental_Ocos(V_y) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Otan(V_x),c_Transcendental_Otan(V_y)))))) # label(fact_lemma__tan__add1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 240 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 241 (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]. 1.47/1.69 242 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 243 (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]. 1.47/1.69 244 (all V_w_2 all V_c_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_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_w_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_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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),c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_2))))) # label(fact_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 245 (all V_b all V_a all V_x all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Orderings_Oord__class_Omin(T_a,V_a,V_b)))))) # label(fact_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 246 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 247 (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]. 1.47/1.69 248 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 249 (all V_n_2 all V_m_2 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_m_2 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n_2 <-> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 250 (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,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) | 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,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 251 (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]. 1.47/1.69 252 (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,V_a_2,V_b_2) <-> 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))))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 253 (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]. 1.47/1.69 254 (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]. 1.47/1.69 255 (all V_b c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)) # label(fact_zmod__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 256 (all V_a all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Ofield(T_a) -> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))))) # label(fact_divide__numeral__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 257 (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]. 1.47/1.69 258 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 259 (all V_a_2 all V_w_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_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_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_w_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_w_2))))))) # label(fact_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 260 (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]. 1.47/1.69 261 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarcsin(V_y))))) # label(fact_arcsin__lbound) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 262 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m) = c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 263 (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_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,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)))) # label(fact_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 264 (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_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 265 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 266 (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,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__disj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 267 (all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 268 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 269 (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]. 1.47/1.69 270 (all V_w all V_z c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 271 (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,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)) = 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)) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 272 (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]. 1.47/1.69 273 (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_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 274 (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]. 1.47/1.69 275 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) <-> V_n_2 = V_m_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 276 (all V_k c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k))) # label(fact_minus__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 277 (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_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_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_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 278 (all V_l_2 all V_k_2 (V_l_2 = V_k_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]. 1.47/1.69 279 (all V_a_H all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_H),V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)))) # label(fact_mod__minus__cong) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 280 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_minus__divide__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 281 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> 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)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 282 (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,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_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 283 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) | V_x_2 = V_y_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 284 (all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> V_a = c_Groups_Otimes__class_Otimes(T_a,V_a,V_a))) # label(fact_times_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 285 (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]. 1.47/1.69 286 (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_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)))) # label(fact_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 287 (all V_z_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_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 288 (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]. 1.47/1.69 289 (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]. 1.47/1.69 290 (all V_d_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_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_d_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_d_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 291 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2))) # label(fact_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 292 (all V_y_2 all V_x_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = V_y_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]. 1.47/1.69 293 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_Omin(T_a,V_x,V_y),V_y))) # label(fact_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 294 (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]. 1.47/1.69 295 (all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) & class_Int_Onumber__ring(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]. 1.47/1.69 296 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y)) = V_y))) # label(fact_cos__arccos) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 297 (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]. 1.47/1.69 298 (all T_2 all T_1 (class_Lattices_Oboolean__algebra(T_1) -> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 299 (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_n_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 300 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = 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)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 301 (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]. 1.47/1.69 302 (all V_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(V_y)) & V_y = c_Transcendental_Otan(c_Transcendental_Oarctan(V_y)) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_arctan) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 303 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Transcendental_Opi) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x))))) # label(fact_sin__ge__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 304 (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_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 305 (all V_w_2 all V_x_2 all V_z_2 all V_y_2 all T_a (class_Fields_Ofield(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_y_2 -> (V_z_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2) <-> c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2) = c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 306 (all V_y_2 all V_x_2 all T_a (class_Lattices_Oboolean__algebra(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 307 (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(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_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,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_less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 308 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) | V_x = V_y)) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 309 (all V_b all 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)))) = 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)) # label(fact_real__average__minus__first) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 310 (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,V_v),c_Groups_Ominus__class_Ominus(T_a,V_c,c_Int_Onumber__class_Onumber__of(T_a,V_w))) = 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))) # label(fact_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 311 (all V_z V_z = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 312 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 313 (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]. 1.47/1.69 314 (all V_b 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_b))) # label(fact_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 315 (all V_v_H_2 all V_v_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)) <-> 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)))) # label(fact_less__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 316 (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,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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),c_Transcendental_Otan(V_x))))) # label(fact_tan__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 317 (all V_y_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,c_Int_OBit1(c_Int_OPls),V_y_2) <-> 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))))) # label(fact_le__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 318 (all V_n_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & c_Groups_Oone__class_Oone(tc_Nat_Onat) = V_m_2)) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 319 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 320 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 321 (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]. 1.47/1.69 322 (all V_c all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_a,c_Orderings_Oord__class_Omin(T_a,V_b,V_c)) = c_Orderings_Oord__class_Omin(T_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b),V_c))) # label(fact_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 323 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> (exists B_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_x,c_Transcendental_Opi) & (all B_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) & V_y = c_Transcendental_Ocos(B_y) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,c_Transcendental_Opi) -> B_x = B_y)) & c_Transcendental_Ocos(B_x) = V_y & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)))))) # label(fact_cos__total) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 324 (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]. 1.47/1.69 325 (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_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__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 326 (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]. 1.47/1.69 327 (all V_y all V_x (c_Transcendental_Ocos(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Transcendental_Ocos(V_y) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Transcendental_Otan(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Otan(V_x),c_Transcendental_Otan(V_y)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Otan(V_x),c_Transcendental_Otan(V_y)))))))) # label(fact_tan__add) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 328 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 329 (all T_2 all T_1 (class_Groups_Ouminus(T_1) -> class_Groups_Ouminus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 330 (all V_x_2 all V_w_2 all T_a (class_Int_Onumber(T_a) -> (V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2) <-> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))) # label(fact_number__of__reorient) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 331 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> (exists B_x (V_y = c_Transcendental_Otan(B_x) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x))))) # label(fact_tan__total__pos) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 332 (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]. 1.47/1.69 333 (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_rx),V_ly) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 334 (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]. 1.47/1.69 335 (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]. 1.47/1.69 336 (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]. 1.47/1.69 337 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) -> (V_y_2 = V_x_2 <-> -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2))))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 338 (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]. 1.47/1.69 339 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 340 (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]. 1.47/1.69 341 (all V_a all T_a (class_Rings_Ocomm__semiring__1(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_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 342 (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]. 1.47/1.69 343 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Oring(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]. 1.47/1.69 344 (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_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,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)))) # label(fact_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 345 (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]. 1.47/1.69 346 (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]. 1.47/1.69 347 (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]. 1.47/1.69 348 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Orderings_Oord__class_Omin(T_a,V_x_2,V_y_2),V_z_2) <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_z_2) | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_z_2)))) # label(fact_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 349 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 350 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_mod__by__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 351 (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) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2 <-> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 352 (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 -> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) = V_b -> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 353 (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]. 1.47/1.69 354 (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]. 1.47/1.69 355 (all V_b all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))) # label(fact_mult__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 356 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(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))))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 357 (all T_a (class_Rings_Osemiring__1(T_a) -> -c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_not__iszero__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 358 (all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m))) # label(fact_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 359 (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]. 1.47/1.69 360 (all V_y all V_x c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Transcendental_Osin(V_y))) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y))) # label(fact_cos__add) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 361 (all V_n all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m -> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_n)) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 362 (all V_a_2 all V_b_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = V_b_2 <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 363 (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]. 1.47/1.69 364 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 365 (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,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__eq(tc_Nat_Onat,V_m_2,V_n_2))))) # label(fact_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 366 (all V_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarccos(V_y),c_Transcendental_Opi) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oarccos(V_y))))) # label(fact_arccos__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 367 (all V_k c_Int_OBit1(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)) # label(fact_Bit1__def) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 368 (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]. 1.47/1.69 369 (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]. 1.47/1.69 370 (all V_x all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_y),c_Transcendental_Osin(V_x)))))) # label(fact_sin__monotone__2pi_H) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 371 (all V_m all T_a (class_Rings_Ocomm__semiring__1(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)),V_m) = c_Groups_Oplus__class_Oplus(T_a,V_m,V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 372 (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]. 1.47/1.69 373 (all V_a c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)) # label(fact_zmod__self) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 374 (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]. 1.47/1.69 375 (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(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))) & (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)))))) # label(fact_divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 376 (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]. 1.47/1.69 377 (all V_v all V_b all V_a 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,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]. 1.47/1.69 378 (all V_x c_Transcendental_Osin(V_x) = c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) # label(fact_sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 379 (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_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls))))) # label(fact_le__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 380 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Opi),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Otan(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_tan__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 381 (all V_y all V_q_1 all V_b_1 all V_a_1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_1,V_q_1),V_y) = V_a_1 -> ((-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_y)) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_b_1) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> V_y = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1))))) # label(fact_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 382 (all V_k c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OMin,V_k) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)) # label(fact_mult__Min) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 383 (all V_k c_Int_OPls != c_Int_OBit1(V_k)) # label(fact_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 384 (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]. 1.47/1.69 385 (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_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b)) # label(fact_minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 386 (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]. 1.47/1.69 387 (all V_k_2 (c_Orderings_Oord__class_Oless(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_I12_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 388 (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_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_right__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 389 (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]. 1.47/1.69 390 (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,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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),c_Transcendental_Ocos(V_x))))) # label(fact_cos__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 391 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 392 (all V_n all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 393 (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]. 1.47/1.69 394 (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]. 1.47/1.69 395 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__self) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 396 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (V_x_2 = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 397 (all V_n c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) = V_n) # label(fact_nat__mult__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 398 (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]. 1.47/1.69 399 (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]. 1.47/1.69 400 (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]. 1.47/1.69 401 (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]. 1.47/1.69 402 (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_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 403 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2))) # label(fact_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 404 (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]. 1.47/1.69 405 (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]. 1.47/1.69 406 (all V_y_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (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)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)))) # label(fact_less__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 407 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> c_Transcendental_Oarcsin(c_Transcendental_Osin(V_x)) = V_x))) # label(fact_arcsin__sin) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 408 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_neg__mod__bound) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 409 (all V_w all V_z c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w))) # label(fact_zmult__zminus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.69 410 (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]. 1.47/1.69 411 (all V_d_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_d_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_d_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]. 1.47/1.70 412 (all V_z c_Groups_Ozero__class_Ozero(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_z),V_z)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 413 (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,V_a_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_b_2,V_a_2) <-> 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))))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 414 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)))) # label(fact_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 415 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)))) # label(fact_number__of__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 416 (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]. 1.47/1.70 417 (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) -> V_b = c_Groups_Ozero__class_Ozero(T_a) | V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 418 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Transcendental_Opi) -> c_Transcendental_Oarccos(c_Transcendental_Ocos(V_x)) = V_x))) # label(fact_arccos__cos) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 419 (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]. 1.47/1.70 420 (all V_a_2 all V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = V_a_2)) # label(fact_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 421 (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]. 1.47/1.70 422 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 423 (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]. 1.47/1.70 424 (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]. 1.47/1.70 425 (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]. 1.47/1.70 426 (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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2))) # label(fact_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 427 (all V_d_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_d_2) = c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) -> (V_a_2 = V_b_2 <-> V_c_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 428 (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,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,V_m_2,V_n_2)))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 429 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_z,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) = c_Groups_Ouminus__class_Ouminus(T_a,V_z))) # label(fact_mult__minus1__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 430 (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_OBit0(V_l_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 431 (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]. 1.47/1.70 432 (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]. 1.47/1.70 433 (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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 434 (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]. 1.47/1.70 435 (all V_a all T_a (class_Orderings_Olinorder(T_a) -> V_a = c_Orderings_Oord__class_Omin(T_a,V_a,V_a))) # label(fact_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 436 (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]. 1.47/1.70 437 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 438 (all V_b_2 all V_a_2 all V_c_2 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != V_c_2 -> (V_b_2 = V_a_2 <-> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 439 (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]. 1.47/1.70 440 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oarccos(V_y))))) # label(fact_arccos__lbound) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 441 (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]. 1.47/1.70 442 (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]. 1.47/1.70 443 (all V_x c_Transcendental_Otan(V_x) = c_Transcendental_Otan(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi))) # label(fact_tan__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 444 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> ((all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 445 (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]. 1.47/1.70 446 (all V_d_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,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_d_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_d_2))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 447 (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]. 1.47/1.70 448 (all V_n all V_m (V_m = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) -> V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = V_m)) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 449 (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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 450 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(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__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 451 (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]. 1.47/1.70 452 (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]. 1.47/1.70 453 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 454 (all V_z_2 all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_Omin(T_a,V_x_2,V_y_2),V_z_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_z_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_z_2)))) # label(fact_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 455 (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]. 1.47/1.70 456 (all V_c_2 all V_a_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (V_b_2 = V_c_2 <-> c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 457 (all V_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> (exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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,V_y,c_Transcendental_Otan(B_x)))))) # label(fact_lemma__tan__total) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 458 (all V_d_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_d_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_d_2))))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 459 (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]. 1.47/1.70 460 (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,c_Groups_Ozero__class_Ozero(T_a),V_b) & 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_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]. 1.47/1.70 461 (all V_k_2 (c_Int_OMin = c_Int_OBit1(V_k_2) <-> V_k_2 = c_Int_OMin)) # label(fact_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 462 (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]. 1.47/1.70 463 (all V_b_2 all V_a_2 all T_a (class_Rings_Oidom(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 | V_b_2 = V_a_2 <-> c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2) = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_a_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 464 (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]. 1.47/1.70 465 (all V_x c_Transcendental_Ocos(V_x) = c_Transcendental_Ocos(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) # label(fact_cos__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 466 (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]. 1.47/1.70 467 (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_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 468 (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]. 1.47/1.70 469 (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]. 1.47/1.70 470 (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]. 1.47/1.70 471 (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]. 1.47/1.70 472 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),c_Transcendental_Ocos(V_x))) # label(fact_cos__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 473 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_c))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 474 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b))) # label(fact_mod__add__self2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 475 (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]. 1.47/1.70 476 (all V_d_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_d_2)) <-> 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_d_2)))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 477 (all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_mod__minus__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 478 (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]. 1.47/1.70 479 (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,V_b_2) <-> 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))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 480 (all V_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarcsin(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarcsin(V_y))))) # label(fact_arcsin__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 481 (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]. 1.47/1.70 482 (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]. 1.47/1.70 483 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 484 (all V_x all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Transcendental_Opi) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y)))))) # label(fact_cos__monotone__0__pi) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 485 (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]. 1.47/1.70 486 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarcsin(V_y),c_Transcendental_Opi) & c_Transcendental_Osin(c_Transcendental_Oarcsin(V_y)) = V_y & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarcsin(V_y))))) # label(fact_arcsin__pi) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 487 (all V_n all V_m (c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n) -> V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) = V_m)) # label(fact_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 488 (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,V_a_2,V_b_2) <-> 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))))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 489 (all V_y all V_x c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x)))) # label(fact_sin__diff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 490 (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]. 1.47/1.70 491 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 492 (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]. 1.47/1.70 493 (all V_a all V_x all V_b all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless(T_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b),V_x)))) # label(fact_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 494 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 495 (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]. 1.47/1.70 496 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> V_a = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))))) # label(fact_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 497 (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]. 1.47/1.70 498 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 499 (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]. 1.47/1.70 500 (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]. 1.47/1.70 501 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oarccos(V_y)) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarccos(V_y),c_Transcendental_Opi)))) # label(fact_arccos__bounded) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 502 (all V_b all V_x all V_a all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b),V_x)))) # label(fact_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 503 (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]. 1.47/1.70 504 (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]. 1.47/1.70 505 (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]. 1.47/1.70 506 (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]. 1.47/1.70 507 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__add__cong) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 508 (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]. 1.47/1.70 509 (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]. 1.47/1.70 510 (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]. 1.47/1.70 511 (all V_x c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x)) = c_Transcendental_Oarctan(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) # label(fact_arctan__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 512 (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]. 1.47/1.70 513 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_b != V_a -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 514 (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]. 1.47/1.70 515 (all V_q all V_b all V_r all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (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,V_r,V_b) -> 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,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_c)))))) # label(fact_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 516 (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_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 517 (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_c = V_b))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 518 (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]. 1.47/1.70 519 (all V_a all T_a (class_Rings_Omult__zero(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_mult__zero__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 520 (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]. 1.47/1.70 521 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x))))) # label(fact_cos__ge__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 522 (all V_x c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))) # label(fact_sin__periodic__pi2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 523 (all V_z c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)) # label(fact_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 524 (all V_d_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_d_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_d_2))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 525 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> V_y = c_Transcendental_Osin(c_Transcendental_Oarcsin(V_y))))) # label(fact_sin__arcsin) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 526 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> 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)))) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z))) # label(fact_mult__2__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 527 (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_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__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 528 (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]. 1.47/1.70 529 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_mod__add__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 530 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 531 (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_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,V_b_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_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]. 1.47/1.70 532 (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]. 