TSTP Solution File: SWW216+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW216+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:15:52 EDT 2022
% Result : Theorem 8.61s 8.84s
% Output : Refutation 8.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW216+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 6 08:37:49 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.45/1.77 ============================== Prover9 ===============================
% 1.45/1.77 Prover9 (32) version 2009-11A, November 2009.
% 1.45/1.77 Process 15281 was started by sandbox on n029.cluster.edu,
% 1.45/1.77 Mon Jun 6 08:37:50 2022
% 1.45/1.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15128_n029.cluster.edu".
% 1.45/1.77 ============================== end of head ===========================
% 1.45/1.77
% 1.45/1.77 ============================== INPUT =================================
% 1.45/1.77
% 1.45/1.77 % Reading from file /tmp/Prover9_15128_n029.cluster.edu
% 1.45/1.77
% 1.45/1.77 set(prolog_style_variables).
% 1.45/1.77 set(auto2).
% 1.45/1.77 % set(auto2) -> set(auto).
% 1.45/1.77 % set(auto) -> set(auto_inference).
% 1.45/1.77 % set(auto) -> set(auto_setup).
% 1.45/1.77 % set(auto_setup) -> set(predicate_elim).
% 1.45/1.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.45/1.77 % set(auto) -> set(auto_limits).
% 1.45/1.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.45/1.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.45/1.77 % set(auto) -> set(auto_denials).
% 1.45/1.77 % set(auto) -> set(auto_process).
% 1.45/1.77 % set(auto2) -> assign(new_constants, 1).
% 1.45/1.77 % set(auto2) -> assign(fold_denial_max, 3).
% 1.45/1.77 % set(auto2) -> assign(max_weight, "200.000").
% 1.45/1.77 % set(auto2) -> assign(max_hours, 1).
% 1.45/1.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.45/1.77 % set(auto2) -> assign(max_seconds, 0).
% 1.45/1.77 % set(auto2) -> assign(max_minutes, 5).
% 1.45/1.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.45/1.77 % set(auto2) -> set(sort_initial_sos).
% 1.45/1.77 % set(auto2) -> assign(sos_limit, -1).
% 1.45/1.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.45/1.77 % set(auto2) -> assign(max_megs, 400).
% 1.45/1.77 % set(auto2) -> assign(stats, some).
% 1.45/1.77 % set(auto2) -> clear(echo_input).
% 1.45/1.77 % set(auto2) -> set(quiet).
% 1.45/1.77 % set(auto2) -> clear(print_initial_clauses).
% 1.45/1.77 % set(auto2) -> clear(print_given).
% 1.45/1.77 assign(lrs_ticks,-1).
% 1.45/1.77 assign(sos_limit,10000).
% 1.45/1.77 assign(order,kbo).
% 1.45/1.77 set(lex_order_vars).
% 1.45/1.77 clear(print_given).
% 1.45/1.77
% 1.45/1.77 % formulas(sos). % not echoed (1250 formulas)
% 1.45/1.77
% 1.45/1.77 ============================== end of input ==========================
% 1.45/1.77
% 1.45/1.77 % From the command line: assign(max_seconds, 300).
% 1.45/1.77
% 1.45/1.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.45/1.77
% 1.45/1.77 % Formulas that are not ordinary clauses:
% 1.45/1.77 1 (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].
% 1.45/1.77 2 (all V_w all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 3 (all V_z3 all V_z2 all V_z1 hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_z3))) # label(fact_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 4 (all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a) = V_a)) # label(fact_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 5 (all V_x all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = V_x)) # label(fact_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 6 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = hAPP(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].
% 1.45/1.77 7 (all V_b all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))) # label(fact_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 8 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 9 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 10 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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].