1.47/1.70 533 (all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_x),V_m)) # label(fact_zminus__zmod) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 534 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a) -> V_a = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 535 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 536 (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]. 1.47/1.70 537 (all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_a,V_b) = c_Orderings_Oord__class_Omin(T_a,V_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b)))) # label(fact_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 538 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(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_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 539 (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]. 1.47/1.70 540 (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]. 1.47/1.70 541 (all V_l_2 (c_Int_OBit0(V_l_2) = c_Int_OPls <-> V_l_2 = c_Int_OPls)) # label(fact_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 542 (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__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]. 1.47/1.70 543 (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]. 1.47/1.70 544 (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]. 1.47/1.70 545 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_number__of__Min) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 546 (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]. 1.47/1.70 547 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oarccos(V_y)) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarccos(V_y),c_Transcendental_Opi) & V_y = c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y))))) # label(fact_arccos) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 548 (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_Oone__class_Oone(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) -> 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]. 1.47/1.70 549 (all V_x c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_x)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Transcendental_Osin(V_x)))) # label(fact_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 550 (all V_c_2 all V_b_2 all V_w_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_Int_Onumber__class_Onumber__of(T_a,V_w_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,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_b_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_2),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 551 (all V_x c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) = c_Transcendental_Osin(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) # label(fact_sin__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 552 (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]. 1.47/1.70 553 (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,V_q),V_r) = 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,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]. 1.47/1.70 554 (all V_y exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),B_x) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) & V_y = c_Transcendental_Otan(B_x) & (all B_y (V_y = c_Transcendental_Otan(B_y) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),B_y) -> B_y = B_x)))) # label(fact_tan__total) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 555 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b) = 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)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 556 (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]. 1.47/1.70 557 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_x,c_Orderings_Oord__class_Omin(T_a,V_y,V_z)) = c_Orderings_Oord__class_Omin(T_a,V_y,c_Orderings_Oord__class_Omin(T_a,V_x,V_z)))) # label(fact_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 558 (all V_b all V_a c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))) # label(fact_zmod__zminus2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 559 (all V_w_2 all V_c_2 all V_b_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Ofield__inverse__zero(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) <-> (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_w_2),V_c_2)) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 560 (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]. 1.47/1.70 561 (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]. 1.47/1.70 562 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 563 (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]. 1.47/1.70 564 (all V_x c_Transcendental_Otan(V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_x))) # label(fact_tan__def) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 565 (all V_r_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_r_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_r_2)))) # label(fact_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 566 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (V_y != V_x -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 567 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n),V_k)) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 568 (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]. 1.47/1.70 569 (all V_x all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> V_x = c_Groups_Otimes__class_Otimes(T_a,V_x,V_x))) # label(fact_mult__idem) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 570 (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]. 1.47/1.70 571 (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,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_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 572 (all V_n (V_n != 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))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 573 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 574 (all V_c_2 all V_b_2 all V_a_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_a_2,V_c_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 575 (all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,V_x))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 576 (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_Ozero__class_Ozero(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))))) # label(fact_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 577 (all V_y all V_x c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_y),c_Transcendental_Osin(V_x))) = c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))) # label(fact_cos__diff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 578 (all V_b_2 all V_a_2 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_2,V_b_2) <-> V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))) # label(fact_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 579 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 580 (all V_w_2 all V_b_2 all V_a_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_w_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_w_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_w_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_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_w_2)))))) # label(fact_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 581 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 582 (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,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]. 1.47/1.70 583 (all V_y c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_arctan__ubound) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 584 (all V_x c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi))) # label(fact_cos__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 585 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> (exists B_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) & c_Transcendental_Osin(B_x) = V_y & (all B_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) & V_y = c_Transcendental_Osin(B_y) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),B_y) -> B_x = B_y)) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),B_x)))))) # label(fact_sin__total) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 586 (all V_z all V_w all T_a (class_Int_Onumber__ring(T_a) -> 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) = 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))) # label(fact_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 587 (all V_v all V_u all T_b (class_Int_Onumber(T_b) & class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_u),c_Int_Onumber__class_Onumber__of(T_b,V_v)) -> c_Orderings_Oord__class_Omin(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_u),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Int_Onumber__class_Onumber__of(T_b,V_u)) & (-c_Orderings_Oord__class_Oless__eq(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_u),c_Int_Onumber__class_Onumber__of(T_b,V_v)) -> c_Int_Onumber__class_Onumber__of(T_b,V_v) = c_Orderings_Oord__class_Omin(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_u),c_Int_Onumber__class_Onumber__of(T_b,V_v))))) # label(fact_min__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 588 (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]. 1.47/1.70 589 (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]. 1.47/1.70 590 (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) <-> c_Groups_Oone__class_Oone(tc_Int_Oint) = V_m_2 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 591 (all V_a_2 all V_b_2 all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_b_2 -> (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]. 1.47/1.70 592 (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]. 1.47/1.70 593 (all V_l all V_k c_Int_OBit0(V_l) != c_Int_OBit1(V_k)) # label(fact_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 594 (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]. 1.47/1.70 595 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_neg__mod__conj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 596 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) # label(fact_minus__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 597 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> V_a = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)),V_a))) # label(fact_mult__numeral__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 598 (all V_n c_Orderings_Oord__class_Omin(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_min__0R) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 599 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 600 (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,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 601 (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]. 1.47/1.70 602 (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]. 1.47/1.70 603 (all V_w all T_a (class_Int_Onumber__ring(T_a) & class_Int_Oring__char__0(T_a) -> -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))))) # label(fact_iszero__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 604 (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]. 1.47/1.70 605 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 606 (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_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 607 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a) <-> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))))) # label(fact_eq__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.70 608 (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]. 1.47/1.70 609 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 610 (all V_n_2 all V_m_2 all V_k_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) <-> V_n_2 = V_m_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 611 (all V_y_2 all V_x_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_z_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]. 1.47/1.71 612 (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]. 1.47/1.71 613 (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]. 1.47/1.71 614 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 615 (all V_c all V_b all V_v all T_b (class_Rings_Oring(T_b) & class_Int_Onumber(T_b) -> 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)) = 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)))) # label(fact_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 616 (all V_z_2 all V_x_2 all V_y_2 all V_w_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2)) <-> V_w_2 = V_x_2 | V_z_2 = V_y_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 617 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b))) # label(fact_minus__unique) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 618 (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]. 1.47/1.71 619 (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]. 1.47/1.71 620 (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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_v_H)),V_k) = 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_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)))) # label(fact_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 621 (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]. 1.47/1.71 622 (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,V_x,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_Transcendental_Ocos(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)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_cos__double__less__one) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 623 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(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_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 624 (all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (class_Groups_Ominus(T_a) -> c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) = hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 625 (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]. 1.47/1.71 626 (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]. 1.47/1.71 627 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 628 (all V_x (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(V_x) -> (c_Transcendental_Ocos(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)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Rings_Oinverse__class_Odivide(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))),c_Transcendental_Otan(V_x)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Transcendental_Otan(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = c_Transcendental_Otan(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))))) # label(fact_tan__double) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 629 (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]. 1.47/1.71 630 (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]. 1.47/1.71 631 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_y != V_x))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 632 (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) -> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a)))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 633 (all V_n all V_i all V_m c_Orderings_Oord__class_Omin(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,V_m,V_n),V_i)) # label(fact_min__diff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 634 (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]. 1.47/1.71 635 (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]. 1.47/1.71 636 (all V_z_2 all T_a (class_Rings_Osemiring__1(T_a) -> (c_Int_Oiszero(T_a,V_z_2) <-> V_z_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_iszero__def) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 637 (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]. 1.47/1.71 638 (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]. 1.47/1.71 639 (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]. 1.47/1.71 640 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 641 (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]. 1.47/1.71 642 (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]. 1.47/1.71 643 (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]. 1.47/1.71 644 (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]. 1.47/1.71 645 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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),c_Transcendental_Ocos(V_x))))) # label(fact_cos__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 646 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 647 (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_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)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)))) # label(fact_number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 648 (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,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_x)))) # label(fact_minus1__divide) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 649 (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]. 1.47/1.71 650 (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]. 1.47/1.71 651 (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]. 1.47/1.71 652 (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]. 1.47/1.71 653 (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]. 1.47/1.71 654 (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]. 1.47/1.71 655 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> V_a = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 656 (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]. 1.47/1.71 657 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 658 (all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> c_Groups_Ozero__class_Ozero(T_a) = V_a_2))) # label(fact_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 659 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_c,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = c_Divides_Odiv__class_Omod(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_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 660 (all V_a all T_a (class_Groups_Omonoid__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__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 661 (all V_y_2 all 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)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)))) # label(fact_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 662 (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]. 1.47/1.71 663 (all V_z V_z = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_zmult__1__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 664 (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]. 1.47/1.71 665 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 666 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2)))) # label(fact_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 667 (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]. 1.47/1.71 668 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_b = V_a -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 669 (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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_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_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 670 (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]. 1.47/1.71 671 (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]. 1.47/1.71 672 (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]. 1.47/1.71 673 (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]. 1.47/1.71 674 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Orderings_Oord__class_Omin(T_a,V_x,V_y) = V_y))) # label(fact_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 675 (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_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))) # label(fact_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 676 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),c_Transcendental_Osin(V_x))) # label(fact_sin__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 677 (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_a_2 = V_b_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 678 (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]. 1.47/1.71 679 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b))) # label(fact_pos__mod__bound) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 680 (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]. 1.47/1.71 681 (all V_y all V_x c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y))) = c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))) # label(fact_sin__diff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 682 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = c_Orderings_Oord__class_Omin(T_a,V_x,V_y)))) # label(fact_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 683 (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]. 1.47/1.71 684 (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,V_n_2,V_m_2) <-> V_n_2 != V_m_2)) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 685 (all V_a all T_a (class_Rings_Ocomm__semiring__1(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_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 686 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-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]. 1.47/1.71 687 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 688 (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]. 1.47/1.71 689 (all V_n_2 all V_k_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_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_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)))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 690 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (-c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 691 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 692 (all V_y all V_x c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y))) = c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y))) # label(fact_sin__add) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 693 (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),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 694 (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]. 1.47/1.71 695 (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]. 1.47/1.71 696 (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]. 1.47/1.71 697 (all V_d_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,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_d_2) <-> V_d_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)))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 698 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x))))) # label(fact_compl__mono) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 699 (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]. 1.47/1.71 700 (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_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),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]. 1.47/1.71 701 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_x = V_y | c_Orderings_Oord__class_Oless(T_a,V_y,V_x))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 702 (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]. 1.47/1.71 703 (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]. 1.47/1.71 704 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OMin) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin))) # label(fact_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 705 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 706 (all V_a all V_x all V_b all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b),V_x)))) # label(fact_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 707 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_pos__mod__conj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 708 (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]. 1.47/1.71 709 (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]. 1.47/1.71 710 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = 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)))) # label(fact_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 711 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> c_Transcendental_Oarctan(c_Transcendental_Otan(V_x)) = V_x))) # label(fact_arctan__tan) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 712 (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]. 1.47/1.71 713 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 714 (all V_b all V_a all T_a (class_Rings_Oordered__ring(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,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_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 715 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_c_2 != V_d_2 & V_a_2 != V_b_2 <-> c_Groups_Oplus__class_Oplus(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_d_2)) != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 716 (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]. 1.47/1.71 717 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c))) # label(fact_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 718 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) | V_z_2 = V_w_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 719 (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]. 1.47/1.71 720 (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]. 1.47/1.71 721 (all V_b_2 all V_a_2 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_2,V_b_2) <-> V_b_2 = V_a_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 722 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 723 (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]. 1.47/1.71 724 (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]. 1.47/1.71 725 (all V_w all V_v c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(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_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))) # label(fact_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 726 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> 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)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 727 (all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 728 (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__eq(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,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(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,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))))) # label(fact_le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 729 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> V_a = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 730 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_x,V_y) = c_Orderings_Oord__class_Omin(T_a,V_y,V_x))) # label(fact_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 731 (all V_l all V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 732 (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]. 1.47/1.71 733 (all V_w_2 all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(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_w_2))) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_2)) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_2)))) & (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 734 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin))) # label(fact_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 735 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) # label(fact_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 736 (all V_x all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Opi),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x)))))) # label(fact_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 737 (all V_n all V_x c_Transcendental_Otan(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n),c_Transcendental_Opi))) = c_Transcendental_Otan(V_x)) # label(fact_tan__periodic__n) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 738 (all V_a_2 all V_w_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__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_2)))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) -> (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_2)),V_b_2)))))) # label(fact_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 739 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 740 (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]. 1.47/1.71 741 (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]. 1.47/1.71 742 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 743 (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]. 1.47/1.71 744 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 745 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 746 (all V_a_2 all V_w_2 all V_b_2 all T_a (class_Int_Onumber(T_a) & class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_a_2 <-> (c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_2) != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))))) # label(fact_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 747 (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]. 1.47/1.71 748 (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_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 749 (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]. 1.47/1.71 750 (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_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x)))) # label(fact_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 751 (all V_l_2 all V_k_2 ((exists B_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) = V_l_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 752 (all T_2 all T_1 (class_Groups_Ominus(T_1) -> class_Groups_Ominus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ominus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 753 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 754 (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]. 1.47/1.71 755 (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]. 1.47/1.71 756 (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]. 1.47/1.71 757 (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]. 1.47/1.71 758 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 759 (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]. 1.47/1.71 760 (all V_x all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Opi),V_y) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x)))))) # label(fact_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 761 (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,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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),c_Transcendental_Osin(V_x))))) # label(fact_sin__gt__zero2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 762 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 763 (all V_c_2 all V_b_2 all V_w_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_w_2),V_c_2)) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)) <-> c_Int_Onumber__class_Onumber__of(T_a,V_w_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]. 1.47/1.71 764 (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_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = V_b_2))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 765 (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]. 1.47/1.71 766 (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]. 1.47/1.71 767 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 768 (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]. 1.47/1.71 769 (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]. 1.47/1.71 770 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 771 (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]. 1.47/1.71 772 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a) <-> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))))) # label(fact_eq__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 773 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 774 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 775 (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]. 1.47/1.71 776 (all V_l all V_k c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l))) # label(fact_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 777 (all V_x_2 all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (c_Groups_Oone__class_Oone(T_a) = c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2) <-> 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)))) # label(fact_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 778 (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]. 1.47/1.71 779 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 780 (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]. 1.47/1.71 781 (all V_x all V_z all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_y != 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_y) = c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))) # label(fact_add__num__frac) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 782 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != V_n)) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 783 (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]. 1.47/1.71 784 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c))) # label(fact_mod__diff__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 785 (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_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))) # label(fact_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 786 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Omin(T_a,V_x_2,V_y_2) = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)))) # label(fact_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 787 (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]. 1.47/1.71 788 (all V_n_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> c_Groups_Oone__class_Oone(tc_Nat_Onat) = V_n_2 & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 789 (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(tc_Int_Oint,V_x_2,V_y_2) <-> 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))))) # label(fact_less__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 790 (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_Groups_Otimes__class_Otimes(T_a,V_a_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),V_a_2))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 791 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a))) # label(fact_diff__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 792 (all V_y_2 all V_x_2 all T_a (class_Int_Oring__char__0(T_a) & class_Int_Onumber__ring(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_y_2) = c_Int_Onumber__class_Onumber__of(T_a,V_x_2) <-> V_y_2 = V_x_2))) # label(fact_eq__number__of) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 793 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> c_Transcendental_Otan(V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Osin(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)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Ocos(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)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_tan__half) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 794 (all V_w_2 all V_v_2 all T_a (class_Int_Onumber(T_a) & class_Orderings_Olinorder(T_a) -> (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_w_2)) <-> -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2))))) # label(fact_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 795 (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]. 1.47/1.71 796 (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_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_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))) # label(fact_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 797 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> V_a = c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 798 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 799 (all V_d_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> (exists B_q V_m_2 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_d_2,B_q)))) # label(fact_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 800 (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_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 801 (all V_b_H all V_b 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,V_b_H)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.71 802 (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,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_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_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 803 (all V_y c_Transcendental_Otan(c_Transcendental_Oarctan(V_y)) = V_y) # label(fact_tan__arctan) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 804 (all V_x_2 all V_y_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) -> (V_x_2 = V_y_2 <-> -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2))))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 805 (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]. 1.47/1.72 806 (all V_k c_Int_OBit0(V_k) != c_Int_OMin) # label(fact_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 807 (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]. 1.47/1.72 808 (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_a_2,V_b_2) <-> 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))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 809 (all V_x_2 (c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) <-> c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_neq__one__mod__two) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 810 (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]. 1.47/1.72 811 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_a -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)) & (c_Groups_Ozero__class_Ozero(T_a) = V_a -> c_Groups_Ozero__class_Ozero(T_a) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)))) # label(fact_divide__self__if) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 812 (all V_x all T_a (class_Int_Onumber__ring(T_a) & class_Fields_Ofield__inverse__zero(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]. 1.47/1.72 813 (all V_z_2 all V_y_2 all 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_z_2)) <-> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_z_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))) # label(fact_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 814 (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),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)))) # label(fact_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 815 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> 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]. 1.47/1.72 816 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 817 (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]. 1.47/1.72 818 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 819 (all V_y_2 all V_x_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)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 820 (all V_l all V_k (c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k),V_l) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 821 (all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) # label(fact_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 822 (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]. 1.47/1.72 823 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b_H),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c))))) # label(fact_mod__mult__cong) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 824 (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]. 1.47/1.72 825 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 826 (all V_c all V_b all V_v 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,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]. 1.47/1.72 827 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Int_Oint) = V_m_2 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) = V_n_2 & c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) = 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))) # label(fact_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 828 (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]. 1.47/1.72 829 (all V_x_2 all V_y_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_y_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_x_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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_Transcendental_Otan(V_y_2),c_Transcendental_Otan(V_x_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,V_x_2))))))) # label(fact_tan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 830 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 831 (all V_y_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))))) # label(fact_eq__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 832 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(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__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 833 (all V_y_2 all V_x_2 all V_z_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_z_2,V_x_2) & c_Orderings_Oord__class_Oless(T_a,V_z_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_z_2,c_Orderings_Oord__class_Omin(T_a,V_x_2,V_y_2))))) # label(fact_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 834 (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]. 1.47/1.72 835 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_Omin(T_a,V_x,V_y),V_x))) # label(fact_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 836 (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]. 1.47/1.72 837 (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]. 1.47/1.72 838 (all V_y_2 all V_x_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_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_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_z_2))))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 839 (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]. 1.47/1.72 840 (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]. 1.47/1.72 841 (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]. 1.47/1.72 842 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_b),V_c)) # label(fact_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 843 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarcsin(V_y)) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarcsin(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) & c_Transcendental_Osin(c_Transcendental_Oarcsin(V_y)) = V_y))) # label(fact_arcsin) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 844 (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]. 1.47/1.72 845 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c))) # label(fact_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 846 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 847 (all V_x c_Transcendental_Ocos(V_x) = c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) # label(fact_cos__sin__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 848 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 849 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2)))) # label(fact_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 850 (all V_d all V_c all V_b all V_a all V_r all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) != V_r -> (V_c != V_d & V_b = V_a -> c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d)) != c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 851 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__diff__cong) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 852 (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,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 853 (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_Ominus__class_Ominus(tc_Int_Oint,V_v,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_number__of__diff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 854 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Opi),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_sin__less__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 855 (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]. 1.47/1.72 856 (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]. 1.47/1.72 857 (all V_l_2 all V_k_2 (c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) <-> V_l_2 = V_k_2)) # label(fact_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 858 (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]. 1.47/1.72 859 (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]. 1.47/1.72 860 (all T_a (class_Int_Onumber__ring(T_a) -> -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)))) # label(fact_nonzero__number__of__Min) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 861 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 862 (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]. 1.47/1.72 863 (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]. 1.47/1.72 864 (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]. 1.47/1.72 865 (all V_l_2 (c_Int_OMin = V_l_2 <-> c_Int_OBit1(V_l_2) = c_Int_OMin)) # label(fact_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 866 (all V_w all V_z c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 867 (all V_x c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) = c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi))) # label(fact_sin__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 868 (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]. 1.47/1.72 869 (all V_a all T_a (class_Rings_Omult__zero(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__zero__right) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 870 (all V_m_2 all 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)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 871 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 872 (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]. 1.47/1.72 873 (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]. 1.47/1.72 874 (all V_a all V_r c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,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))) # label(fact_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 875 (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]. 1.47/1.72 876 (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]. 1.47/1.72 877 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 878 (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,V_x,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),c_Transcendental_Osin(V_x))))) # label(fact_sin__gt__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 879 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless(T_a,V_a,V_c))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 880 (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]. 1.47/1.72 881 (all V_x c_Transcendental_Otan(V_x) = c_Transcendental_Otan(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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))),c_Transcendental_Opi)))) # label(fact_tan__periodic) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 882 (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]. 1.47/1.72 883 (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]. 1.47/1.72 884 (all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin))) # label(fact_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 885 (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]. 1.47/1.72 886 (all V_d all V_b all V_c all V_a all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Oord__class_Omin(T_a,V_a,V_b),c_Orderings_Oord__class_Omin(T_a,V_c,V_d)))))) # label(fact_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 887 (all V_y (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarcsin(V_y)) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarcsin(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_arcsin__bounded) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 888 (all V_y_2 all V_x_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_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_z_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z_2,V_y_2))))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 889 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_x,c_Orderings_Oord__class_Omin(T_a,V_x,V_y)) = c_Orderings_Oord__class_Omin(T_a,V_x,V_y))) # label(fact_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 890 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)),V_b))) # label(fact_mod__mult__self1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 891 (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]. 1.47/1.72 892 (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_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 893 (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]. 1.47/1.72 894 (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]. 1.47/1.72 895 (all V_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,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_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(V_y)))) # label(fact_arctan__bounded) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 896 (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]. 1.47/1.72 897 (all V_q all V_r all V_b all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,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__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 898 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_arith__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 899 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 900 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_b != V_a -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 901 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_sin__le__one) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 902 (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]. 1.47/1.72 903 (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_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)))) # label(fact_arctan__monotone) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 904 (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]. 1.47/1.72 905 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 906 (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]. 1.47/1.72 907 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__zero) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 908 (all V_y_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Int_Oiszero(T_a,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_y_2)))) <-> c_Int_Onumber__class_Onumber__of(T_a,V_y_2) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 909 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2))) # label(fact_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 910 (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]. 1.47/1.72 911 (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]. 1.47/1.72 912 (all V_l c_Int_OMin != c_Int_OBit0(V_l)) # label(fact_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 913 (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]. 1.47/1.72 914 (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]. 1.47/1.72 915 (all V_x c_Transcendental_Osin(V_x) = c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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))),c_Transcendental_Opi)))) # label(fact_sin__periodic) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 916 (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]. 1.47/1.72 917 (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]. 1.47/1.72 918 (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]. 1.47/1.72 919 (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_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(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_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]. 1.47/1.72 920 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 921 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (V_y_2 = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2))))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 922 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 923 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> V_a = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a))) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption]. 1.47/1.72 924 (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]. 1.47/1.72 925 (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]. 1.47/1.72 926 (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]. 1.47/1.72 927 (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]. 1.47/1.72 928 (all V_c all V_a all V_b all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Omin(T_a,V_b,c_Orderings_Oord__class_Omin(T_a,V_a,V_c)) = c_Orderings_Oord__class_Omin(T_a,V_a,c_Orderings_Oord__class_Omin(T_a,V_b,V_c)))) # label(fact_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 1.47/1.75 929 -(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_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2)) # label(conj_2) # label(negated_conjecture) # label(non_clause). [assumption]. 1.47/1.75 1.47/1.75 ============================== end of process non-clausal formulas === 1.47/1.75 1.47/1.75 ============================== PROCESS INITIAL CLAUSES =============== 1.47/1.75 1.47/1.75 ============================== PREDICATE ELIMINATION ================= 1.47/1.75 930 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),B) = c_Divides_Odiv__class_Omod(A,C,B) # label(fact_mod__add__self1) # label(axiom). [clausify(31)]. 1.47/1.75 931 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A). [resolve(930,a,931,a)]. 1.47/1.75 932 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_mod__by__0) # label(axiom). [clausify(102)]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(932,a,931,a)]. 1.47/1.75 933 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A). [resolve(933,a,930,a)]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(933,a,932,a)]. 1.47/1.75 934 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_zmod__simps_I1_J) # label(axiom). [clausify(147)]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),B). [resolve(934,a,931,a)]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). [resolve(934,a,933,a)]. 1.47/1.75 935 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Otimes__class_Otimes(A,C,D)),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mult__self2) # label(axiom). [clausify(248)]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(935,a,931,a)]. 1.47/1.75 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(935,a,933,a)]. 1.47/1.75 936 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self1__is__0) # label(axiom). [clausify(320)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(936,a,931,a)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(936,a,933,a)]. 1.47/1.77 937 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Oone__class_Oone(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__by__1) # label(axiom). [clausify(350)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(937,a,931,a)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(937,a,933,a)]. 1.47/1.77 938 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),D) # label(fact_mod__mult__right__eq) # label(axiom). [clausify(364)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),C). [resolve(938,a,933,a)]. 1.47/1.77 939 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__self) # label(axiom). [clausify(395)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(939,a,931,a)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(939,a,933,a)]. 1.47/1.77 940 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D) # label(fact_zmod__simps_I2_J) # label(axiom). [clausify(422)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C). [resolve(940,a,931,a)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C). [resolve(940,a,933,a)]. 1.47/1.77 941 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mod__add__left__eq) # label(axiom). [clausify(453)]. 1.47/1.77 942 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__add__self2) # label(axiom). [clausify(474)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(942,a,931,a)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(942,a,933,a)]. 1.47/1.77 943 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,E),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,D,F),C) # label(fact_mod__add__cong) # label(axiom). [clausify(507)]. 1.47/1.77 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,E),B). [resolve(943,a,931,a)]. 1.57/1.80 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E),B). [resolve(943,a,933,a)]. 1.57/1.80 944 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mod__add__eq) # label(axiom). [clausify(529)]. 1.57/1.80 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),B). [resolve(944,a,931,a)]. 1.57/1.80 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). [resolve(944,a,933,a)]. 1.57/1.80 945 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mod__trivial) # label(axiom). [clausify(530)]. 1.57/1.80 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(945,a,931,a)]. 1.57/1.80 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(945,a,933,a)]. 1.57/1.80 946 -class_Divides_Osemiring__div(A) | c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mod__mult__mult2) # label(axiom). [clausify(623)]. 1.57/1.80 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(946,a,931,a)]. 1.57/1.80 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(946,a,933,a)]. 1.57/1.80 947 -class_Divides_Osemiring__div(A) | c_Groups_Otimes__class_Otimes(A,B,c_Divides_Odiv__class_Omod(A,C,D)) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mod__mult__mult1) # label(axiom). [clausify(659)]. 1.57/1.80 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(947,a,931,a)]. 1.57/1.80 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)). [resolve(947,a,933,a)]. 1.57/1.80 948 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_mod__mult__eq) # label(axiom). [clausify(691)]. 1.57/1.80 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),B). [resolve(948,a,931,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),B). [resolve(948,a,933,a)]. 1.60/1.82 949 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__0) # label(axiom). [clausify(705)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(949,a,931,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(949,a,933,a)]. 1.60/1.82 950 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D) # label(fact_mod__add__right__eq) # label(axiom). [clausify(713)]. 1.60/1.82 951 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_zmod__simps_I4_J) # label(axiom). [clausify(717)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C),B). [resolve(951,a,931,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),B). [resolve(951,a,933,a)]. 1.60/1.82 952 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) # label(axiom). [assumption]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),A) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(952,a,930,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(952,a,932,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(952,a,934,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(952,a,935,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(952,a,936,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(952,a,937,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),C). [resolve(952,a,938,a)]. 1.60/1.82 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(952,a,939,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),C). [resolve(952,a,940,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(952,a,942,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,D,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,E,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,D),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,E),B). [resolve(952,a,943,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(952,a,944,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(952,a,945,a)]. 1.62/1.84 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(952,a,946,a)]. 1.62/1.84 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,C)) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(952,a,947,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(952,a,948,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(952,a,949,a)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(952,a,951,a)]. 1.62/1.84 953 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,E),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,D,F),C) # label(fact_mod__mult__cong) # label(axiom). [clausify(823)]. 1.62/1.84 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,E),B). [resolve(953,a,931,a)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,E),B). [resolve(953,a,933,a)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,D,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,E,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,D),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,E),B). [resolve(953,a,952,a)]. 1.70/1.96 954 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_mod__mult__left__eq) # label(axiom). [clausify(845)]. 1.70/1.96 955 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self2__is__0) # label(axiom). [clausify(877)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(955,a,931,a)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(955,a,933,a)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(955,a,952,a)]. 1.70/1.96 956 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Otimes__class_Otimes(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,B,D) # label(fact_mod__mult__self1) # label(axiom). [clausify(890)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C). [resolve(956,a,931,a)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C). [resolve(956,a,933,a)]. 1.70/1.96 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(956,a,952,a)]. 1.70/1.96 957 class_Int_Onumber__ring(tc_Int_Oint) # label(arity_Int__Oint__Int_Onumber__ring) # label(axiom). [assumption]. 1.70/1.96 958 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,c_Int_OPls) = c_Groups_Ozero__class_Ozero(A) # label(fact_number__of__Pls) # label(axiom). [clausify(2)]. 1.70/1.96 959 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,B) # label(fact_le__special_I1_J) # label(axiom). [clausify(40)]. 1.70/1.96 960 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,B) # label(fact_le__special_I1_J) # label(axiom). [clausify(40)]. 1.70/1.96 961 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)) # label(fact_arith__simps_I32_J) # label(axiom). [clausify(61)]. 1.70/1.96 962 -class_Int_Onumber__ring(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin),B) # label(fact_mult__minus1) # label(axiom). [clausify(66)]. 1.70/1.96 963 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B))) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_iszero__number__of__Bit0) # label(axiom). [clausify(74)]. 1.70/1.96 964 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B))) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_iszero__number__of__Bit0) # label(axiom). [clausify(74)]. 1.70/1.96 965 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)) # label(fact_number__of__mult) # label(axiom). [clausify(87)]. 1.70/1.96 966 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)),D) = c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,C),D)) # label(fact_add__number__of__left) # label(axiom). [clausify(89)]. 1.70/1.96 967 -class_Int_Onumber__ring(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) # label(fact_not__iszero__Numeral1) # label(axiom). [clausify(148)]. 1.70/1.96 968 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Int_Onumber__class_Onumber__of(A,C) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C)))) # label(fact_eq__number__of__eq) # label(axiom). [clausify(178)]. 1.70/1.96 969 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Int_Onumber__class_Onumber__of(A,C) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C)))) # label(fact_eq__number__of__eq) # label(axiom). [clausify(178)]. 1.70/1.96 970 -class_Int_Onumber__ring(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) # label(fact_diff__special_I1_J) # label(axiom). [clausify(181)]. 1.70/1.96 971 -class_Int_Onumber__ring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) # label(fact_arith__simps_I30_J) # label(axiom). [clausify(182)]. 1.70/1.96 972 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_less__special_I1_J) # label(axiom). [clausify(208)]. 1.70/1.96 973 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_less__special_I1_J) # label(axiom). [clausify(208)]. 1.70/1.96 974 -class_Int_Onumber__ring(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin)) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_divide__minus1) # label(axiom). [clausify(215)]. 1.70/1.96 975 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(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(222)]. 1.70/1.96 976 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(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(222)]. 1.70/1.96 977 -class_Int_Onumber__ring(A) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls)) # label(fact_iszero__Numeral0) # label(axiom). [clausify(238)]. 1.70/1.96 978 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,C),D)) = c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)),D) # label(fact_add__number__of__diff1) # label(axiom). [clausify(251)]. 1.70/1.96 979 -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__numeral__1) # label(axiom). [clausify(256)]. 1.70/1.96 980 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(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(295)]. 1.70/1.96 981 -class_Rings_Olinordered__idom(A) | -class_Int_Onumber__ring(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(295)]. 1.70/1.96 982 -class_Int_Onumber__ring(A) | c_Groups_Oone__class_Oone(A) = c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)) # label(fact_numeral__1__eq__1) # label(axiom). [clausify(304)]. 1.70/1.96 983 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C))),D) = c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ominus__class_Ominus(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_add__number__of__diff2) # label(axiom). [clausify(310)]. 1.70/1.96 984 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__special_I2_J) # label(axiom). [clausify(317)]. 1.70/1.96 985 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_le__special_I2_J) # label(axiom). [clausify(317)]. 1.70/1.96 986 -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_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) # label(fact_le__special_I4_J) # label(axiom). [clausify(379)]. 1.70/1.96 987 -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_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) # label(fact_le__special_I4_J) # label(axiom). [clausify(379)]. 1.70/1.96 988 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,c_Int_OPls) = c_Groups_Ozero__class_Ozero(A) # label(fact_semiring__norm_I112_J) # label(axiom). [clausify(391)]. 1.70/1.96 989 -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(400)]. 1.70/1.96 990 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) # label(fact_less__special_I2_J) # label(axiom). [clausify(406)]. 1.70/1.96 991 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) # label(fact_less__special_I2_J) # label(axiom). [clausify(406)]. 1.70/1.96 992 -class_Int_Onumber__ring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) # label(fact_number__of__minus) # label(axiom). [clausify(415)]. 1.70/1.96 993 -class_Int_Onumber__ring(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin)) # label(fact_mult__minus1__right) # label(axiom). [clausify(429)]. 1.70/1.96 994 -class_Int_Onumber__ring(A) | c_Groups_Oone__class_Oone(A) = c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)) # label(fact_semiring__norm_I110_J) # label(axiom). [clausify(468)]. 1.70/1.96 995 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)) # label(fact_add__number__of__eq) # label(axiom). [clausify(470)]. 1.70/1.96 996 -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(485)]. 1.70/1.96 997 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) = B # label(fact_mult__numeral__1__right) # label(axiom). [clausify(496)]. 1.70/1.96 998 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_mult__2__right) # label(axiom). [clausify(526)]. 1.70/1.96 999 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(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(542)]. 1.70/1.96 1000 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(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(542)]. 1.70/1.96 1001 -class_Int_Onumber__ring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = c_Int_Onumber__class_Onumber__of(A,c_Int_OMin) # label(fact_number__of__Min) # label(axiom). [clausify(545)]. 1.70/1.96 1002 -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(565)]. 1.70/1.96 1003 -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(565)]. 1.70/1.96 1004 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B)) # label(fact_add__special_I2_J) # label(axiom). [clausify(570)]. 1.70/1.96 1005 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B)),C) = c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)),C) # label(fact_minus__number__of__mult) # label(axiom). [clausify(586)]. 1.70/1.96 1006 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)),B) = B # label(fact_mult__numeral__1) # label(axiom). [clausify(597)]. 1.70/1.96 1007 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B) # label(fact_mult__2) # label(axiom). [clausify(602)]. 1.70/1.96 1008 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(B))) # label(fact_iszero__number__of__Bit1) # label(axiom). [clausify(603)]. 1.70/1.96 1009 -class_Int_Onumber__ring(A) | c_Groups_Oone__class_Oone(A) != c_Int_Onumber__class_Onumber__of(A,B) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) # label(fact_eq__special_I4_J) # label(axiom). [clausify(607)]. 1.70/1.96 1010 -class_Int_Onumber__ring(A) | c_Groups_Oone__class_Oone(A) = c_Int_Onumber__class_Onumber__of(A,B) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) # label(fact_eq__special_I4_J) # label(axiom). [clausify(607)]. 1.70/1.96 1011 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B)) # label(fact_number__of__Bit0) # label(axiom). [clausify(625)]. 1.70/1.96 1012 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(B)) # label(fact_number__of__Bit1) # label(axiom). [clausify(647)]. 1.70/1.96 1013 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin),B) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B)) # label(fact_minus1__divide) # label(axiom). [clausify(648)]. 1.70/1.96 1014 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)) # label(fact_number__of__add) # label(axiom). [clausify(673)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -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)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A). [resolve(957,a,959,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | 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)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A). [resolve(957,a,960,a)]. 1.70/1.96 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(957,a,961,a)]. 1.70/1.96 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),A). [resolve(957,a,962,a)]. 1.70/1.96 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A))) | c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(957,a,963,b)]. 1.70/1.96 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A))) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). [resolve(957,a,964,b)]. 1.70/1.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),C)). [resolve(957,a,966,a)]. 1.70/1.96 Derived: -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))). [resolve(957,a,967,a)]. 1.70/1.96 Derived: c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) | c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))). [resolve(957,a,968,a)]. 1.70/1.96 Derived: c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))). [resolve(957,a,969,a)]. 1.70/1.96 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))). [resolve(957,a,970,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A) | 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)). [resolve(957,a,972,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A) | -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)). [resolve(957,a,973,a)]. 1.70/1.96 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A). [resolve(957,a,974,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(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(957,a,975,b)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(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(957,a,976,b)]. 1.70/1.96 Derived: c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)). [resolve(957,a,977,a)]. 1.70/1.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),C)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),C). [resolve(957,a,978,a)]. 1.70/1.96 Derived: -class_Fields_Ofield(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))) = A. [resolve(957,a,979,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(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(957,a,980,b)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(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(957,a,981,b)]. 1.70/1.96 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)). [resolve(957,a,982,a)]. 1.70/1.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))). [resolve(957,a,983,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | 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)). [resolve(957,a,984,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | -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)). [resolve(957,a,985,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -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)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(957,a,986,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | 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)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(957,a,987,a)]. 1.70/1.96 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(957,a,989,b)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -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)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(957,a,990,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | 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)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(957,a,991,a)]. 1.70/1.96 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)). [resolve(957,a,993,a)]. 1.70/1.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). [resolve(957,a,995,a)]. 1.70/1.96 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))) = A. [resolve(957,a,997,a)]. 1.70/1.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(957,a,998,a)]. 1.70/1.96 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)). [resolve(957,a,999,a)]. 1.70/1.97 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)). [resolve(957,a,1000,a)]. 1.70/1.97 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin). [resolve(957,a,1001,a)]. 1.70/1.97 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(957,a,1002,a)]. 1.70/1.97 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(957,a,1003,a)]. 1.70/1.97 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A)). [resolve(957,a,1004,a)]. 1.70/1.97 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)),B) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B). [resolve(957,a,1005,a)]. 1.70/1.97 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),A) = A. [resolve(957,a,1006,a)]. 1.70/1.97 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),A). [resolve(957,a,1007,a)]. 1.70/1.97 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(A))). [resolve(957,a,1008,a)]. 1.70/1.97 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) | c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))). [resolve(957,a,1009,a)]. 1.70/1.97 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))). [resolve(957,a,1010,a)]. 1.70/1.97 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A)). [resolve(957,a,1011,a)]. 1.70/1.97 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(A)). [resolve(957,a,1012,a)]. 1.70/1.97 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)). [resolve(957,a,1013,b)]. 1.77/1.99 1015 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(A,B)) = c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B)) # label(fact_double__number__of__Bit0) # label(axiom). [clausify(710)]. 1.77/1.99 Derived: c_Groups_Otimes__class_Otimes(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)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A)). [resolve(1015,a,957,a)]. 1.77/1.99 1016 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls)) = B # label(fact_add__numeral__0__right) # label(axiom). [clausify(719)]. 1.77/1.99 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)) = A. [resolve(1016,a,957,a)]. 1.77/1.99 1017 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls))) # label(fact_add__special_I3_J) # label(axiom). [clausify(723)]. 1.77/1.99 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls))). [resolve(1017,a,957,a)]. 1.77/1.99 1018 -class_Int_Onumber__ring(A) | c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C))) # label(fact_diff__number__of__eq) # label(axiom). [clausify(732)]. 1.77/1.99 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))). [resolve(1018,a,957,a)]. 1.77/1.99 1019 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls),B) = B # label(fact_add__numeral__0) # label(axiom). [clausify(766)]. 1.77/1.99 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),A) = A. [resolve(1019,a,957,a)]. 1.77/1.99 1020 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) # label(fact_eq__special_I3_J) # label(axiom). [clausify(772)]. 1.77/1.99 Derived: c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))). [resolve(1020,a,957,a)]. 1.77/1.99 1021 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Groups_Ozero__class_Ozero(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) # label(fact_eq__special_I3_J) # label(axiom). [clausify(772)]. 1.77/1.99 Derived: c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))). [resolve(1021,a,957,a)]. 1.77/1.99 1022 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_less__number__of) # label(axiom). [clausify(789)]. 1.77/1.99 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | 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)). [resolve(1022,a,957,a)]. 1.77/2.00 1023 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_less__number__of) # label(axiom). [clausify(789)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -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)). [resolve(1023,a,957,a)]. 1.77/2.00 1024 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Int_Onumber__class_Onumber__of(A,C) | B = C # label(fact_eq__number__of) # label(axiom). [clausify(792)]. 1.77/2.00 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) | A = B. [resolve(1024,b,957,a)]. 