% 1.45/1.77 11 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 12 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 13 (all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z) # label(fact_real__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 14 (all V_b_2 all V_a_2 all V_ca_2 (V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_b_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 15 (all V_b_2 all V_a_2 all V_ca_2 (V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2),V_ca_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 16 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_y))))) # label(fact_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 17 (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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y))))) # label(fact_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 18 (all V_y_2 all V_x_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 19 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),hAPP(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].
% 1.45/1.77 20 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(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].
% 1.45/1.77 21 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),hAPP(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].
% 1.45/1.77 22 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ly))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 23 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(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].
% 1.45/1.77 24 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(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].
% 1.45/1.77 25 -(all B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))))) # label(fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 26 (exists B_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)))) # label(fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 27 (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),hAPP(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].
% 1.45/1.77 28 (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),hAPP(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].
% 1.45/1.77 29 (all V_a_2 all V_b_2 all V_ca_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 30 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))))) # label(fact_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 31 (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,hAPP(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].
% 1.45/1.77 32 (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,hAPP(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].
% 1.45/1.77 33 (all V_a_2 all V_b_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))))) # label(fact_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 34 (all V_b_2 all V_a_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 35 (all V_a_2 all V_ca_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_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)))))) # label(fact_divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 36 (all V_ca_2 all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 37 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_w)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 38 (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].
% 1.45/1.77 39 (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].
% 1.45/1.77 40 (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].
% 1.45/1.77 41 (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].
% 1.45/1.77 42 (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].
% 1.45/1.77 43 (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].
% 1.45/1.77 44 (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_Rings_Oinverse__class_Odivide(T_a,V_a_2,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,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.45/1.77 45 (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),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,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,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 46 (all V_wa_2 all V_x_2 all V_za_2 all V_y_2 all T_a (class_Fields_Ofield(T_a) -> (V_y_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_za_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2) <-> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 47 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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].
% 1.57/1.77 48 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 49 (all V_a_2 all V_ca_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2 <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 50 (all V_ca_2 all V_b_2 all V_a_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_ca_2) <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 51 (all V_x_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2)) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 52 (all V_a_2 all V_b_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_b_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a) <-> V_a_2 = V_b_2)))) # label(fact_right__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 53 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__self) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 54 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (V_a = c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_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) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__self__if) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 55 (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) -> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c) = V_b -> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 56 (all V_a all V_b all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (V_b = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c) -> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 57 (all V_a_2 all V_b_2 all V_ca_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2 <-> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 58 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) <-> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2)))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 59 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_m),V_n)))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 60 (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].
% 1.57/1.77 61 (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].
% 1.57/1.77 62 (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].
% 1.57/1.77 63 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a) | V_b = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 64 (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) -> hAPP(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].
% 1.57/1.77 65 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) | V_b_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 66 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(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].
% 1.57/1.77 67 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(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].
% 1.57/1.77 68 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 69 (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].
% 1.57/1.77 70 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 71 (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].
% 1.57/1.77 72 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_c))) # label(fact_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 73 (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].
% 1.57/1.77 74 (all V_a all V_r c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r)) # label(fact_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 75 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 76 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 77 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 78 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 79 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 80 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 81 (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,hAPP(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].
% 1.57/1.77 82 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 83 (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),hAPP(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].
% 1.57/1.77 84 (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),hAPP(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].
% 1.57/1.77 85 (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,hAPP(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].
% 1.57/1.77 86 (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,hAPP(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].
% 1.57/1.77 87 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 88 (all V_b_2 all V_a_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 89 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 90 (all V_b_2 all V_ca_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 91 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,hAPP(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].
% 1.57/1.77 92 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 93 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 94 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(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].
% 1.57/1.77 95 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 96 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(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].
% 1.57/1.77 97 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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].
% 1.57/1.77 98 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 99 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 100 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 101 (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].
% 1.57/1.77 102 (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))) # label(fact_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.77 103 (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].
% 1.57/1.77 104 (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_z = V_w))) # label(fact_real__le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 105 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) & V_x_2 != V_y_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 106 (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].