1.77/2.00 1025 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Int_Onumber__class_Onumber__of(A,C) | B != C # label(fact_eq__number__of) # label(axiom). [clausify(792)]. 1.77/2.00 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) | A != B. [resolve(1025,b,957,a)]. 1.77/2.00 1026 -class_Int_Onumber__ring(A) | c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) # label(fact_diff__special_I2_J) # label(axiom). [clausify(796)]. 1.77/2.00 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))). [resolve(1026,a,957,a)]. 1.77/2.00 1027 -class_Int_Onumber__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(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_one__add__one__is__two) # label(axiom). [clausify(807)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))). [resolve(1027,a,957,a)]. 1.77/2.00 1028 -class_Int_Onumber__ring(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__Numeral0) # label(axiom). [clausify(812)]. 1.77/2.00 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1028,a,957,a)]. 1.77/2.00 1029 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption]. 1.77/2.00 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1029,a,958,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | -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)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A). [resolve(1029,a,959,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | 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)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,A). [resolve(1029,a,960,a)]. 1.77/2.00 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1029,a,961,a)]. 1.77/2.00 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),A). [resolve(1029,a,962,a)]. 1.77/2.00 Derived: -class_Int_Oring__char__0(tc_RealDef_Oreal) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(A))) | c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1029,a,963,b)]. 1.77/2.00 Derived: -class_Int_Oring__char__0(tc_RealDef_Oreal) | c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(A))) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). [resolve(1029,a,964,b)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)). [resolve(1029,a,966,a)]. 1.77/2.00 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls))). [resolve(1029,a,967,a)]. 1.77/2.00 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) | c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))). [resolve(1029,a,968,a)]. 1.77/2.00 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))). [resolve(1029,a,969,a)]. 1.77/2.00 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))). [resolve(1029,a,970,a)]. 1.77/2.00 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1029,a,971,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,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,A)). [resolve(1029,a,972,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,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,A)). [resolve(1029,a,973,a)]. 1.77/2.00 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A). [resolve(1029,a,974,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(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(1029,a,975,b)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(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(1029,a,976,b)]. 1.77/2.00 Derived: c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)). [resolve(1029,a,977,a)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),C). [resolve(1029,a,978,a)]. 1.77/2.00 Derived: -class_Fields_Ofield(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(1029,a,979,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(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(1029,a,980,b)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(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(1029,a,981,b)]. 1.77/2.00 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls)). [resolve(1029,a,982,a)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1029,a,983,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | 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)). [resolve(1029,a,984,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A) | -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)). [resolve(1029,a,985,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | -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)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1029,a,986,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | 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)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1029,a,987,a)]. 1.77/2.00 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1029,a,989,b)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | -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)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1029,a,990,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | 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)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1029,a,991,a)]. 1.77/2.00 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)). [resolve(1029,a,993,a)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). [resolve(1029,a,995,a)]. 1.77/2.00 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls))) = A. [resolve(1029,a,997,a)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(1029,a,998,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(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(1029,a,999,a)]. 1.77/2.00 Derived: -class_Rings_Olinordered__idom(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(1029,a,1000,a)]. 1.77/2.00 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin). [resolve(1029,a,1001,a)]. 1.77/2.00 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1029,a,1002,a)]. 1.77/2.00 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1029,a,1003,a)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A)). [resolve(1029,a,1004,a)]. 1.77/2.00 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B). [resolve(1029,a,1005,a)]. 1.77/2.00 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls)),A) = A. [resolve(1029,a,1006,a)]. 1.77/2.00 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = 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))),A). [resolve(1029,a,1007,a)]. 1.77/2.00 Derived: -class_Int_Oring__char__0(tc_RealDef_Oreal) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(A))). [resolve(1029,a,1008,a)]. 1.77/2.00 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) | c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))). [resolve(1029,a,1009,a)]. 1.77/2.01 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))). [resolve(1029,a,1010,a)]. 1.77/2.01 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(A)). [resolve(1029,a,1011,a)]. 1.77/2.01 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(A)). [resolve(1029,a,1012,a)]. 1.77/2.01 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)). [resolve(1029,a,1013,b)]. 1.77/2.01 Derived: c_Groups_Otimes__class_Otimes(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)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(A)). [resolve(1029,a,1015,a)]. 1.77/2.01 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)) = A. [resolve(1029,a,1016,a)]. 1.77/2.01 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls))). [resolve(1029,a,1017,a)]. 1.77/2.01 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))). [resolve(1029,a,1018,a)]. 1.77/2.01 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),A) = A. [resolve(1029,a,1019,a)]. 1.77/2.01 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))). [resolve(1029,a,1020,a)]. 1.77/2.01 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))). [resolve(1029,a,1021,a)]. 1.77/2.01 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | 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)). [resolve(1029,a,1022,a)]. 1.77/2.01 Derived: -class_Rings_Olinordered__idom(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -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)). [resolve(1029,a,1023,a)]. 1.77/2.01 Derived: -class_Int_Oring__char__0(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) | A = B. [resolve(1029,a,1024,b)]. 1.77/2.01 Derived: -class_Int_Oring__char__0(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) | A != B. [resolve(1029,a,1025,b)]. 1.77/2.01 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))). [resolve(1029,a,1026,a)]. 1.77/2.01 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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(1029,a,1027,a)]. 1.77/2.01 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1029,a,1028,a)]. 1.77/2.01 1030 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))) # label(fact_eq__special_I1_J) # label(axiom). [clausify(831)]. 1.77/2.01 Derived: c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))). [resolve(1030,a,957,a)]. 1.77/2.01 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))). [resolve(1030,a,1029,a)]. 1.77/2.01 1031 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Groups_Ozero__class_Ozero(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))) # label(fact_eq__special_I1_J) # label(axiom). [clausify(831)]. 1.77/2.01 Derived: c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))). [resolve(1031,a,957,a)]. 1.77/2.01 Derived: c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))). [resolve(1031,a,1029,a)]. 1.77/2.01 1032 -class_Int_Onumber__ring(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)),D) = c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D)) # label(fact_mult__number__of__left) # label(axiom). [clausify(839)]. 1.77/2.01 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)),C) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),C)). [resolve(1032,a,957,a)]. 1.77/2.01 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)),C) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),C)). [resolve(1032,a,1029,a)]. 1.77/2.02 1033 -class_Int_Onumber__ring(A) | c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C)) # label(fact_number__of__diff) # label(axiom). [clausify(853)]. 1.77/2.02 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)). [resolve(1033,a,957,a)]. 1.77/2.02 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)). [resolve(1033,a,1029,a)]. 1.77/2.02 1034 -class_Int_Onumber__ring(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin)) # label(fact_nonzero__number__of__Min) # label(axiom). [clausify(860)]. 1.77/2.02 Derived: -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)). [resolve(1034,a,957,a)]. 1.77/2.02 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)). [resolve(1034,a,1029,a)]. 1.77/2.02 1035 -class_Int_Onumber__ring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = c_Int_Onumber__class_Onumber__of(A,c_Int_OMin) # label(fact_arith__simps_I31_J) # label(axiom). [clausify(898)]. 1.77/2.02 1036 -class_Int_Onumber__ring(A) | -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))) | c_Groups_Oone__class_Oone(A) = c_Int_Onumber__class_Onumber__of(A,B) # label(fact_eq__special_I2_J) # label(axiom). [clausify(908)]. 1.77/2.02 Derived: -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))) | c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A). [resolve(1036,a,957,a)]. 1.77/2.02 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A). [resolve(1036,a,1029,a)]. 1.77/2.02 1037 -class_Int_Onumber__ring(A) | c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))) | c_Groups_Oone__class_Oone(A) != c_Int_Onumber__class_Onumber__of(A,B) # label(fact_eq__special_I2_J) # label(axiom). [clausify(908)]. 1.77/2.02 Derived: c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))) | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A). [resolve(1037,a,957,a)]. 1.77/2.02 Derived: c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)))) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A). [resolve(1037,a,1029,a)]. 1.77/2.02 1038 -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(916)]. 1.77/2.06 1039 -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(917)]. 1.77/2.06 Derived: -class_Rings_Olinordered__idom(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(1039,a,957,a)]. 1.77/2.06 Derived: -class_Rings_Olinordered__idom(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(1039,a,1029,a)]. 1.77/2.06 1040 -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(917)]. 1.77/2.06 Derived: -class_Rings_Olinordered__idom(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(1040,a,957,a)]. 1.77/2.06 Derived: -class_Rings_Olinordered__idom(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(1040,a,1029,a)]. 1.77/2.06 1041 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption]. 1.77/2.06 1042 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(3)]. 1.77/2.06 1043 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_linorder__neq__iff) # label(axiom). [clausify(39)]. 1.77/2.06 1044 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | B != C # label(fact_linorder__neq__iff) # label(axiom). [clausify(39)]. 1.77/2.06 1045 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | C = B # label(fact_linorder__neq__iff) # label(axiom). [clausify(39)]. 1.77/2.06 1046 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neqE) # label(axiom). [clausify(65)]. 1.77/2.06 1047 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_min__max_Ole__inf__iff) # label(axiom). [clausify(72)]. 1.77/2.06 1048 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_min__max_Ole__inf__iff) # label(axiom). [clausify(72)]. 1.77/2.06 1049 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_min__max_Ole__inf__iff) # label(axiom). [clausify(72)]. 1.77/2.06 1050 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_min__max_Ole__infE) # label(axiom). [clausify(73)]. 1.77/2.06 1051 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_min__max_Ole__infE) # label(axiom). [clausify(73)]. 1.77/2.06 1052 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) # label(fact_min__max_Oinf__greatest) # label(axiom). [clausify(79)]. 1.87/2.07 1053 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(107)]. 1.87/2.07 1054 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(107)]. 1.87/2.07 1055 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(A,B,D),C) # label(fact_min__max_Oless__infI1) # label(axiom). [clausify(126)]. 1.87/2.07 1056 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__leE) # label(axiom). [clausify(137)]. 1.87/2.07 1057 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,C) = c_Orderings_Oord__class_Omin(A,C,B) # label(fact_min__max_Oinf_Ocommute) # label(axiom). [clausify(139)]. 1.87/2.07 1058 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_leI) # label(axiom). [clausify(167)]. 1.87/2.07 1059 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_leD) # label(axiom). [clausify(171)]. 1.87/2.07 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1041,a,1042,a)]. 1.87/2.07 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(1041,a,1047,a)]. 1.87/2.07 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1041,a,1048,a)]. 1.87/2.07 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1041,a,1049,a)]. 1.87/2.07 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1041,a,1053,a)]. 1.87/2.07 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,C),B). [resolve(1041,a,1055,a)]. 1.87/2.07 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B) = c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,A). [resolve(1041,a,1057,a)]. 1.87/2.07 1060 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B = C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(185)]. 1.87/2.07 1061 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,C) | B != C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(185)]. 1.87/2.07 1062 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__linear) # label(axiom). [clausify(192)]. 1.87/2.07 1063 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,C),D) = c_Orderings_Oord__class_Omin(A,B,c_Orderings_Oord__class_Omin(A,C,D)) # label(fact_min__max_Oinf__assoc) # label(axiom). [clausify(217)]. 1.87/2.07 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),C) = c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)). [resolve(1063,a,1041,a)]. 1.87/2.07 1064 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__cases) # label(axiom). [clausify(242)]. 1.87/2.07 1065 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,B,c_Orderings_Oord__class_Omin(A,C,D)) # label(fact_min__max_Ole__infI) # label(axiom). [clausify(245)]. 1.87/2.07 1066 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | B = C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(283)]. 1.88/2.09 1067 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(283)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1067,a,1041,a)]. 1.88/2.09 1068 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | B != C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(283)]. 1.88/2.09 1069 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,B,C),C) # label(fact_min__max_Oinf__le2) # label(axiom). [clausify(293)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),B). [resolve(1069,a,1041,a)]. 1.88/2.09 1070 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,C),D) = c_Orderings_Oord__class_Omin(A,B,c_Orderings_Oord__class_Omin(A,C,D)) # label(fact_min__max_Oinf_Oassoc) # label(axiom). [clausify(322)]. 1.88/2.09 1071 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(337)]. 1.88/2.09 1072 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | B = C | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(337)]. 1.88/2.09 1073 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(A,B,C),D) | c_Orderings_Oord__class_Oless(A,B,D) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_min__less__iff__disj) # label(axiom). [clausify(348)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1073,a,1041,a)]. 1.88/2.09 1074 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,B,D) # label(fact_min__less__iff__disj) # label(axiom). [clausify(348)]. 1.88/2.09 1075 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_min__less__iff__disj) # label(axiom). [clausify(348)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1075,a,1041,a)]. 1.88/2.09 1076 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,B) = B # label(fact_min__max_Oinf_Oidem) # label(axiom). [clausify(435)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,A) = A. [resolve(1076,a,1041,a)]. 1.88/2.09 1077 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,B,C),D) | c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_min__le__iff__disj) # label(axiom). [clausify(454)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1077,a,1041,a)]. 1.88/2.09 1078 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_min__le__iff__disj) # label(axiom). [clausify(454)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1078,a,1041,a)]. 1.88/2.09 1079 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_min__le__iff__disj) # label(axiom). [clausify(454)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1079,a,1041,a)]. 1.88/2.09 1080 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) # label(axiom). [assumption]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1080,a,1042,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | B != A. [resolve(1080,a,1043,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | A != B. [resolve(1080,a,1044,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,A) | B = A. [resolve(1080,a,1045,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(1080,a,1047,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1080,a,1048,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1080,a,1049,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1080,a,1053,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(1080,a,1055,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B) = c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1080,a,1057,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | A = B. [resolve(1080,a,1060,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | A != B. [resolve(1080,a,1061,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1080,a,1062,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1080,a,1063,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1080,a,1067,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),B). [resolve(1080,a,1069,a)]. 1.88/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1080,a,1073,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1080,a,1075,a)]. 1.88/2.09 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,A) = A. [resolve(1080,a,1076,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1080,a,1077,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1080,a,1078,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1080,a,1079,a)]. 1.88/2.10 1081 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(A,D,B),C) # label(fact_min__max_Oless__infI2) # label(axiom). [clausify(493)]. 1.88/2.10 1082 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,B,D),C) # label(fact_min__max_Ole__infI1) # label(axiom). [clausify(502)]. 1.88/2.10 1083 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1083,a,1042,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | B != A. [resolve(1083,a,1043,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | A != B. [resolve(1083,a,1044,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | B = A. [resolve(1083,a,1045,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1083,a,1047,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1083,a,1048,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1083,a,1049,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1083,a,1053,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,C),B). [resolve(1083,a,1055,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B) = c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,A). [resolve(1083,a,1057,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | A = B. [resolve(1083,a,1060,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | A != B. [resolve(1083,a,1061,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),C) = c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)). [resolve(1083,a,1063,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1083,a,1067,a)]. 1.88/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),B). [resolve(1083,a,1069,a)]. 1.88/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1083,a,1073,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1083,a,1075,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,A) = A. [resolve(1083,a,1076,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1083,a,1077,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1083,a,1078,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1083,a,1079,a)]. 1.91/2.11 1084 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1084,a,1042,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | B != A. [resolve(1084,a,1043,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | A != B. [resolve(1084,a,1044,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | B = A. [resolve(1084,a,1045,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1084,a,1047,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1084,a,1048,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1084,a,1049,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1084,a,1053,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,C),B). [resolve(1084,a,1055,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B) = c_Orderings_Oord__class_Omin(tc_Int_Oint,B,A). [resolve(1084,a,1057,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | A = B. [resolve(1084,a,1060,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | A != B. [resolve(1084,a,1061,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1084,a,1062,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),C) = c_Orderings_Oord__class_Omin(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)). [resolve(1084,a,1063,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1084,a,1067,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),B). [resolve(1084,a,1069,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1084,a,1073,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1084,a,1075,a)]. 1.91/2.11 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,A,A) = A. [resolve(1084,a,1076,a)]. 1.91/2.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1084,a,1077,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1084,a,1078,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1084,a,1079,a)]. 1.93/2.13 1085 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,c_Orderings_Oord__class_Omin(A,B,C)) = c_Orderings_Oord__class_Omin(A,B,C) # label(fact_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(537)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B)) = c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B). [resolve(1085,a,1041,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B)) = c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(1085,a,1080,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B)) = c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B). [resolve(1085,a,1083,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B)) = c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B). [resolve(1085,a,1084,a)]. 1.93/2.13 1086 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,c_Orderings_Oord__class_Omin(A,C,D)) = c_Orderings_Oord__class_Omin(A,C,c_Orderings_Oord__class_Omin(A,B,D)) # label(fact_min__max_Oinf__left__commute) # label(axiom). [clausify(557)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)) = c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,C)). [resolve(1086,a,1041,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)) = c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1086,a,1080,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)) = c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,C)). [resolve(1086,a,1083,a)]. 1.93/2.13 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)) = c_Orderings_Oord__class_Omin(tc_Int_Oint,B,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,C)). [resolve(1086,a,1084,a)]. 1.93/2.13 1087 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__cases) # label(axiom). [clausify(566)]. 1.93/2.13 1088 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Omin(A,C,B) = B # label(fact_min__max_Oinf__absorb2) # label(axiom). [clausify(674)]. 1.93/2.13 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,A) = A. [resolve(1088,a,1041,a)]. 1.93/2.13 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,A) = A. [resolve(1088,a,1080,a)]. 1.93/2.13 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,A) = A. [resolve(1088,a,1083,a)]. 1.93/2.13 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Omin(tc_Int_Oint,B,A) = A. [resolve(1088,a,1084,a)]. 1.93/2.13 1089 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Omin(A,B,C) = B # label(fact_min__max_Oinf__absorb1) # label(axiom). [clausify(682)]. 1.93/2.13 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B) = A. [resolve(1089,a,1041,a)]. 1.93/2.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B) = A. [resolve(1089,a,1080,a)]. 1.93/2.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B) = A. [resolve(1089,a,1083,a)]. 1.93/2.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B) = A. [resolve(1089,a,1084,a)]. 1.93/2.16 1090 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__less__linear) # label(axiom). [clausify(701)]. 1.93/2.16 1091 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,D,B),C) # label(fact_min__max_Ole__infI2) # label(axiom). [clausify(706)]. 1.93/2.16 1092 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,C) = c_Orderings_Oord__class_Omin(A,C,B) # label(fact_min__max_Oinf__commute) # label(axiom). [clausify(730)]. 1.93/2.16 1093 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(773)]. 1.93/2.16 1094 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(773)]. 1.93/2.16 1095 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,C) != B | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_min__max_Ole__iff__inf) # label(axiom). [clausify(786)]. 1.93/2.16 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B) != A | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B). [resolve(1095,a,1041,a)]. 1.93/2.16 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B) != A | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(1095,a,1080,a)]. 1.93/2.16 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B) != A | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1095,a,1083,a)]. 1.93/2.16 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B) != A | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1095,a,1084,a)]. 1.93/2.16 1096 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,C) = B | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_min__max_Ole__iff__inf) # label(axiom). [clausify(786)]. 1.93/2.16 1097 -class_Int_Onumber(A) | -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(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(794)]. 1.93/2.16 1098 -class_Int_Onumber(A) | -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(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(794)]. 1.93/2.16 1099 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C != B | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(804)]. 1.93/2.16 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B != A | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1099,a,1041,a)]. 1.93/2.16 1100 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(804)]. 1.93/2.16 1101 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,D) | c_Orderings_Oord__class_Oless(A,B,c_Orderings_Oord__class_Omin(A,C,D)) # label(fact_min__less__iff__conj) # label(axiom). [clausify(833)]. 1.93/2.16 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)). [resolve(1101,a,1041,a)]. 1.93/2.17 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1101,a,1080,a)]. 1.93/2.17 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)). [resolve(1101,a,1083,a)]. 1.93/2.17 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)). [resolve(1101,a,1084,a)]. 1.93/2.17 1102 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,c_Orderings_Oord__class_Omin(A,C,D)) # label(fact_min__less__iff__conj) # label(axiom). [clausify(833)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,C)). [resolve(1102,a,1041,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1102,a,1080,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,C)). [resolve(1102,a,1083,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,B,C)). [resolve(1102,a,1084,a)]. 1.93/2.17 1103 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,c_Orderings_Oord__class_Omin(A,D,C)) # label(fact_min__less__iff__conj) # label(axiom). [clausify(833)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Orderings_Oord__class_Omin(tc_Nat_Onat,C,B)). [resolve(1103,a,1041,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,C,B)). [resolve(1103,a,1080,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,C,B)). [resolve(1103,a,1083,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Orderings_Oord__class_Omin(tc_Int_Oint,C,B)). [resolve(1103,a,1084,a)]. 1.93/2.17 1104 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_Omin(A,B,C),B) # label(fact_min__max_Oinf__le1) # label(axiom). [clausify(835)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,B),A). [resolve(1104,a,1041,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,B),A). [resolve(1104,a,1080,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,B),A). [resolve(1104,a,1083,a)]. 1.93/2.17 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,B),A). [resolve(1104,a,1084,a)]. 1.93/2.17 1105 -class_Orderings_Olinorder(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_Orderings_Oord__class_Omin(A,B,D),c_Orderings_Oord__class_Omin(A,C,E)) # label(fact_min__max_Oinf__mono) # label(axiom). [clausify(886)]. 1.93/2.17 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_Orderings_Oord__class_Omin(tc_Nat_Onat,A,C),c_Orderings_Oord__class_Omin(tc_Nat_Onat,B,D)). [resolve(1105,a,1041,a)]. 2.09/2.34 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,C),c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1105,a,1080,a)]. 2.09/2.34 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_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,C),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,B,D)). [resolve(1105,a,1083,a)]. 2.09/2.34 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_Orderings_Oord__class_Omin(tc_Int_Oint,A,C),c_Orderings_Oord__class_Omin(tc_Int_Oint,B,D)). [resolve(1105,a,1084,a)]. 2.09/2.34 1106 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,c_Orderings_Oord__class_Omin(A,B,C)) = c_Orderings_Oord__class_Omin(A,B,C) # label(fact_min__max_Oinf__left__idem) # label(axiom). [clausify(889)]. 2.09/2.34 1107 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A,B,c_Orderings_Oord__class_Omin(A,C,D)) = c_Orderings_Oord__class_Omin(A,C,c_Orderings_Oord__class_Omin(A,B,D)) # label(fact_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(928)]. 2.09/2.34 1108 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_one__neq__zero) # label(axiom). [clausify(26)]. 2.09/2.34 1109 class_Rings_Ozero__neq__one(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ozero__neq__one) # label(axiom). [assumption]. 2.09/2.34 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1108,a,1109,a)]. 2.09/2.34 1110 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_zero__neq__one) # label(axiom). [clausify(219)]. 2.09/2.34 1111 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ozero__neq__one) # label(axiom). [assumption]. 2.09/2.34 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1111,a,1108,a)]. 2.09/2.34 1112 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) # label(axiom). [assumption]. 2.09/2.34 Derived: c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1112,a,1108,a)]. 2.09/2.34 1113 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom). [assumption]. 2.09/2.34 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1113,a,1108,a)]. 2.09/2.34 1114 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 2.09/2.34 1115 -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(6)]. 2.09/2.34 1116 -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(41)]. 2.09/2.34 1117 -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(41)]. 2.09/2.35 1118 -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(67)]. 2.09/2.35 1119 -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(67)]. 2.09/2.35 1120 -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(67)]. 2.09/2.35 1121 -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(67)]. 2.09/2.35 1122 -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,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(67)]. 2.09/2.35 1123 -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),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(67)]. 2.09/2.35 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(1114,a,1115,a)]. 2.09/2.35 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(1114,a,1117,a)]. 2.09/2.35 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(1114,a,1118,a)]. 2.09/2.35 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(1114,a,1121,a)]. 2.09/2.35 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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1114,a,1122,a)]. 2.09/2.35 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),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1114,a,1123,a)]. 2.09/2.35 1124 -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(145)]. 2.09/2.35 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(1124,a,1114,a)]. 2.09/2.35 1125 -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(145)]. 2.09/2.35 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(1125,a,1114,a)]. 2.09/2.35 1126 -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(145)]. 2.09/2.35 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(1126,a,1114,a)]. 2.09/2.35 1127 -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(176)]. 2.09/2.35 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(1127,a,1114,a)]. 2.09/2.35 1128 -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_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(227)]. 2.09/2.35 1129 -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_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(227)]. 2.09/2.35 1130 -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__disj) # label(axiom). [clausify(266)]. 2.09/2.36 1131 -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__disj) # label(axiom). [clausify(266)]. 2.09/2.36 1132 -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,B,c_Groups_Ozero__class_Ozero(A)) | -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__disj) # label(axiom). [clausify(266)]. 2.09/2.36 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,A,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1132,a,1114,a)]. 2.09/2.36 1133 -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,D),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(266)]. 2.09/2.36 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,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)). [resolve(1133,a,1114,a)]. 2.09/2.36 1134 -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,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(266)]. 2.09/2.36 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,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)). [resolve(1134,a,1114,a)]. 2.09/2.36 1135 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | -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__less__cancel__left__disj) # label(axiom). [clausify(266)]. 2.09/2.36 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)). [resolve(1135,a,1114,a)]. 2.09/2.36 1136 -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__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)) # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(356)]. 2.09/2.36 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | 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)). [resolve(1136,a,1114,a)]. 2.09/2.36 1137 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = B | -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)) # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(356)]. 2.09/2.36 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -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)). [resolve(1137,a,1114,a)]. 2.09/2.36 1138 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,C),c_Groups_Otimes__class_Otimes(A,B,B)),c_Groups_Ozero__class_Ozero(A)) # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(356)]. 2.09/2.36 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -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,B,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1138,a,1114,a)]. 2.09/2.36 1139 -class_Rings_Olinordered__ring__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__less__cancel__right__disj) # label(axiom). [clausify(413)]. 2.09/2.36 1140 -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,D,B),c_Groups_Otimes__class_Otimes(A,C,B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(413)]. 2.09/2.36 1141 -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,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(413)]. 2.09/2.36 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,A,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)). [resolve(1141,a,1114,a)]. 2.09/2.36 1142 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | -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__less__cancel__right__disj) # label(axiom). [clausify(413)]. 2.09/2.36 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | -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,C)). [resolve(1142,a,1114,a)]. 2.09/2.36 1143 -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,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(413)]. 2.09/2.36 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_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)). [resolve(1143,a,1114,a)]. 2.09/2.36 1144 -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,D,B),c_Groups_Otimes__class_Otimes(A,C,B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(413)]. 2.18/2.38 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,C,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)). [resolve(1144,a,1114,a)]. 2.18/2.38 1145 -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(424)]. 2.18/2.38 1146 -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(424)]. 2.18/2.38 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(1146,a,1114,a)]. 2.18/2.38 1147 -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(556)]. 2.18/2.38 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(1147,a,1114,a)]. 2.18/2.38 1148 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 2.18/2.38 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(1148,a,1115,a)]. 2.18/2.38 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(1148,a,1117,a)]. 2.18/2.38 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(1148,a,1118,a)]. 2.18/2.38 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(1148,a,1121,a)]. 2.18/2.38 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,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1148,a,1122,a)]. 2.18/2.38 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),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1148,a,1123,a)]. 2.18/2.38 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(1148,a,1124,a)]. 2.18/2.38 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(1148,a,1125,a)]. 2.18/2.38 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(1148,a,1126,a)]. 2.18/2.38 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(1148,a,1127,a)]. 2.18/2.38 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,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,B,C). [resolve(1148,a,1128,a)]. 2.18/2.38 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,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,B,C). [resolve(1148,a,1129,a)]. 2.18/2.38 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,A,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_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1148,a,1132,a)]. 2.18/2.38 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,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)). [resolve(1148,a,1133,a)]. 2.18/2.38 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,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)). [resolve(1148,a,1134,a)]. 2.18/2.38 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | -c_Orderings_Oord__class_Oless(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,1135,a)]. 2.18/2.38 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != 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,A,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1148,a,1136,a)]. 2.18/2.38 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -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)). [resolve(1148,a,1137,a)]. 2.19/2.39 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -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,B,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1148,a,1138,a)]. 2.19/2.39 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -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,C)). [resolve(1148,a,1139,a)]. 2.19/2.39 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,A,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C)). [resolve(1148,a,1141,a)]. 2.19/2.39 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | -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,C)). [resolve(1148,a,1142,a)]. 2.19/2.39 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,A,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_Otimes__class_Otimes(tc_Int_Oint,C,A)). [resolve(1148,a,1143,a)]. 2.19/2.39 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,C,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A)). [resolve(1148,a,1144,a)]. 2.19/2.39 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(1148,a,1146,a)]. 2.19/2.39 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(1148,a,1147,a)]. 2.19/2.39 1149 -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(662)]. 2.19/2.39 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(1149,a,1114,a)]. 2.19/2.39 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(1149,a,1148,a)]. 2.19/2.39 1150 -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(662)]. 2.21/2.41 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(1150,a,1114,a)]. 2.21/2.41 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(1150,a,1148,a)]. 2.21/2.41 1151 -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,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(802)]. 2.21/2.41 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,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(1151,a,1114,a)]. 2.21/2.41 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,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)). [resolve(1151,a,1148,a)]. 2.21/2.41 1152 -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,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom). [clausify(802)]. 2.21/2.41 1153 -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,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(802)]. 2.21/2.41 1154 -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_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom). [clausify(802)]. 2.21/2.41 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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1154,a,1114,a)]. 2.21/2.41 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,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). [resolve(1154,a,1148,a)]. 2.21/2.41 1155 -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,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(802)]. 2.21/2.41 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,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(1155,a,1114,a)]. 2.21/2.42 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,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(1155,a,1148,a)]. 2.21/2.42 1156 -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),C) # label(fact_mult__le__0__iff) # label(axiom). [clausify(802)]. 2.21/2.42 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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1156,a,1114,a)]. 2.21/2.42 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),B). [resolve(1156,a,1148,a)]. 2.21/2.42 1157 -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(832)]. 2.21/2.42 Derived: 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(1157,a,1114,a)]. 2.21/2.42 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(1157,a,1148,a)]. 2.21/2.42 1158 -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(832)]. 2.21/2.42 Derived: 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(1158,a,1114,a)]. 2.21/2.42 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(1158,a,1148,a)]. 2.21/2.42 1159 -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 | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(832)]. 2.21/2.42 Derived: 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(1159,a,1114,a)]. 2.30/2.50 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 | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1159,a,1148,a)]. 2.30/2.50 1160 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption]. 2.30/2.50 1161 -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(7)]. 2.30/2.50 1162 -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(132)]. 2.30/2.50 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(1160,a,1161,a)]. 2.30/2.50 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(1160,a,1162,a)]. 2.30/2.50 1163 -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(292)]. 2.30/2.50 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(1163,a,1160,a)]. 2.30/2.50 1164 -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(292)]. 2.30/2.50 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(1164,a,1160,a)]. 2.30/2.50 1165 -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(321)]. 2.30/2.50 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),B) = A. [resolve(1165,a,1160,a)]. 2.30/2.50 1166 -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(353)]. 2.30/2.50 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(1166,a,1160,a)]. 2.30/2.50 1167 -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(385)]. 2.30/2.50 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(1167,a,1160,a)]. 2.30/2.50 1168 -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(388)]. 2.30/2.50 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(1168,a,1160,a)]. 2.30/2.50 1169 -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(466)]. 2.30/2.50 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(1169,a,1160,a)]. 2.30/2.50 1170 -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(471)]. 2.30/2.52 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),B) = A. [resolve(1170,a,1160,a)]. 2.30/2.52 1171 -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(494)]. 2.30/2.52 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A. [resolve(1171,a,1160,a)]. 2.30/2.52 1172 -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(494)]. 2.30/2.52 1173 -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(546)]. 2.30/2.52 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) = A. [resolve(1173,a,1160,a)]. 2.30/2.52 1174 -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(578)]. 2.30/2.52 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(1174,a,1160,a)]. 2.30/2.52 1175 -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(578)]. 2.30/2.52 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(1175,a,1160,a)]. 2.30/2.52 1176 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom). [assumption]. 2.30/2.52 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(1176,a,1161,a)]. 2.30/2.52 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(1176,a,1162,a)]. 2.30/2.52 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(1176,a,1163,a)]. 2.30/2.52 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(1176,a,1164,a)]. 2.30/2.52 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),B) = A. [resolve(1176,a,1165,a)]. 2.30/2.52 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(1176,a,1167,a)]. 2.30/2.52 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(1176,a,1168,a)]. 2.30/2.52 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(1176,a,1169,a)]. 2.30/2.52 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),B) = A. [resolve(1176,a,1170,a)]. 2.30/2.52 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) = A. [resolve(1176,a,1171,a)]. 2.30/2.52 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = A. [resolve(1176,a,1173,a)]. 2.30/2.52 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(1176,a,1174,a)]. 2.30/2.53 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(1176,a,1175,a)]. 2.30/2.53 1177 -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(600)]. 2.30/2.53 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1177,a,1160,a)]. 2.30/2.53 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(1177,a,1176,a)]. 2.30/2.53 1178 -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(617)]. 2.30/2.53 1179 -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__equal__0__iff__equal) # label(axiom). [clausify(658)]. 2.30/2.53 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1179,a,1160,a)]. 2.30/2.53 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1179,a,1176,a)]. 2.30/2.53 1180 -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__equal__0__iff__equal) # label(axiom). [clausify(658)]. 2.30/2.53 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1180,a,1160,a)]. 2.30/2.53 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1180,a,1176,a)]. 2.30/2.53 1181 -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(665)]. 2.30/2.53 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1181,a,1160,a)]. 2.30/2.53 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1181,a,1176,a)]. 2.30/2.53 1182 -class_Groups_Ogroup__add(A) | B != C | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ouminus__class_Ouminus(A,C) # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(675)]. 2.30/2.53 Derived: A != B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B). [resolve(1182,a,1160,a)]. 2.30/2.53 Derived: A != B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B). [resolve(1182,a,1176,a)]. 2.30/2.53 1183 -class_Groups_Ogroup__add(A) | B = C | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ouminus__class_Ouminus(A,C) # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(675)]. 2.30/2.53 Derived: A = B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B). [resolve(1183,a,1160,a)]. 2.30/2.53 Derived: A = B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B). [resolve(1183,a,1176,a)]. 2.30/2.53 1184 -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(694)]. 2.30/2.53 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1184,a,1160,a)]. 2.30/2.53 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(1184,a,1176,a)]. 2.38/2.64 1185 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | C = B # label(fact_right__minus__eq) # label(axiom). [clausify(721)]. 2.38/2.64 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | B = A. [resolve(1185,a,1160,a)]. 2.38/2.64 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | B = A. [resolve(1185,a,1176,a)]. 2.38/2.64 1186 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | C != B # label(fact_right__minus__eq) # label(axiom). [clausify(721)]. 2.38/2.64 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | B != A. [resolve(1186,a,1160,a)]. 2.38/2.64 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | B != A. [resolve(1186,a,1176,a)]. 2.38/2.64 1187 -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__0__equal__iff__equal) # label(axiom). [clausify(785)]. 2.38/2.64 1188 -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__0__equal__iff__equal) # label(axiom). [clausify(785)]. 2.38/2.64 1189 -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(791)]. 2.38/2.64 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(1189,a,1160,a)]. 2.38/2.64 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(1189,a,1176,a)]. 2.38/2.64 1190 -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(797)]. 2.38/2.64 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1190,a,1160,a)]. 2.38/2.64 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1190,a,1176,a)]. 2.38/2.64 1191 -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(816)]. 2.38/2.64 1192 -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(816)]. 2.38/2.64 1193 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption]. 2.38/2.64 1194 -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(8)]. 2.38/2.64 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(1193,a,1194,a)]. 2.38/2.64 1195 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) # label(axiom). [assumption]. 2.38/2.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1195,a,1194,a)]. 2.38/2.67 1196 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom). [assumption]. 2.38/2.67 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(1196,a,1194,a)]. 2.38/2.67 1197 -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(724)]. 2.38/2.67 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(1197,a,1193,a)]. 2.38/2.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1197,a,1195,a)]. 2.38/2.67 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(1197,a,1196,a)]. 2.38/2.67 1198 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption]. 2.38/2.67 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(1198,a,1194,a)]. 2.38/2.67 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(1198,a,1197,a)]. 2.38/2.67 1199 -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(841)]. 2.51/2.76 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(1199,a,1193,a)]. 2.51/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1199,a,1195,a)]. 2.51/2.76 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(1199,a,1196,a)]. 2.51/2.76 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(1199,a,1198,a)]. 2.51/2.76 1200 -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(891)]. 2.51/2.76 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(1200,a,1193,a)]. 2.51/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,B)). [resolve(1200,a,1195,a)]. 2.51/2.76 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(1200,a,1196,a)]. 2.51/2.76 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,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)). [resolve(1200,a,1198,a)]. 2.51/2.76 1201 -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(528)]. 2.61/2.87 1202 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 2.61/2.87 1203 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 2.61/2.87 1204 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 2.61/2.87 1205 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption]. 2.61/2.87 1206 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]. 2.61/2.87 1207 -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(9)]. 2.61/2.87 1208 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]. 2.61/2.87 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(1208,a,1207,a)]. 2.61/2.87 1209 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Omin(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) = c_Groups_Oplus__class_Oplus(A,c_Orderings_Oord__class_Omin(A,B,D),C) # label(fact_min__add__distrib__left) # label(axiom). [clausify(50)]. 2.61/2.87 Derived: c_Orderings_Oord__class_Omin(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat,A,C),B). [resolve(1209,a,1206,a)]. 2.61/2.87 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,C),B). [resolve(1209,a,1208,a)]. 2.61/2.87 1210 -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(55)]. 2.61/2.87 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(1210,a,1206,a)]. 2.61/2.87 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(1210,a,1208,a)]. 2.61/2.87 1211 -class_Groups_Oordered__ab__semigroup__add__imp__le(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__less__cancel__right) # label(axiom). [clausify(252)]. 2.61/2.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | 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,C)). [resolve(1211,a,1208,a)]. 2.61/2.87 1212 -class_Groups_Oordered__ab__semigroup__add__imp__le(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__less__cancel__right) # label(axiom). [clausify(252)]. 2.61/2.87 1213 -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(253)]. 2.61/2.89 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(1213,a,1206,a)]. 2.61/2.89 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(1213,a,1208,a)]. 2.61/2.89 1214 -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(459)]. 2.61/2.89 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(1214,a,1206,a)]. 2.61/2.89 1215 -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(459)]. 2.61/2.89 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(1215,a,1206,a)]. 2.61/2.89 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(1215,a,1208,a)]. 2.61/2.89 1216 -class_Groups_Oordered__ab__semigroup__add__imp__le(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__le__cancel__right) # label(axiom). [clausify(488)]. 2.61/2.89 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | 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,C)). [resolve(1216,a,1208,a)]. 2.61/2.89 1217 -class_Groups_Oordered__ab__semigroup__add__imp__le(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__le__cancel__right) # label(axiom). [clausify(488)]. 2.61/2.89 1218 -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(592)]. 2.61/2.89 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,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1218,a,1208,a)]. 2.61/2.89 1219 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]. 2.61/2.89 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(1219,a,1207,a)]. 2.61/2.89 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,C),B). [resolve(1219,a,1209,a)]. 2.61/2.89 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(1219,a,1210,a)]. 2.70/2.92 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(1219,a,1213,a)]. 2.70/2.92 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(1219,a,1215,a)]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | 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,C)). [resolve(1219,a,1216,a)]. 2.70/2.92 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(1219,a,1218,a)]. 2.70/2.92 1220 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1220,a,1207,a)]. 2.70/2.92 Derived: c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,B)) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(1220,a,1209,a)]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,B)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1220,a,1210,a)]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1220,a,1211,a)]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1220,a,1213,a)]. 2.70/2.92 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1220,a,1215,a)]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1220,a,1216,a)]. 2.70/2.92 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1220,a,1218,a)]. 2.70/2.92 1221 -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(876)]. 2.70/2.92 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(1221,a,1206,a)]. 2.79/3.01 1222 -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(876)]. 2.79/3.01 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(1222,a,1206,a)]. 2.79/3.01 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(1222,a,1208,a)]. 2.79/3.01 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(1222,a,1219,a)]. 2.79/3.01 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1222,a,1220,a)]. 2.79/3.01 1223 -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(43)]. 2.79/3.01 1224 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption]. 2.79/3.01 1225 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) # label(axiom). [assumption]. 2.79/3.01 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1225,a,1223,a)]. 2.79/3.01 1226 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption]. 2.79/3.01 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(1226,a,1223,a)]. 2.79/3.01 1227 -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(500)]. 2.79/3.01 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1227,a,1225,a)]. 2.79/3.01 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(1227,a,1226,a)]. 2.79/3.01 1228 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom). [assumption]. 2.90/3.11 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(1228,a,1223,a)]. 2.90/3.11 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(1228,a,1227,a)]. 2.90/3.11 1229 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.90/3.11 1230 -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(10)]. 2.90/3.11 1231 -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(32)]. 2.90/3.11 1232 -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(93)]. 2.90/3.11 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1229,a,1230,a)]. 2.90/3.11 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1229,a,1231,a)]. 2.90/3.11 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1229,a,1232,a)]. 2.90/3.11 1233 -class_Rings_Ocomm__semiring__1(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__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(155)]. 2.90/3.11 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,B)) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(1233,a,1229,a)]. 2.90/3.11 1234 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.90/3.11 1235 -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(173)]. 2.90/3.11 1236 -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(232)]. 2.90/3.11 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,D)) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1236,a,1229,a)]. 2.90/3.12 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(1236,a,1234,a)]. 2.90/3.12 1237 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Otimes__class_Otimes(A,C,B)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oone__class_Oone(A)),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(262)]. 2.90/3.12 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,A)) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A). [resolve(1237,a,1229,a)]. 2.90/3.12 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A). [resolve(1237,a,1234,a)]. 2.90/3.12 1238 -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(273)]. 2.90/3.12 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1238,a,1229,a)]. 2.90/3.12 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(1238,a,1234,a)]. 2.90/3.12 1239 -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(282)]. 2.90/3.12 1240 -class_Rings_Ocomm__semiring__1(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_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(319)]. 2.90/3.12 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C)) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1240,a,1229,a)]. 2.90/3.12 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,A,C)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(1240,a,1234,a)]. 2.90/3.12 1241 -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(324)]. 2.90/3.12 1242 -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(333)]. 2.90/3.14 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(1242,a,1229,a)]. 2.90/3.14 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(1242,a,1234,a)]. 2.90/3.14 1243 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(341)]. 2.90/3.14 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1243,a,1229,a)]. 2.90/3.14 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1243,a,1234,a)]. 2.90/3.14 1244 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(371)]. 2.90/3.14 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,A) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A). [resolve(1244,a,1229,a)]. 2.90/3.14 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,A) = c_Groups_Otimes__class_Otimes(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)),A). [resolve(1244,a,1234,a)]. 2.90/3.14 1245 -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(449)]. 2.90/3.14 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),B). [resolve(1245,a,1229,a)]. 2.90/3.14 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(1245,a,1234,a)]. 2.90/3.14 1246 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(483)]. 2.90/3.14 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A) = A. [resolve(1246,a,1229,a)]. 2.90/3.14 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) = A. [resolve(1246,a,1234,a)]. 2.90/3.14 1247 -class_Rings_Ocomm__semiring__1(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__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(527)]. 2.90/3.14 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(1247,a,1234,a)]. 2.90/3.16 1248 -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(589)]. 2.90/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1248,a,1229,a)]. 2.90/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A). [resolve(1248,a,1234,a)]. 2.90/3.16 1249 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(614)]. 2.90/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(1249,a,1229,a)]. 2.90/3.16 1250 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),C) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(646)]. 2.90/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),B) = c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),B). [resolve(1250,a,1229,a)]. 2.90/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),B) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)),B). [resolve(1250,a,1234,a)]. 2.90/3.16 1251 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(655)]. 2.90/3.16 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(1251,a,1229,a)]. 2.90/3.16 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1251,a,1234,a)]. 2.90/3.16 1252 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(657)]. 2.90/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) = A. [resolve(1252,a,1229,a)]. 2.90/3.16 1253 -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(670)]. 2.90/3.16 1254 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(685)]. 2.90/3.16 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1254,a,1229,a)]. 2.90/3.16 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1254,a,1234,a)]. 2.90/3.16 1255 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.90/3.16 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(1255,a,1230,a)]. 2.90/3.17 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,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C)). [resolve(1255,a,1231,a)]. 2.90/3.17 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(1255,a,1236,a)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). [resolve(1255,a,1237,a)]. 2.90/3.17 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(1255,a,1238,a)]. 2.90/3.17 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(1255,a,1240,a)]. 2.90/3.17 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(1255,a,1242,a)]. 2.90/3.17 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1255,a,1243,a)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = c_Groups_Otimes__class_Otimes(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)),A). [resolve(1255,a,1244,a)]. 2.90/3.17 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(1255,a,1245,a)]. 2.90/3.17 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) = A. [resolve(1255,a,1246,a)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,A). [resolve(1255,a,1248,a)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1255,a,1249,a)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),B) = 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)),B). [resolve(1255,a,1250,a)]. 2.90/3.17 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1255,a,1251,a)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = A. [resolve(1255,a,1252,a)]. 2.90/3.17 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1255,a,1254,a)]. 2.90/3.17 1256 -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(852)]. 2.90/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C)) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1256,a,1229,a)]. 2.90/3.18 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1256,a,1234,a)]. 2.90/3.18 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(1256,a,1255,a)]. 2.90/3.18 1257 class_Rings_Ocomm__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.90/3.18 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(1257,a,1230,a)]. 2.90/3.18 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(1257,a,1231,a)]. 2.90/3.18 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A). [resolve(1257,a,1232,a)]. 2.90/3.18 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(1257,a,1233,a)]. 2.90/3.18 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(1257,a,1236,a)]. 2.90/3.18 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)),A). [resolve(1257,a,1237,a)]. 2.90/3.18 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(1257,a,1238,a)]. 2.90/3.18 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,A,C)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)). [resolve(1257,a,1240,a)]. 2.90/3.18 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(1257,a,1242,a)]. 2.90/3.18 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1257,a,1243,a)]. 2.90/3.18 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Groups_Otimes__class_Otimes(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)),A). [resolve(1257,a,1244,a)]. 2.90/3.18 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(1257,a,1245,a)]. 2.90/3.18 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) = A. [resolve(1257,a,1246,a)]. 2.90/3.18 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A). [resolve(1257,a,1248,a)]. 2.90/3.18 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1257,a,1249,a)]. 2.90/3.18 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),B) = 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)),B). [resolve(1257,a,1250,a)]. 2.90/3.18 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1257,a,1251,a)]. 3.09/3.39 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = A. [resolve(1257,a,1252,a)]. 3.09/3.39 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1257,a,1254,a)]. 3.09/3.39 1258 -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(892)]. 3.09/3.39 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,D)) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1258,a,1229,a)]. 3.09/3.39 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(1258,a,1234,a)]. 3.09/3.39 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(1258,a,1255,a)]. 3.09/3.39 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(1258,a,1257,a)]. 3.09/3.39 1259 -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(464)]. 3.09/3.39 1260 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) # label(axiom). [assumption]. 3.09/3.39 1261 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption]. 3.09/3.39 1262 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption]. 3.09/3.39 1263 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption]. 3.09/3.39 1264 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom). [clausify(362)]. 3.09/3.39 1265 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) # label(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption]. 3.09/3.39 1266 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption]. 3.09/3.39 1267 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) # label(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption]. 3.09/3.39 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1264,a,1265,a)]. 3.09/3.39 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1264,a,1266,a)]. 3.09/3.39 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1264,a,1267,a)]. 3.19/3.41 1268 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom). [clausify(362)]. 3.19/3.41 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1268,a,1265,a)]. 3.19/3.41 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1268,a,1266,a)]. 3.19/3.41 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1268,a,1267,a)]. 3.19/3.41 1269 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom). [clausify(616)]. 3.19/3.41 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,D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | A = C | B = D. [resolve(1269,a,1265,a)]. 3.19/3.41 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,D)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,D),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | A = C | B = D. [resolve(1269,a,1266,a)]. 3.19/3.41 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,D)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,D),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | A = C | B = D. [resolve(1269,a,1267,a)]. 3.19/3.41 1270 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C)) | B != D # label(fact_crossproduct__eq) # label(axiom). [clausify(616)]. 3.19/3.41 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,D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | A != C. [resolve(1270,a,1265,a)]. 3.19/3.41 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,D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,D),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | A != C. [resolve(1270,a,1266,a)]. 3.19/3.41 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,D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,D),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | A != C. [resolve(1270,a,1267,a)]. 3.19/3.41 1271 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C)) | C != E # label(fact_crossproduct__eq) # label(axiom). [clausify(616)]. 3.19/3.41 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,D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | B != D. [resolve(1271,a,1265,a)]. 3.21/3.43 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,D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,D),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)) | B != D. [resolve(1271,a,1266,a)]. 3.21/3.43 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,D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,D),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)) | B != D. [resolve(1271,a,1267,a)]. 3.21/3.43 1272 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,D,C)) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(715)]. 3.21/3.43 Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,D,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,D,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A)). [resolve(1272,a,1265,a)]. 3.21/3.43 Derived: A = B | C = D | 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,C,B)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D,B),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)). [resolve(1272,a,1266,a)]. 3.21/3.43 Derived: A = B | C = D | 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,C,B)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,D,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,A)). [resolve(1272,a,1267,a)]. 3.21/3.43 1273 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,E,C)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(715)]. 3.21/3.43 1274 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,E),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(715)]. 3.21/3.43 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)). [resolve(1274,a,1265,a)]. 3.21/3.43 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,C),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,D),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1274,a,1266,a)]. 3.21/3.43 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,D),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1274,a,1267,a)]. 3.21/3.43 1275 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Ozero__class_Ozero(A) = B | C = D | E != F | c_Groups_Oplus__class_Oplus(A,E,c_Groups_Otimes__class_Otimes(A,B,C)) != c_Groups_Oplus__class_Oplus(A,F,c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(850)]. 3.21/3.51 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B = C | D != E | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,D,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,E,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)). [resolve(1275,a,1265,a)]. 3.21/3.51 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | B = C | D != E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,D,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,E,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,C)). [resolve(1275,a,1266,a)]. 3.21/3.51 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | B = C | D != E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,E,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C)). [resolve(1275,a,1267,a)]. 3.21/3.51 1276 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 3.21/3.51 1277 -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(13)]. 3.21/3.51 1278 -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(13)]. 3.21/3.51 1279 -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(134)]. 3.21/3.51 1280 -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(134)]. 3.21/3.51 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(1276,a,1277,a)]. 3.21/3.51 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(1276,a,1278,a)]. 3.21/3.51 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(1276,a,1279,a)]. 3.21/3.51 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(1276,a,1280,a)]. 3.31/3.51 1281 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Omin(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,C)) = c_Groups_Ominus__class_Ominus(A,c_Orderings_Oord__class_Omin(A,B,D),C) # label(fact_min__diff__distrib__left) # label(axiom). [clausify(206)]. 3.31/3.51 Derived: c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,B)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,A,C),B). [resolve(1281,a,1276,a)]. 3.31/3.51 1282 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 3.31/3.51 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(1282,a,1277,a)]. 3.31/3.53 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(1282,a,1278,a)]. 3.31/3.53 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(1282,a,1279,a)]. 3.31/3.53 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(1282,a,1280,a)]. 3.31/3.53 Derived: c_Orderings_Oord__class_Omin(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,B)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint,A,C),B). [resolve(1282,a,1281,a)]. 3.31/3.53 1283 -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(340)]. 3.31/3.53 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(1283,a,1276,a)]. 3.31/3.53 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(1283,a,1282,a)]. 3.31/3.53 1284 -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(340)]. 3.31/3.53 1285 -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(411)]. 3.31/3.53 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(1285,a,1276,a)]. 3.31/3.53 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(1285,a,1282,a)]. 3.31/3.53 1286 -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(411)]. 3.31/3.53 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(1286,a,1276,a)]. 3.31/3.53 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(1286,a,1282,a)]. 3.31/3.53 1287 -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(434)]. 3.31/3.53 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(1287,a,1276,a)]. 3.31/3.55 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(1287,a,1282,a)]. 3.31/3.55 1288 -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_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(479)]. 3.31/3.55 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | 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)). [resolve(1288,a,1282,a)]. 3.31/3.55 1289 -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_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(479)]. 3.31/3.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -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)). [resolve(1289,a,1282,a)]. 3.31/3.55 1290 -class_Groups_Oordered__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_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(576)]. 3.31/3.55 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1290,a,1276,a)]. 3.31/3.55 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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1290,a,1282,a)]. 3.31/3.55 1291 -class_Groups_Oordered__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_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(576)]. 3.31/3.55 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1291,a,1276,a)]. 3.31/3.55 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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1291,a,1282,a)]. 3.31/3.55 1292 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(693)]. 3.31/3.55 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1292,a,1276,a)]. 3.31/3.55 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1292,a,1282,a)]. 3.31/3.55 1293 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(693)]. 3.31/3.57 Derived: 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)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1293,a,1276,a)]. 3.31/3.57 Derived: 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)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1293,a,1282,a)]. 3.31/3.57 1294 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(808)]. 3.31/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | 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)). [resolve(1294,a,1276,a)]. 3.31/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | 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)). [resolve(1294,a,1282,a)]. 3.31/3.57 1295 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(808)]. 3.31/3.57 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -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)). [resolve(1295,a,1276,a)]. 3.31/3.57 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -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)). [resolve(1295,a,1282,a)]. 3.31/3.57 1296 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(814)]. 3.31/3.57 Derived: -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)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1296,a,1276,a)]. 3.31/3.57 Derived: -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)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1296,a,1282,a)]. 3.31/3.57 1297 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(814)]. 3.31/3.57 Derived: 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)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1297,a,1276,a)]. 3.31/3.57 Derived: 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)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1297,a,1282,a)]. 3.31/3.57 1298 -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(824)]. 3.31/3.57 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(1298,a,1276,a)]. 3.31/3.57 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(1298,a,1282,a)]. 3.31/3.57 1299 -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(824)]. 3.31/3.57 1300 -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(880)]. 3.31/3.57 1301 -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(880)]. 3.31/3.58 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(1301,a,1276,a)]. 3.31/3.58 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(1301,a,1282,a)]. 3.31/3.58 1302 -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(882)]. 3.31/3.58 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(1302,a,1276,a)]. 3.31/3.58 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(1302,a,1282,a)]. 3.31/3.58 1303 -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(882)]. 3.31/3.58 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(1303,a,1276,a)]. 3.31/3.58 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(1303,a,1282,a)]. 3.31/3.58 1304 -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(894)]. 3.31/3.58 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(1304,a,1276,a)]. 3.31/3.58 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(1304,a,1282,a)]. 3.31/3.58 1305 -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(894)]. 3.40/3.66 1306 -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(902)]. 3.40/3.66 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(1306,a,1276,a)]. 3.40/3.66 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(1306,a,1282,a)]. 3.40/3.66 1307 -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(902)]. 3.40/3.66 1308 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption]. 3.40/3.66 1309 -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(14)]. 3.40/3.66 1310 -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(17)]. 3.40/3.66 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1308,a,1309,a)]. 3.40/3.66 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(1308,a,1310,a)]. 3.40/3.66 1311 -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(142)]. 3.40/3.66 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(1311,a,1308,a)]. 3.40/3.66 1312 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) # label(axiom). [assumption]. 3.40/3.66 Derived: c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(1312,a,1309,a)]. 3.40/3.66 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(1312,a,1310,a)]. 3.40/3.66 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(1312,a,1311,a)]. 3.40/3.66 1313 -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(359)]. 3.40/3.66 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(1313,a,1308,a)]. 3.40/3.66 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(1313,a,1312,a)]. 3.40/3.67 1314 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption]. 3.40/3.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1314,a,1309,a)]. 3.40/3.67 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(1314,a,1310,a)]. 3.40/3.67 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(1314,a,1311,a)]. 3.40/3.67 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(1314,a,1313,a)]. 3.40/3.67 1315 -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(510)]. 3.40/3.67 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(1315,a,1308,a)]. 3.40/3.67 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1315,a,1312,a)]. 3.40/3.67 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(1315,a,1314,a)]. 3.40/3.67 1316 -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(532)]. 3.40/3.67 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(1316,a,1308,a)]. 3.40/3.67 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1316,a,1312,a)]. 3.40/3.67 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(1316,a,1314,a)]. 3.40/3.67 1317 -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(536)]. 3.40/3.67 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(1317,a,1308,a)]. 3.40/3.67 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1317,a,1312,a)]. 3.84/4.04 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(1317,a,1314,a)]. 3.84/4.04 1318 -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(634)]. 3.84/4.04 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(1318,a,1308,a)]. 3.84/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1318,a,1312,a)]. 3.84/4.04 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(1318,a,1314,a)]. 3.84/4.04 1319 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption]. 3.84/4.04 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(1319,a,1310,a)]. 3.84/4.04 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(1319,a,1311,a)]. 3.84/4.04 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(1319,a,1313,a)]. 3.84/4.04 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(1319,a,1315,a)]. 3.84/4.04 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,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1319,a,1316,a)]. 3.84/4.04 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1319,a,1317,a)]. 3.84/4.04 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(1319,a,1318,a)]. 3.84/4.04 1320 -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(57)]. 3.84/4.04 1321 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 3.84/4.04 1322 class_Groups_Ocomm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 3.84/4.04 1323 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 3.84/4.04 1324 -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(762)]. 3.84/4.04 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = A. [resolve(1324,a,1323,a)]. 3.84/4.04 1325 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 3.84/4.04 1326 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 3.84/4.04 1327 -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(24)]. 4.22/4.42 1328 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 1329 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 1330 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 1331 -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(548)]. 4.22/4.42 1332 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 4.22/4.42 1333 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption]. 4.22/4.42 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(1331,a,1332,a)]. 4.22/4.42 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(1331,a,1333,a)]. 4.22/4.42 1334 -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(517)]. 4.22/4.42 1335 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 1336 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 1337 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B = C. [resolve(1334,a,1335,a)]. 4.22/4.42 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B = C. [resolve(1334,a,1336,a)]. 4.22/4.42 1338 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 4.22/4.42 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B) != c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C) | B = C. [resolve(1338,a,1334,a)]. 4.22/4.42 1339 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 4.22/4.43 1340 -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(35)]. 4.22/4.43 1341 -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(47)]. 4.22/4.43 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(1341,a,1339,a)]. 4.22/4.43 1342 -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(125)]. 4.22/4.43 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(1342,a,1339,a)]. 4.22/4.43 1343 -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(165)]. 4.22/4.43 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(1343,a,1339,a)]. 4.22/4.43 1344 -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_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(184)]. 4.22/4.43 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_Ozero__class_Ozero(tc_Int_Oint) != B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1344,a,1339,a)]. 4.22/4.43 1345 -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_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(184)]. 4.22/4.43 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_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). [resolve(1345,a,1339,a)]. 4.22/4.43 1346 -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_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(184)]. 4.22/4.45 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_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1346,a,1339,a)]. 4.22/4.45 1347 -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(199)]. 4.22/4.45 1348 -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(332)]. 4.22/4.45 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(1348,a,1339,a)]. 4.22/4.45 1349 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 4.22/4.45 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(1349,a,1340,a)]. 4.22/4.45 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(1349,a,1341,a)]. 4.22/4.45 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(1349,a,1342,a)]. 4.22/4.45 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(1349,a,1343,a)]. 4.22/4.45 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_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1349,a,1344,a)]. 4.22/4.45 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_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). [resolve(1349,a,1345,a)]. 4.22/4.45 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_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1349,a,1346,a)]. 4.22/4.47 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(1349,a,1348,a)]. 4.22/4.47 1350 -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(540)]. 4.22/4.47 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(1350,a,1339,a)]. 4.22/4.47 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(1350,a,1349,a)]. 4.22/4.47 1351 -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(626)]. 4.22/4.47 1352 -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(629)]. 4.22/4.47 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(1352,a,1339,a)]. 4.22/4.47 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(1352,a,1349,a)]. 4.22/4.47 1353 -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(654)]. 4.22/4.47 1354 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 4.22/4.47 Derived: -c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1354,a,1341,a)]. 4.22/4.47 Derived: -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) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1354,a,1342,a)]. 4.22/4.47 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(1354,a,1343,a)]. 4.22/4.48 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_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1354,a,1344,a)]. 4.22/4.48 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_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). [resolve(1354,a,1345,a)]. 4.22/4.48 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_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1354,a,1346,a)]. 4.22/4.48 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(1354,a,1348,a)]. 4.22/4.48 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1354,a,1350,a)]. 4.22/4.48 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1354,a,1352,a)]. 4.22/4.48 1355 -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(755)]. 4.22/4.48 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(1355,a,1339,a)]. 4.22/4.48 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(1355,a,1349,a)]. 4.22/4.48 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(1355,a,1354,a)]. 4.22/4.48 1356 -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(795)]. 4.22/4.48 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(1356,a,1339,a)]. 4.29/4.49 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(1356,a,1349,a)]. 4.29/4.49 1357 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1357,a,1340,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1357,a,1341,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1357,a,1342,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1357,a,1343,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != B | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A | c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1357,a,1344,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B | c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1357,a,1345,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1357,a,1346,a)]. 4.29/4.49 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,A)). [resolve(1357,a,1348,a)]. 4.29/4.57 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1357,a,1350,a)]. 4.29/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1357,a,1352,a)]. 4.29/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1357,a,1355,a)]. 4.29/4.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(1357,a,1356,a)]. 4.29/4.57 1358 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.29/4.57 1359 -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(37)]. 4.29/4.57 1360 -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(51)]. 4.29/4.57 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(1360,a,1358,a)]. 4.29/4.57 1361 -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(96)]. 4.29/4.57 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(1361,a,1358,a)]. 4.38/4.58 1362 -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(124)]. 4.38/4.58 1363 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.38/4.58 1364 -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(190)]. 4.38/4.58 1365 -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(231)]. 4.38/4.58 1366 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.38/4.58 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,B)). [resolve(1366,a,1359,a)]. 4.38/4.58 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1366,a,1360,a)]. 4.38/4.58 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A). [resolve(1366,a,1361,a)]. 4.38/4.58 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1366,a,1365,a)]. 4.38/4.58 1367 -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(313)]. 4.38/4.58 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_Otimes__class_Otimes(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1367,a,1358,a)]. 4.38/4.58 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1367,a,1366,a)]. 4.38/4.59 1368 -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(401)]. 4.38/4.59 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(1368,a,1358,a)]. 4.38/4.59 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(1368,a,1363,a)]. 4.38/4.59 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,D) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1368,a,1366,a)]. 4.38/4.59 1369 -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(419)]. 4.38/4.59 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(1369,a,1358,a)]. 4.38/4.59 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(1369,a,1363,a)]. 4.38/4.59 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1369,a,1366,a)]. 4.40/4.59 1370 -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(425)]. 4.40/4.59 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(1370,a,1363,a)]. 4.40/4.59 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1370,a,1366,a)]. 4.40/4.59 1371 -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(481)]. 4.40/4.59 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(1371,a,1358,a)]. 4.40/4.59 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(1371,a,1363,a)]. 4.40/4.59 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1371,a,1366,a)]. 4.40/4.59 1372 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 4.40/4.59 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(1372,a,1360,a)]. 4.40/4.60 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(1372,a,1361,a)]. 4.40/4.60 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),B) | 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(1372,a,1367,a)]. 4.40/4.60 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(1372,a,1368,a)]. 4.40/4.60 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(1372,a,1369,a)]. 4.40/4.60 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(1372,a,1370,a)]. 4.40/4.60 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(1372,a,1371,a)]. 4.40/4.60 1373 -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(514)]. 4.40/4.60 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(1373,a,1358,a)]. 4.40/4.60 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(1373,a,1363,a)]. 4.40/4.60 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,D) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1373,a,1366,a)]. 4.40/4.62 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(1373,a,1372,a)]. 4.40/4.62 1374 -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(520)]. 4.40/4.62 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1374,a,1366,a)]. 4.40/4.62 1375 -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(637)]. 4.40/4.62 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(1375,a,1358,a)]. 4.40/4.62 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(1375,a,1363,a)]. 4.40/4.62 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B). [resolve(1375,a,1366,a)]. 4.40/4.62 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(1375,a,1372,a)]. 4.40/4.62 1376 -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(756)]. 4.40/4.62 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(1376,a,1363,a)]. 4.75/4.99 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,B)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1376,a,1366,a)]. 4.75/4.99 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(1376,a,1372,a)]. 4.75/4.99 1377 -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(927)]. 4.75/4.99 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,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1377,a,1363,a)]. 4.75/4.99 1378 -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(729)]. 4.75/4.99 1379 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 4.75/4.99 1380 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 4.75/4.99 1381 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 4.75/4.99 1382 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 4.75/4.99 1383 -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(923)]. 4.75/4.99 1384 -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(133)]. 4.75/4.99 1385 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption]. 4.75/4.99 1386 -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(335)]. 4.75/4.99 1387 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption]. 4.75/4.99 1388 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption]. 4.75/4.99 1389 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) # label(axiom). [assumption]. 4.75/4.99 1390 -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(159)]. 4.75/4.99 1391 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom). [assumption]. 4.75/4.99 1392 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption]. 4.75/4.99 1393 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(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(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_less__add__iff2) # label(axiom). [clausify(446)]. 4.75/4.99 Derived: -c_Orderings_Oord__class_Oless(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(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(1393,a,1391,a)]. 4.75/4.99 Derived: -c_Orderings_Oord__class_Oless(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(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(1393,a,1392,a)]. 4.75/4.99 1394 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(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(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_less__add__iff2) # label(axiom). [clausify(446)]. 4.75/4.99 Derived: c_Orderings_Oord__class_Oless(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(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(1394,a,1391,a)]. 4.75/4.99 Derived: c_Orderings_Oord__class_Oless(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(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(1394,a,1392,a)]. 4.75/4.99 1395 -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(458)]. 4.75/4.99 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(1395,a,1391,a)]. 4.75/4.99 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(1395,a,1392,a)]. 4.75/4.99 1396 -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(458)]. 4.81/5.00 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(1396,a,1391,a)]. 4.81/5.00 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(1396,a,1392,a)]. 4.81/5.00 1397 -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,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F) # label(fact_less__add__iff1) # label(axiom). [clausify(476)]. 4.81/5.00 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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D),B),C),E). [resolve(1397,a,1391,a)]. 4.81/5.00 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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D),B),C),E). [resolve(1397,a,1392,a)]. 4.81/5.00 1398 -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,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F) # label(fact_less__add__iff1) # label(axiom). [clausify(476)]. 4.81/5.00 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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D),B),C),E). [resolve(1398,a,1391,a)]. 4.81/5.00 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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D),B),C),E). [resolve(1398,a,1392,a)]. 4.81/5.00 1399 -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(504)]. 4.81/5.01 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(1399,a,1391,a)]. 4.81/5.01 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(1399,a,1392,a)]. 4.81/5.01 1400 -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(524)]. 4.81/5.01 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(1400,a,1391,a)]. 4.81/5.01 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(1400,a,1392,a)]. 4.81/5.01 1401 -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(524)]. 4.81/5.01 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(1401,a,1391,a)]. 4.81/5.01 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(1401,a,1392,a)]. 4.81/5.01 1402 -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(667)]. 4.81/5.01 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(1402,a,1391,a)]. 5.05/5.28 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(1402,a,1392,a)]. 5.05/5.28 1403 -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(714)]. 5.05/5.28 1404 -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(714)]. 5.05/5.28 1405 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption]. 5.05/5.28 1406 -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(42)]. 5.05/5.28 1407 -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(127)]. 5.05/5.28 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(1405,a,1406,a)]. 5.05/5.28 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(1405,a,1407,a)]. 5.05/5.28 1408 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide_Oadd) # label(axiom). [clausify(837)]. 5.05/5.28 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1408,a,1405,a)]. 5.05/5.28 1409 -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(859)]. 5.05/5.28 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(1409,a,1405,a)]. 5.05/5.28 1410 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom). [assumption]. 5.05/5.28 1411 -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(45)]. 5.05/5.28 1412 -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(46)]. 5.33/5.53 1413 -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(260)]. 5.33/5.53 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(1410,a,1411,a)]. 5.33/5.53 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(1410,a,1412,a)]. 5.33/5.53 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(1410,a,1413,a)]. 5.33/5.53 1414 -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(765)]. 5.33/5.53 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(1414,a,1410,a)]. 5.33/5.53 1415 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption]. 5.33/5.53 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(1415,a,1411,a)]. 5.33/5.53 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(1415,a,1412,a)]. 5.33/5.53 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(1415,a,1413,a)]. 5.33/5.53 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(1415,a,1414,a)]. 5.33/5.53 1416 -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(640)]. 5.33/5.53 1417 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption]. 5.33/5.53 1418 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption]. 5.33/5.53 1419 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) # label(axiom). [assumption]. 5.33/5.53 1420 -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(660)]. 5.33/5.53 1421 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption]. 5.33/5.53 1422 -class_Rings_Oring__1(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))) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Oone__class_Oone(A)) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(410)]. 5.33/5.53 1423 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption]. 5.33/5.53 1424 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption]. 5.33/5.53 Derived: 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))) = 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)). [resolve(1422,a,1423,a)]. 5.43/5.69 Derived: 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))) = 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)). [resolve(1422,a,1424,a)]. 5.43/5.69 1425 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom). [assumption]. 5.43/5.69 1426 -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(48)]. 5.43/5.69 1427 -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(108)]. 5.43/5.69 1428 -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(108)]. 5.43/5.69 1429 -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(194)]. 5.43/5.69 1430 -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(205)]. 5.43/5.69 1431 -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(213)]. 5.43/5.69 1432 -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(236)]. 5.43/5.69 1433 -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(280)]. 5.43/5.69 1434 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_add__divide__distrib) # label(axiom). [clausify(281)]. 5.43/5.69 1435 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | c_Groups_Otimes__class_Otimes(A,D,B) = C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(351)]. 5.43/5.69 1436 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | c_Groups_Otimes__class_Otimes(A,D,B) != C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(351)]. 5.43/5.69 1437 -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(352)]. 5.43/5.69 1438 -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(376)]. 5.43/5.69 1439 -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(582)]. 5.59/5.79 1440 -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) | B = C # label(fact_right__inverse__eq) # label(axiom). [clausify(591)]. 5.59/5.79 1441 -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) | B != C # label(fact_right__inverse__eq) # label(axiom). [clausify(591)]. 5.59/5.79 1442 -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(632)]. 5.59/5.79 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(1425,a,1427,a)]. 5.59/5.79 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(1425,a,1428,a)]. 5.59/5.79 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(1425,a,1430,a)]. 5.59/5.79 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1425,a,1431,a)]. 5.59/5.79 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(1425,a,1432,a)]. 5.59/5.79 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(1425,a,1438,a)]. 5.59/5.79 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(1425,a,1439,a)]. 5.59/5.79 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) | A = B. [resolve(1425,a,1440,a)]. 5.59/5.79 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) | A != B. [resolve(1425,a,1441,a)]. 5.59/5.79 1443 -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(90)]. 5.59/5.79 1444 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 5.59/5.79 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1443,a,1444,a)]. 5.59/5.79 1445 -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(90)]. 5.59/5.79 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1445,a,1444,a)]. 5.59/5.79 1446 -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(169)]. 5.59/5.79 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(1446,a,1444,a)]. 5.61/5.81 1447 -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(169)]. 5.61/5.81 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(1447,a,1444,a)]. 5.61/5.81 1448 -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(243)]. 5.61/5.81 1449 -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(243)]. 5.61/5.81 1450 -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(272)]. 5.61/5.81 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(1450,a,1444,a)]. 5.61/5.81 1451 -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(272)]. 5.61/5.81 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(1451,a,1444,a)]. 5.61/5.81 1452 -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(368)]. 5.61/5.81 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(1452,a,1444,a)]. 5.61/5.81 1453 -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(368)]. 5.61/5.81 1454 -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(613)]. 5.61/5.81 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(1454,a,1444,a)]. 5.61/5.81 1455 -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(613)]. 5.61/5.81 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(1455,a,1444,a)]. 5.61/5.81 1456 -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(621)]. 5.63/5.83 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(1456,a,1444,a)]. 5.63/5.83 1457 -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(621)]. 5.63/5.83 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(1457,a,1444,a)]. 5.63/5.83 1458 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 5.63/5.83 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1458,a,1443,a)]. 5.63/5.83 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1458,a,1445,a)]. 5.63/5.83 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(1458,a,1446,a)]. 5.63/5.83 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(1458,a,1447,a)]. 5.63/5.83 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(1458,a,1450,a)]. 5.63/5.83 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(1458,a,1451,a)]. 5.63/5.83 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(1458,a,1452,a)]. 5.63/5.83 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(1458,a,1454,a)]. 5.63/5.83 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(1458,a,1455,a)]. 5.63/5.83 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(1458,a,1456,a)]. 5.63/5.83 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(1458,a,1457,a)]. 5.63/5.83 1459 -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(800)]. 5.63/5.83 1460 -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(800)]. 5.63/5.83 1461 -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(828)]. 5.63/5.83 1462 -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(828)]. 5.73/5.94 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(1462,a,1444,a)]. 5.73/5.94 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(1462,a,1458,a)]. 5.73/5.94 1463 -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(863)]. 5.73/5.94 1464 -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(863)]. 5.73/5.94 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(1464,a,1444,a)]. 5.73/5.94 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(1464,a,1458,a)]. 5.73/5.94 1465 -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(910)]. 5.73/5.94 1466 -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(910)]. 5.73/5.94 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(1466,a,1444,a)]. 5.73/5.94 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(1466,a,1458,a)]. 5.73/5.94 1467 class_Rings_Osemiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__1) # label(axiom). [assumption]. 5.73/5.94 1468 -class_Rings_Osemiring__1(A) | c_Int_Oiszero(A,c_Groups_Ozero__class_Ozero(A)) # label(fact_iszero__0) # label(axiom). [clausify(58)]. 5.73/5.94 Derived: c_Int_Oiszero(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1467,a,1468,a)]. 5.73/5.94 1469 -class_Rings_Osemiring__1(A) | -c_Int_Oiszero(A,c_Groups_Oone__class_Oone(A)) # label(fact_not__iszero__1) # label(axiom). [clausify(357)]. 5.73/5.94 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1469,a,1467,a)]. 5.73/5.94 1470 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) # label(axiom). [assumption]. 5.73/5.94 Derived: c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1470,a,1468,a)]. 5.73/5.94 Derived: -c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(1470,a,1469,a)]. 5.81/6.06 1471 -class_Rings_Osemiring__1(A) | -c_Int_Oiszero(A,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_iszero__def) # label(axiom). [clausify(636)]. 5.81/6.06 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1471,a,1467,a)]. 5.81/6.06 Derived: -c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,A) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(1471,a,1470,a)]. 5.81/6.06 1472 -class_Rings_Osemiring__1(A) | c_Int_Oiszero(A,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_iszero__def) # label(axiom). [clausify(636)]. 5.81/6.06 Derived: c_Int_Oiszero(tc_RealDef_Oreal,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1472,a,1467,a)]. 5.81/6.06 Derived: c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,A) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A. [resolve(1472,a,1470,a)]. 5.81/6.06 1473 class_Rings_Osemiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__1) # label(axiom). [assumption]. 5.81/6.06 Derived: c_Int_Oiszero(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1473,a,1468,a)]. 5.81/6.06 Derived: -c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1473,a,1469,a)]. 5.81/6.06 Derived: -c_Int_Oiszero(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1473,a,1471,a)]. 5.81/6.06 Derived: c_Int_Oiszero(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1473,a,1472,a)]. 5.81/6.06 1474 class_Rings_Osemiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__1) # label(axiom). [assumption]. 5.81/6.06 Derived: c_Int_Oiszero(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1474,a,1468,a)]. 5.81/6.06 Derived: -c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1474,a,1469,a)]. 5.81/6.06 Derived: -c_Int_Oiszero(tc_Nat_Onat,A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1474,a,1471,a)]. 5.81/6.06 Derived: c_Int_Oiszero(tc_Nat_Onat,A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A. [resolve(1474,a,1472,a)]. 5.81/6.06 1475 -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(289)]. 5.81/6.06 1476 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom). [assumption]. 5.81/6.06 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(1475,a,1476,a)]. 5.81/6.06 1477 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption]. 5.81/6.06 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(1477,a,1475,a)]. 5.94/6.19 1478 class_Int_Onumber(tc_Int_Oint) # label(arity_Int__Oint__Int_Onumber) # label(axiom). [assumption]. 5.94/6.19 1479 -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(59)]. 5.94/6.19 1480 -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(A,B,c_Groups_Ozero__class_Ozero(A)) | 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(59)]. 5.94/6.19 1481 -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_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) | 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(59)]. 5.94/6.19 1482 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(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(59)]. 5.94/6.19 1483 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(A,C,c_Groups_Ozero__class_Ozero(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_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(59)]. 5.94/6.19 1484 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,D,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | 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(59)]. 5.94/6.19 1485 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,D,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C)) | -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_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(59)]. 5.94/6.19 1486 -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(59)]. 5.94/6.19 1487 -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(59)]. 5.94/6.19 1488 -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(59)]. 5.94/6.19 1489 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != C | c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)) = C # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(85)]. 5.94/6.19 1490 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)) != D | c_Int_Onumber__class_Onumber__of(A,C) = c_Groups_Ozero__class_Ozero(A) | c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C)) = B # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(85)]. 5.94/6.19 1491 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,C)) != D | c_Groups_Ozero__class_Ozero(A) != B | c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,C)) = B # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(85)]. 5.94/6.19 1492 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B)) = D | c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)) != C # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(85)]. 5.94/6.19 1493 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B)) != C # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(85)]. 5.94/6.19 1494 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,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,c_Int_Onumber__class_Onumber__of(A,D),C)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1495 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,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,c_Int_Onumber__class_Onumber__of(A,D),C),B) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1496 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,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),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1497 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,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),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1498 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1499 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1500 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1501 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(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_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1502 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1503 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__le__eq__number__of) # label(axiom). [clausify(226)]. 5.94/6.19 1504 -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_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(244)]. 5.94/6.19 1505 -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,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(244)]. 5.94/6.19 1506 -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_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(244)]. 5.94/6.19 1507 -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_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(244)]. 5.94/6.19 1508 -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),c_Int_Onumber__class_Onumber__of(A,C)) | 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(244)]. 5.94/6.19 1509 -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_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(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(244)]. 5.94/6.19 1510 -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_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),D),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_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(244)]. 5.94/6.19 1511 -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,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(244)]. 5.94/6.19 1512 -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_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(244)]. 5.94/6.19 1513 -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_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(244)]. 5.94/6.19 1514 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1515 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1516 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1517 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1518 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1519 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1520 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1521 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1522 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 1523 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(259)]. 5.94/6.19 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = B. [resolve(1478,a,1489,a)]. 5.94/6.19 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) != C | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = A. [resolve(1478,a,1490,a)]. 5.94/6.19 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) != C | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = A. [resolve(1478,a,1491,a)]. 5.94/6.19 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) = C | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) != B. [resolve(1478,a,1492,a)]. 5.94/6.21 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) != B. [resolve(1478,a,1493,a)]. 5.94/6.21 1524 -class_Int_Onumber(A) | -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Int_Onumber__class_Onumber__of(A,D)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_left__diff__distrib__number__of) # label(axiom). [clausify(343)]. 5.94/6.21 Derived: -class_Rings_Oring(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)) = 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,C)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))). [resolve(1524,a,1478,a)]. 5.94/6.21 1525 -class_Rings_Osemiring(A) | -class_Int_Onumber(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(377)]. 5.94/6.21 1526 -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_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,c_Int_Onumber__class_Onumber__of(A,B),D),C) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | -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,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C),B). [resolve(1526,a,1478,a)]. 5.94/6.21 1527 -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_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,c_Int_Onumber__class_Onumber__of(A,B),D)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | 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,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C)). [resolve(1527,a,1478,a)]. 5.94/6.21 1528 -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_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_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | 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,c_Groups_Ozero__class_Ozero(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)). [resolve(1528,a,1478,a)]. 5.94/6.21 1529 -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_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_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | 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,c_Groups_Ozero__class_Ozero(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)). [resolve(1529,a,1478,a)]. 5.94/6.21 1530 -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_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,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | 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,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1530,a,1478,a)]. 5.94/6.21 1531 -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_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,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | 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,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C)) | -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(1531,a,1478,a)]. 5.94/6.21 1532 -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_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C),B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C). [resolve(1532,a,1478,a)]. 5.94/6.21 1533 -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_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D),C) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C),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_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1533,a,1478,a)]. 5.94/6.21 1534 -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_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 1535 -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_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),D)) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of) # label(axiom). [clausify(550)]. 5.94/6.21 1536 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != c_Int_Onumber__class_Onumber__of(A,D) | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C) = B # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(559)]. 5.94/6.21 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,B) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),B) = A. [resolve(1536,a,1478,a)]. 5.94/6.21 1537 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != c_Int_Onumber__class_Onumber__of(A,D) | c_Groups_Ozero__class_Ozero(A) != C | c_Int_Onumber__class_Onumber__of(A,D) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(559)]. 5.94/6.21 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,B) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1537,a,1478,a)]. 5.94/6.22 1538 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Int_Onumber__class_Onumber__of(A,D) | c_Groups_Ozero__class_Ozero(A) != C | c_Int_Onumber__class_Onumber__of(A,D) != c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(559)]. 5.94/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,B) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1538,a,1478,a)]. 5.94/6.22 1539 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Int_Onumber__class_Onumber__of(A,D) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(559)]. 5.94/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,B) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1539,a,1478,a)]. 5.94/6.22 1540 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Int_Onumber__class_Onumber__of(A,D) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D),C) != B | c_Int_Onumber__class_Onumber__of(A,D) != c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(559)]. 5.94/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Int_Oint) | c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,B) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),B) != A | c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1540,a,1478,a)]. 5.94/6.22 1541 -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(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(580)]. 5.94/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(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_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))). [resolve(1541,b,1478,a)]. 5.94/6.22 1542 -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,c_Groups_Ozero__class_Ozero(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_Rings_Oinverse__class_Odivide(A,D,c_Int_Onumber__class_Onumber__of(A,B))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(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,B,c_Groups_Ozero__class_Ozero(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_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))). [resolve(1542,b,1478,a)]. 6.04/6.22 1543 -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,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Otimes__class_Otimes(A,C,c_Int_Onumber__class_Onumber__of(A,B))) | 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(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(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,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))). [resolve(1543,b,1478,a)]. 6.04/6.22 1544 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,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(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | -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,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))). [resolve(1544,b,1478,a)]. 6.04/6.22 1545 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Otimes__class_Otimes(A,B,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(580)]. 6.04/6.22 1546 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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_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,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(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),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_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))). [resolve(1546,b,1478,a)]. 6.04/6.22 1547 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Otimes__class_Otimes(A,B,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(580)]. 6.04/6.22 1548 -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_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(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(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_Groups_Otimes__class_Otimes(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)),C) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))). [resolve(1548,b,1478,a)]. 6.04/6.22 1549 -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(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(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(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_Onumber__class_Onumber__of(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,B,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))). [resolve(1549,b,1478,a)]. 6.04/6.22 1550 -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(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(580)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(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_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))). [resolve(1550,b,1478,a)]. 6.04/6.22 1551 -class_Int_Onumber(A) | -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Omin(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,B) # label(fact_min__number__of) # label(axiom). [clausify(587)]. 6.04/6.22 1552 -class_Int_Onumber(A) | -class_Orderings_Oord(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Omin(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) = c_Int_Onumber__class_Onumber__of(A,C) # label(fact_min__number__of) # label(axiom). [clausify(587)]. 6.04/6.22 Derived: -class_Orderings_Oord(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(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_Omin(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B). [resolve(1552,a,1478,a)]. 6.04/6.22 1553 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Int_Onumber) # label(axiom). [assumption]. 6.04/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != B | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) = B. [resolve(1553,a,1489,a)]. 6.04/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) != C | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) = A. [resolve(1553,a,1490,a)]. 6.04/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) != C | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) = A. [resolve(1553,a,1491,a)]. 6.04/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) = C | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) != B. [resolve(1553,a,1492,a)]. 6.04/6.22 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) != B. [resolve(1553,a,1493,a)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B)). [resolve(1553,a,1494,a)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B),A). [resolve(1553,a,1495,a)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)). [resolve(1553,a,1496,a)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)). [resolve(1553,a,1497,a)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1498,a)]. 6.04/6.22 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)). [resolve(1553,a,1499,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B). [resolve(1553,a,1500,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)). [resolve(1553,a,1501,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B),A) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1502,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)). [resolve(1553,a,1503,a)]. 6.04/6.23 Derived: -class_Rings_Oring(tc_Code__Numeral_Ocode__numeral) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))). [resolve(1553,a,1524,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C),B). [resolve(1553,a,1526,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C)). [resolve(1553,a,1527,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1528,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1529,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1530,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1531,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C),B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C). [resolve(1553,a,1532,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1553,a,1533,a)]. 6.04/6.23 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B) != c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B) = A. [resolve(1553,a,1536,a)]. 6.04/6.23 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B) != c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != B | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1553,a,1537,a)]. 6.04/6.23 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != B | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1553,a,1538,a)]. 6.04/6.23 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B) != A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B. [resolve(1553,a,1539,a)]. 6.04/6.23 Derived: -class_Fields_Ofield__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,B) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),B) != A | c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1553,a,1540,a)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))). [resolve(1553,a,1541,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))). [resolve(1553,a,1542,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))). [resolve(1553,a,1543,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))). [resolve(1553,a,1544,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))). [resolve(1553,a,1546,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))). [resolve(1553,a,1548,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))). [resolve(1553,a,1549,b)]. 6.04/6.23 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A))). [resolve(1553,a,1550,b)]. 6.04/6.23 Derived: -class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B). [resolve(1553,a,1552,a)]. 6.04/6.23 1554 -class_Rings_Oring(A) | -class_Int_Onumber(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ominus__class_Ominus(A,C,D)) = 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)) # label(fact_right__diff__distrib__number__of) # label(axiom). [clausify(615)]. 6.04/6.23 Derived: -class_Rings_Oring(tc_Int_Oint) | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),C)). [resolve(1554,b,1478,a)]. 6.04/6.24 Derived: -class_Rings_Oring(tc_Code__Numeral_Ocode__numeral) | c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral,B,C)) = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),B),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,A),C)). [resolve(1554,b,1553,a)]. 6.04/6.24 1555 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(733)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -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,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),B). [resolve(1555,b,1478,a)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)),B). [resolve(1555,b,1553,a)]. 6.04/6.24 1556 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(733)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | 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,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))). [resolve(1556,b,1478,a)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))). [resolve(1556,b,1553,a)]. 6.04/6.24 1557 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(733)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | 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,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),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)). [resolve(1557,b,1478,a)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1557,b,1553,a)]. 6.04/6.24 1558 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(733)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | 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,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),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)). [resolve(1558,b,1478,a)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1558,b,1553,a)]. 6.04/6.24 1559 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Groups_Otimes__class_Otimes(A,B,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)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(733)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | 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,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1559,b,1478,a)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1559,b,1553,a)]. 6.04/6.24 1560 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(733)]. 6.04/6.24 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | 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,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1560,b,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1560,b,1553,a)]. 6.04/6.25 1561 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) | -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(733)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),B) | -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,C)). [resolve(1561,b,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)),B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)). [resolve(1561,b,1553,a)]. 6.04/6.25 1562 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) | 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(733)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),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)). [resolve(1562,b,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1562,b,1553,a)]. 6.04/6.25 1563 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) | -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_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(733)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1563,b,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1563,b,1553,a)]. 6.04/6.25 1564 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,c_Groups_Otimes__class_Otimes(A,B,c_Int_Onumber__class_Onumber__of(A,D)),C) | -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,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of1) # label(axiom). [clausify(733)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1564,b,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1564,b,1553,a)]. 6.04/6.25 1565 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | -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,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))). [resolve(1565,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))). [resolve(1565,a,1553,a)]. 6.04/6.25 1566 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | 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,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(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),C). [resolve(1566,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C). [resolve(1566,a,1553,a)]. 6.04/6.25 1567 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | 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,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),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,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),A). [resolve(1567,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),A). [resolve(1567,a,1553,a)]. 6.04/6.25 1568 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | 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,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),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,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),A). [resolve(1568,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),A). [resolve(1568,a,1553,a)]. 6.04/6.25 1569 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(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)) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | 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,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_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1569,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1569,a,1553,a)]. 6.04/6.25 1570 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | 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,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,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),A). [resolve(1570,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),A). [resolve(1570,a,1553,a)]. 6.04/6.25 1571 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))) | -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,B)). [resolve(1571,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)). [resolve(1571,a,1553,a)]. 6.04/6.25 1572 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,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__eq(A,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),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,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),A). [resolve(1572,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),A). [resolve(1572,a,1553,a)]. 6.04/6.25 1573 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C))) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(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_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1573,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1573,a,1553,a)]. 6.04/6.25 1574 -class_Int_Onumber(A) | -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(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_Int_Onumber__class_Onumber__of(A,C)),B) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(738)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Rings_Oinverse__class_Odivide(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,c_Int_Onumber__class_Onumber__of(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,C,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)),A). [resolve(1574,a,1478,a)]. 6.04/6.25 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Rings_Oinverse__class_Odivide(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B))) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),C) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C,c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,B)),A). [resolve(1574,a,1553,a)]. 6.04/6.26 1575 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) != D | c_Int_Onumber__class_Onumber__of(A,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = D # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(746)]. 6.04/6.26 1576 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) != D | c_Int_Onumber__class_Onumber__of(A,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)) = B # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(746)]. 6.04/6.26 1577 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | c_Int_Onumber__class_Onumber__of(A,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)) != B # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(746)]. 6.04/6.26 1578 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | c_Groups_Ozero__class_Ozero(A) != D | c_Int_Onumber__class_Onumber__of(A,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(746)]. 6.04/6.26 1579 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | c_Groups_Ozero__class_Ozero(A) != D | c_Groups_Otimes__class_Otimes(A,D,c_Int_Onumber__class_Onumber__of(A,C)) != B # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(746)]. 6.04/6.26 1580 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Int_Onumber__class_Onumber__of(A,C) != c_Groups_Ozero__class_Ozero(A) | c_Rings_Oinverse__class_Odivide(A,D,B) = c_Int_Onumber__class_Onumber__of(A,C) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(763)]. 6.04/6.26 1581 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C) != D | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) = c_Int_Onumber__class_Onumber__of(A,B) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(763)]. 6.04/6.26 1582 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),C) != D | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Rings_Oinverse__class_Odivide(A,D,C) = c_Int_Onumber__class_Onumber__of(A,B) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(763)]. 6.04/6.26 1583 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C),B) = D | c_Rings_Oinverse__class_Odivide(A,D,B) != c_Int_Onumber__class_Onumber__of(A,C) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(763)]. 6.04/6.26 1584 -class_Int_Onumber(A) | -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Int_Onumber__class_Onumber__of(A,C) = c_Groups_Ozero__class_Ozero(A) | c_Rings_Oinverse__class_Odivide(A,D,B) != c_Int_Onumber__class_Onumber__of(A,C) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(763)]. 6.04/6.26 1585 -class_Int_Onumber(A) | -class_Rings_Osemiring(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(826)]. 6.04/6.27 1586 class_Int_Onumber(tc_Nat_Onat) # label(arity_Nat__Onat__Int_Onumber) # label(axiom). [assumption]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,A)). [resolve(1586,a,1479,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,A)). [resolve(1586,a,1480,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),A)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,A)). [resolve(1586,a,1481,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),C) | -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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,B)). [resolve(1586,a,1482,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,B)). [resolve(1586,a,1483,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,B)). [resolve(1586,a,1484,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,B)). [resolve(1586,a,1485,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -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_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),A),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,A)). [resolve(1586,a,1486,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),A)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,A)). [resolve(1586,a,1487,b)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,A)). [resolve(1586,a,1488,b)]. 6.04/6.27 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = B. [resolve(1586,a,1489,a)]. 6.04/6.27 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != C | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = A. [resolve(1586,a,1490,a)]. 6.04/6.27 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != C | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = A. [resolve(1586,a,1491,a)]. 6.04/6.27 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = C | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) != B. [resolve(1586,a,1492,a)]. 6.04/6.27 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) != B. [resolve(1586,a,1493,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | -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_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B)). [resolve(1586,a,1494,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | 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,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B),A). [resolve(1586,a,1495,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | 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,B,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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)). [resolve(1586,a,1497,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | 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_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1498,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | 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_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)). [resolve(1586,a,1499,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). [resolve(1586,a,1500,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)). [resolve(1586,a,1501,a)]. 6.04/6.27 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1502,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)). [resolve(1586,a,1503,a)]. 6.04/6.28 Derived: -class_Rings_Oring(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))). [resolve(1586,a,1524,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | -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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C),B). [resolve(1586,a,1526,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C)). [resolve(1586,a,1527,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1528,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1529,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | 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,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1530,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | 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,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1531,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C). [resolve(1586,a,1532,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1533,a)]. 6.04/6.28 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B) = A. [resolve(1586,a,1536,a)]. 6.04/6.28 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1586,a,1537,a)]. 6.04/6.28 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1586,a,1538,a)]. 6.04/6.28 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1586,a,1539,a)]. 6.04/6.28 Derived: -class_Fields_Ofield__inverse__zero(tc_Nat_Onat) | c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,B) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),B) != A | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1586,a,1540,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))). [resolve(1586,a,1541,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))). [resolve(1586,a,1542,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))). [resolve(1586,a,1543,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -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,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))). [resolve(1586,a,1544,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))). [resolve(1586,a,1546,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -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,A)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))). [resolve(1586,a,1548,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))). [resolve(1586,a,1549,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | 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,A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))). [resolve(1586,a,1550,b)]. 6.04/6.28 Derived: -class_Orderings_Oord(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(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_Omin(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B). [resolve(1586,a,1552,a)]. 6.04/6.28 Derived: -class_Rings_Oring(tc_Nat_Onat) | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)) = c_Groups_Ominus__class_Ominus(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)). [resolve(1586,a,1554,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -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,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),B). [resolve(1586,a,1555,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | 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,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))). [resolve(1586,a,1556,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | 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,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1557,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | 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,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1558,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | 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,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1559,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | 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,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1560,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),B) | -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,C)). [resolve(1586,a,1561,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1562,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1563,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1564,b)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -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,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))). [resolve(1586,a,1565,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | 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,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),A). [resolve(1586,a,1567,a)]. 6.04/6.28 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | 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,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),A). [resolve(1586,a,1568,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | 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,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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1569,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | 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,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,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),A). [resolve(1586,a,1570,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))) | -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,B)). [resolve(1586,a,1571,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),A). [resolve(1586,a,1572,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1586,a,1573,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_Nat_Onat) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,c_Int_Onumber__class_Onumber__of(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,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),A). [resolve(1586,a,1574,a)]. 6.04/6.29 1587 class_Int_Onumber(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Onumber) # label(axiom). [assumption]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(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__eq(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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1587,a,1479,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(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__eq(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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1587,a,1480,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(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__eq(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__eq(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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1587,a,1481,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -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,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1587,a,1482,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -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,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,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1587,a,1483,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -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,A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1587,a,1484,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -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,A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),B)) | -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_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1587,a,1485,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(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__eq(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__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1587,a,1486,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(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__eq(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__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)). [resolve(1587,a,1487,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(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__eq(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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1587,a,1488,b)]. 6.04/6.29 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = B. [resolve(1587,a,1489,a)]. 6.04/6.29 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) != C | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = A. [resolve(1587,a,1490,a)]. 6.04/6.29 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) != C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = A. [resolve(1587,a,1491,a)]. 6.04/6.29 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) = C | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) != B. [resolve(1587,a,1492,a)]. 6.04/6.29 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) != B. [resolve(1587,a,1493,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,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),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),B)). [resolve(1587,a,1494,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,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),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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),B),A). [resolve(1587,a,1495,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,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),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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1587,a,1496,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,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),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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1587,a,1497,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,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),B) | -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),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1498,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,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),B) | -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),B),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,C)). [resolve(1587,a,1499,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1587,a,1500,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)). [resolve(1587,a,1501,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),B)) | -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),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1502,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),B)) | -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),B),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,C)). [resolve(1587,a,1503,a)]. 6.04/6.29 Derived: -class_Rings_Oring(tc_RealDef_Oreal) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)) = 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,C)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C))). [resolve(1587,a,1524,a)]. 6.04/6.29 Derived: -class_Rings_Osemiring(tc_RealDef_Oreal) | c_Groups_Oplus__class_Oplus(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_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). [resolve(1587,a,1525,b)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C),B). [resolve(1587,a,1526,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C)). [resolve(1587,a,1527,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1528,a)]. 6.04/6.29 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1529,a)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1530,a)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C)) | -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(1587,a,1531,a)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1587,a,1532,a)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1533,a)]. 6.04/6.30 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1587,a,1537,a)]. 6.04/6.30 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1587,a,1538,a)]. 6.04/6.30 Derived: -class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C) | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),B) != A | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1587,a,1540,a)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(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(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))). [resolve(1587,a,1541,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,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,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))). [resolve(1587,a,1542,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,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,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))). [resolve(1587,a,1543,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(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(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1587,a,1544,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(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,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,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1587,a,1546,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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_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,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))). [resolve(1587,a,1548,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))). [resolve(1587,a,1549,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(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(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A))). [resolve(1587,a,1550,b)]. 6.04/6.30 Derived: -class_Orderings_Oord(tc_RealDef_Oreal) | 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)) | c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B). [resolve(1587,a,1552,a)]. 6.04/6.30 Derived: -class_Rings_Oring(tc_RealDef_Oreal) | 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)) = 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)). [resolve(1587,a,1554,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1587,a,1555,b)]. 6.04/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1587,a,1556,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1587,a,1557,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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(1587,a,1558,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1559,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1560,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B) | -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(1587,a,1561,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B) | 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(1587,a,1562,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B) | -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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1563,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)),B) | -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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1564,b)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))). [resolve(1587,a,1565,a)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1587,a,1566,a)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1587,a,1567,a)]. 6.14/6.30 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1587,a,1568,a)]. 6.23/6.44 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__eq(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)). [resolve(1587,a,1569,a)]. 6.23/6.44 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1587,a,1570,a)]. 6.23/6.44 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B))) | -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(1587,a,1571,a)]. 6.23/6.44 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,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__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1587,a,1572,a)]. 6.23/6.44 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1587,a,1573,a)]. 6.23/6.44 Derived: -class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(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,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)),A). [resolve(1587,a,1574,a)]. 6.23/6.44 1588 -class_Rings_Ocomm__ring__1(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_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom). [clausify(339)]. 6.34/6.59 1589 class_Rings_Ocomm__ring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__ring__1) # label(axiom). [assumption]. 6.34/6.59 1590 -class_Rings_Ocomm__ring__1(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)),B) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom). [clausify(575)]. 6.34/6.59 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A). [resolve(1590,a,1589,a)]. 6.34/6.59 1591 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__ring__1) # label(axiom). [assumption]. 6.34/6.59 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). [resolve(1591,a,1590,a)]. 6.34/6.59 1592 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption]. 6.34/6.59 1593 -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(64)]. 6.34/6.59 1594 -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(75)]. 6.34/6.59 1595 -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(75)]. 6.34/6.59 1596 -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(103)]. 6.34/6.59 1597 -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(104)]. 6.34/6.59 1598 -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(105)]. 6.34/6.59 1599 -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(113)]. 6.34/6.59 1600 -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(120)]. 6.34/6.59 1601 -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(129)]. 6.34/6.59 1602 -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(138)]. 6.34/6.59 1603 -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(138)]. 6.34/6.59 1604 -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_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),D) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(216)]. 6.34/6.59 1605 -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_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),D) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(216)]. 6.34/6.59 1606 -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(229)]. 6.34/6.59 1607 -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_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_neg__le__divide__eq) # label(axiom). [clausify(277)]. 6.34/6.59 1608 -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_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_neg__le__divide__eq) # label(axiom). [clausify(277)]. 6.34/6.59 1609 -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(301)]. 6.34/6.59 1610 -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(345)]. 6.34/6.59 1611 -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(363)]. 6.34/6.59 1612 -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(394)]. 6.34/6.59 1613 -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(399)]. 6.34/6.59 1614 -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(416)]. 6.34/6.59 1615 -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(416)]. 6.34/6.59 1616 -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(432)]. 6.34/6.59 1617 -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(439)]. 6.34/6.59 1618 -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(455)]. 6.34/6.59 1619 -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(539)]. 6.34/6.59 1620 -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_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(571)]. 6.34/6.59 1621 -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_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(571)]. 6.34/6.59 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(1592,a,1593,a)]. 6.34/6.59 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(1592,a,1594,a)]. 6.34/6.59 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(1592,a,1595,a)]. 6.34/6.59 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(1592,a,1596,a)]. 6.34/6.59 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(1592,a,1597,a)]. 6.34/6.59 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(1592,a,1598,a)]. 6.34/6.59 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(1592,a,1599,a)]. 6.34/6.59 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(1592,a,1600,a)]. 6.34/6.59 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_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)). [resolve(1592,a,1601,a)]. 6.34/6.59 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(1592,a,1602,a)]. 6.34/6.59 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(1592,a,1603,a)]. 6.34/6.59 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),C). [resolve(1592,a,1604,a)]. 6.34/6.59 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),C). [resolve(1592,a,1605,a)]. 6.34/6.60 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(1592,a,1606,a)]. 6.34/6.60 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_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(1592,a,1607,a)]. 6.34/6.60 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_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(1592,a,1608,a)]. 6.34/6.60 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(1592,a,1609,a)]. 6.34/6.60 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(1592,a,1610,a)]. 6.34/6.60 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,A,B)). [resolve(1592,a,1611,a)]. 6.34/6.60 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(1592,a,1612,a)]. 6.34/6.60 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(1592,a,1614,a)]. 6.34/6.60 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(1592,a,1615,a)]. 6.34/6.60 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C). [resolve(1592,a,1616,a)]. 6.44/6.61 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(1592,a,1618,a)]. 6.44/6.61 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(1592,a,1619,a)]. 6.44/6.61 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,A),C). [resolve(1592,a,1620,a)]. 6.44/6.61 1622 -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(588)]. 6.44/6.61 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(1622,a,1592,a)]. 6.44/6.61 1623 -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_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(669)]. 6.44/6.61 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,A)). [resolve(1623,a,1592,a)]. 6.44/6.61 1624 -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_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(669)]. 6.44/6.61 1625 -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(678)]. 6.44/6.61 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(1625,a,1592,a)]. 6.44/6.61 1626 -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(768)]. 6.53/6.74 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(1626,a,1592,a)]. 6.53/6.74 1627 -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(783)]. 6.53/6.74 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(1627,a,1592,a)]. 6.53/6.74 1628 -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_Otimes__class_Otimes(A,C,B),D) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(790)]. 6.53/6.74 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_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(1628,a,1592,a)]. 6.53/6.74 1629 -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_Otimes__class_Otimes(A,C,B),D) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(790)]. 6.53/6.74 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_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(1629,a,1592,a)]. 6.53/6.74 1630 -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(914)]. 6.53/6.74 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(1630,a,1592,a)]. 6.53/6.74 1631 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 6.53/6.74 1632 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult_Odiff__left) # label(axiom). [clausify(84)]. 6.53/6.74 1633 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__right_Odiff) # label(axiom). [clausify(119)]. 6.53/6.75 1634 -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(269)]. 6.53/6.75 1635 -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(300)]. 6.53/6.75 1636 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult_Ozero__left) # label(axiom). [clausify(314)]. 6.53/6.75 1637 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__right_Ozero) # label(axiom). [clausify(336)]. 6.53/6.75 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),C) = 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,C)). [resolve(1631,a,1632,a)]. 6.53/6.75 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,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,A,C)). [resolve(1631,a,1633,a)]. 6.53/6.75 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(1631,a,1634,a)]. 6.53/6.75 1638 -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(414)]. 6.53/6.75 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(1638,a,1631,a)]. 6.53/6.75 1639 -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(469)]. 6.53/6.75 1640 -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(482)]. 6.53/6.75 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(1640,a,1631,a)]. 6.53/6.75 1641 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult_Ozero__right) # label(axiom). [clausify(538)]. 6.53/6.75 1642 -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(555)]. 6.65/6.88 1643 -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(722)]. 6.65/6.88 1644 -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(750)]. 6.65/6.88 1645 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__left_Odiff) # label(axiom). [clausify(754)]. 6.65/6.88 1646 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)) = c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult_Odiff__right) # label(axiom). [clausify(801)]. 6.65/6.88 1647 -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(862)]. 6.65/6.88 1648 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__left_Ozero) # label(axiom). [clausify(873)]. 6.65/6.88 1649 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption]. 6.65/6.88 1650 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(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_mult__eq__0__iff) # label(axiom). [clausify(101)]. 6.65/6.88 1651 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(101)]. 6.65/6.88 1652 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(101)]. 6.65/6.88 Derived: c_Groups_Otimes__class_Otimes(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(1649,a,1650,a)]. 6.65/6.88 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1649,a,1651,a)]. 6.65/6.88 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1649,a,1652,a)]. 6.65/6.88 1653 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption]. 6.65/6.88 Derived: c_Groups_Otimes__class_Otimes(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(1653,a,1650,a)]. 6.65/6.88 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1653,a,1651,a)]. 6.65/6.88 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1653,a,1652,a)]. 6.83/7.04 1654 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 6.83/7.04 1655 -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(115)]. 6.83/7.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,D) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1654,a,1655,a)]. 6.83/7.04 1656 -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(247)]. 6.83/7.04 1657 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 6.83/7.04 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(1657,a,1655,a)]. 6.83/7.04 1658 -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(442)]. 6.83/7.04 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,C,D) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1658,a,1654,a)]. 6.83/7.04 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(1658,a,1657,a)]. 6.83/7.04 1659 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 6.83/7.04 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(1659,a,1655,a)]. 6.83/7.04 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(1659,a,1658,a)]. 6.83/7.04 1660 -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(652)]. 6.83/7.04 1661 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 6.83/7.04 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(1661,a,1655,a)]. 6.95/7.17 1662 -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(904)]. 6.95/7.17 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,C,D) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1662,a,1654,a)]. 6.95/7.17 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(1662,a,1659,a)]. 6.95/7.17 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(1662,a,1661,a)]. 6.95/7.17 1663 class_Groups_Oab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__group__add) # label(axiom). [assumption]. 6.95/7.17 1664 -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(116)]. 6.95/7.17 1665 -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(214)]. 6.95/7.17 1666 -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | E != D | B = C # label(fact_diff__eq__diff__eq) # label(axiom). [clausify(427)]. 6.95/7.17 1667 -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | E = D | B != C # label(fact_diff__eq__diff__eq) # label(axiom). [clausify(427)]. 6.95/7.17 1668 -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(499)]. 6.95/7.17 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | D != C | A = B. [resolve(1663,a,1666,a)]. 6.95/7.17 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | D = C | A != B. [resolve(1663,a,1667,a)]. 6.95/7.17 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(1663,a,1668,a)]. 6.95/7.17 1669 class_Groups_Oab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__group__add) # label(axiom). [assumption]. 6.95/7.17 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | D != C | A = B. [resolve(1669,a,1666,a)]. 6.95/7.17 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | D = C | A != B. [resolve(1669,a,1667,a)]. 6.95/7.17 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(1669,a,1668,a)]. 6.95/7.17 1670 -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(596)]. 7.13/7.32 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(1670,a,1663,a)]. 7.13/7.32 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(1670,a,1669,a)]. 7.13/7.32 1671 -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(726)]. 7.13/7.32 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(1671,a,1663,a)]. 7.13/7.32 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(1671,a,1669,a)]. 7.13/7.32 1672 -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | C = B # label(fact_eq__iff__diff__eq__0) # label(axiom). [clausify(764)]. 7.13/7.32 1673 -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | C != B # label(fact_eq__iff__diff__eq__0) # label(axiom). [clausify(764)]. 7.13/7.32 1674 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.13/7.32 1675 -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(144)]. 7.13/7.32 1676 -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(154)]. 7.13/7.32 1677 -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(460)]. 7.13/7.32 1678 -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_split__mult__neg__le) # label(axiom). [clausify(460)]. 7.13/7.32 1679 -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(543)]. 7.13/7.32 1680 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.13/7.32 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_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | 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(1680,a,1675,a)]. 7.42/7.58 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(1680,a,1677,a)]. 7.42/7.58 1681 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.42/7.58 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1681,a,1675,a)]. 7.42/7.58 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1681,a,1676,a)]. 7.42/7.58 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1681,a,1677,a)]. 7.42/7.58 1682 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 7.42/7.58 1683 -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(855)]. 7.42/7.58 1684 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.42/7.58 1685 -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(162)]. 7.42/7.58 1686 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.42/7.58 1687 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.42/7.58 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(1687,a,1685,a)]. 7.42/7.58 1688 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 7.42/7.58 1689 -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(203)]. 7.42/7.58 1690 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 7.57/7.74 1691 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 7.57/7.74 1692 -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(264)]. 7.57/7.74 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B) != c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,B) | A = C. [resolve(1692,a,1690,a)]. 7.57/7.74 1693 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 7.57/7.74 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A = C. [resolve(1693,a,1692,a)]. 7.57/7.74 1694 -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(456)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C). [resolve(1694,a,1690,a)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C). [resolve(1694,a,1691,a)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C). [resolve(1694,a,1693,a)]. 7.57/7.74 1695 -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(456)]. 7.57/7.74 Derived: A = B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C). [resolve(1695,a,1691,a)]. 7.57/7.74 1696 -class_Groups_Ocancel__semigroup__add(A) | B != C | c_Groups_Oplus__class_Oplus(A,D,B) = c_Groups_Oplus__class_Oplus(A,D,C) # label(fact_add__left__cancel) # label(axiom). [clausify(574)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,A) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,C,B). [resolve(1696,a,1690,a)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B). [resolve(1696,a,1693,a)]. 7.57/7.74 1697 -class_Groups_Ocancel__semigroup__add(A) | B = C | c_Groups_Oplus__class_Oplus(A,D,B) != c_Groups_Oplus__class_Oplus(A,D,C) # label(fact_add__left__cancel) # label(axiom). [clausify(574)]. 7.57/7.74 1698 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 7.57/7.74 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A = C. [resolve(1698,a,1692,a)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C). [resolve(1698,a,1694,a)]. 7.57/7.74 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B). [resolve(1698,a,1696,a)]. 7.57/7.74 1699 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,B) != c_Groups_Oone__class_Oone(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B | c_Groups_Oone__class_Oone(A) = B # label(fact_square__eq__1__iff) # label(axiom). [clausify(777)]. 7.57/7.74 1700 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption]. 7.57/7.74 1701 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption]. 7.57/7.74 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | 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. [resolve(1699,a,1700,a)]. 7.57/7.74 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) != c_Groups_Oone__class_Oone(tc_Int_Oint) | 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. [resolve(1699,a,1701,a)]. 7.72/7.88 1702 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,B) = c_Groups_Oone__class_Oone(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(777)]. 7.72/7.88 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != A. [resolve(1702,a,1700,a)]. 7.72/7.88 Derived: c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) = c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) != A. [resolve(1702,a,1701,a)]. 7.72/7.88 1703 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,B) = c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(777)]. 7.72/7.88 Derived: c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A. [resolve(1703,a,1700,a)]. 7.72/7.88 1704 class_Divides_Oring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption]. 7.72/7.88 1705 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,C),D) # label(fact_mod__diff__right__eq) # label(axiom). [clausify(224)]. 7.72/7.88 1706 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,D),C) # label(fact_mod__minus__cong) # label(axiom). [clausify(279)]. 7.72/7.88 1707 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,c_Divides_Odiv__class_Omod(A,B,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_mod__minus__eq) # label(axiom). [clausify(477)]. 7.72/7.88 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C). [resolve(1704,a,1705,a)]. 7.72/7.88 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C),B). [resolve(1704,a,1706,a)]. 7.72/7.88 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B). [resolve(1704,a,1707,a)]. 7.72/7.88 1708 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mod__diff__eq) # label(axiom). [clausify(784)]. 7.72/7.88 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C),B). [resolve(1708,a,1704,a)]. 7.72/7.88 1709 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,E),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,D,F),C) # label(fact_mod__diff__cong) # label(axiom). [clausify(851)]. 7.72/7.88 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,E),B). [resolve(1709,a,1704,a)]. 8.10/8.29 1710 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mod__diff__left__eq) # label(axiom). [clausify(920)]. 8.10/8.29 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C),B). [resolve(1710,a,1704,a)]. 8.10/8.29 1711 -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(787)]. 8.10/8.29 1712 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 8.10/8.29 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_Otimes__class_Otimes(tc_RealDef_Oreal,C,A),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C,B)). [resolve(1711,a,1712,a)]. 8.10/8.29 1713 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 8.10/8.29 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(1713,a,1711,a)]. 8.10/8.29 1714 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 8.10/8.29 1715 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 8.10/8.29 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -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,C,A),c_Groups_Otimes__class_Otimes(tc_Int_Oint,C,B)). [resolve(1715,a,1711,a)]. 8.10/8.29 1716 -class_Rings_Ono__zero__divisors(A) | c_Groups_Otimes__class_Otimes(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_divisors__zero) # label(axiom). [clausify(417)]. 8.10/8.29 1717 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 8.10/8.29 1718 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 8.10/8.29 Derived: c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A,B) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(1718,a,1716,a)]. 8.10/8.29 1719 class_Rings_Ono__zero__divisors(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 8.10/8.29 Derived: c_Groups_Otimes__class_Otimes(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(1719,a,1716,a)]. 8.63/8.83 1720 class_Rings_Ono__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ono__zero__divisors) # label(axiom). [assumption]. 8.63/8.83 1721 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_no__zero__divisors) # label(axiom). [clausify(815)]. 8.63/8.83 1722 -class_Rings_Omult__zero(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__zero__left) # label(axiom). [clausify(519)]. 8.63/8.83 1723 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) # label(axiom). [assumption]. 8.63/8.83 1724 class_Rings_Omult__zero(tc_Int_Oint) # label(arity_Int__Oint__Rings_Omult__zero) # label(axiom). [assumption]. 8.63/8.83 1725 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom). [assumption]. 8.63/8.83 1726 class_Rings_Omult__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Omult__zero) # label(axiom). [assumption]. 8.63/8.83 1727 -class_Rings_Omult__zero(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__zero__right) # label(axiom). [clausify(869)]. 8.63/8.83 1728 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 8.63/8.83 1729 -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(386)]. 8.63/8.83 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(1728,a,1729,a)]. 8.63/8.83 1730 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 8.63/8.83 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(1730,a,1729,a)]. 8.63/8.83 1731 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 8.63/8.83 1732 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 8.63/8.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(1732,a,1729,a)]. 8.63/8.83 1733 -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(834)]. 8.63/8.83 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,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(1733,a,1731,a)]. 8.63/8.83 1734 -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(856)]. 8.63/8.83 1735 class_Rings_Oidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oidom) # label(axiom). [assumption]. 8.94/9.11 1736 -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(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(463)]. 8.94/9.11 1737 -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(463)]. 8.94/9.11 1738 -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | 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(463)]. 8.94/9.11 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B). [resolve(1735,a,1736,a)]. 8.94/9.11 Derived: A != B | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B). [resolve(1735,a,1737,a)]. 8.94/9.11 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = B | A = B | c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,A) != c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,B). [resolve(1735,a,1738,a)]. 8.94/9.11 1739 class_Rings_Oidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oidom) # label(axiom). [assumption]. 8.94/9.11 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B). [resolve(1739,a,1736,a)]. 8.94/9.11 Derived: A != B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B). [resolve(1739,a,1737,a)]. 8.94/9.11 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = B | A = B | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A,A) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B,B). [resolve(1739,a,1738,a)]. 8.94/9.11 1740 -class_RealVector_Oreal__field(A) | 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,D,E)),F) = 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,E),F)),c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,D),F),E)) # label(fact_DERIV__mult__lemma) # label(axiom). [clausify(926)]. 8.94/9.11 1741 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption]. 8.94/9.11 Derived: 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,C,D)),E) = 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,D),E)),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,C),E),D)). [resolve(1740,a,1741,a)]. 8.94/9.11 1742 -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(811)]. 8.94/9.11 1743 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption]. 8.94/9.11 1744 -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(811)]. 8.94/9.11 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(1744,a,1743,a)]. 8.94/9.11 1745 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Cputime limit exceeded (core dumped) 180.07/180.24 EOF