% 1.57/1.78 107 (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,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,hAPP(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].
% 1.57/1.78 108 (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_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,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 109 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 110 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 111 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 112 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 113 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 114 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 115 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 116 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 117 (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,hAPP(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].
% 1.57/1.78 118 (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,hAPP(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].
% 1.57/1.78 119 (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,hAPP(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].
% 1.57/1.78 120 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 121 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 122 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),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,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 123 (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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 124 (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].
% 1.58/1.78 125 (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].
% 1.58/1.78 126 (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].
% 1.58/1.78 127 (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].
% 1.58/1.78 128 (all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 129 (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,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) | 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))))) # label(fact_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 130 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)) <-> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 131 (all V_b_2 all V_a_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_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].
% 1.58/1.78 132 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_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].
% 1.58/1.78 133 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 134 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 135 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 136 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 137 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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].
% 1.58/1.78 138 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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].
% 1.58/1.78 139 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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].
% 1.58/1.78 140 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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].
% 1.58/1.78 141 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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].
% 1.58/1.78 142 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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].
% 1.58/1.78 143 (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,hAPP(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].
% 1.58/1.78 144 (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,hAPP(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].
% 1.58/1.78 145 (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].
% 1.58/1.78 146 (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].
% 1.58/1.78 147 (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].
% 1.58/1.78 148 (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].
% 1.58/1.78 149 (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].
% 1.58/1.78 150 (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].
% 1.58/1.78 151 (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].
% 1.58/1.78 152 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_x_2 <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 153 (all V_y_2 all V_x_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 154 (all V_y_2 all V_x_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 155 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)),V_c) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 156 (all V_x_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_x_2 <-> V_x_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 157 (all V_ca_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_ca_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_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) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 158 (all V_a_2 all V_ca_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_ca_2),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_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_divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 159 (all V_b_2 all V_a_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 160 (all V_a_2 all V_b_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))))) # label(fact_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 161 (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,hAPP(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].
% 1.58/1.78 162 (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,hAPP(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].
% 1.58/1.78 163 (all V_b_2 all V_a_2 all V_ca_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))))) # label(fact_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 164 (all V_a_2 all V_b_2 all V_ca_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))))) # label(fact_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 165 (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),hAPP(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].
% 1.58/1.78 166 (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),hAPP(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].
% 1.58/1.78 167 (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].
% 1.58/1.78 168 (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_y_2,V_x_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 169 (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].
% 1.58/1.78 170 (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(T_a,V_y,V_x))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 171 (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].
% 1.58/1.78 172 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(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) & -c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 173 (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].
% 1.58/1.78 174 (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].
% 1.58/1.78 175 (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].
% 1.58/1.78 176 (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) <-> (all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 177 (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__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 178 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> 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)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 179 (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].
% 1.58/1.78 180 (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].
% 1.58/1.78 181 (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) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 182 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (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].
% 1.58/1.78 183 (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].
% 1.58/1.78 184 (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_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 185 (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].
% 1.58/1.78 186 (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].
% 1.58/1.78 187 (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].
% 1.58/1.78 188 (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].
% 1.58/1.78 189 (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].
% 1.58/1.78 190 (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].
% 1.58/1.78 191 (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].
% 1.58/1.78 192 (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__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 193 (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].
% 1.58/1.78 194 (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].
% 1.58/1.78 195 (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].
% 1.58/1.78 196 (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].
% 1.58/1.78 197 (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].
% 1.58/1.78 198 (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(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].
% 1.58/1.78 199 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (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].
% 1.58/1.78 200 (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].
% 1.58/1.78 201 (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].
% 1.58/1.78 202 (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__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 203 (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__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 204 (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].
% 1.58/1.78 205 (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].
% 1.58/1.78 206 (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].
% 1.58/1.78 207 (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].
% 1.58/1.78 208 (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) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 209 (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].
% 1.58/1.78 210 (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].
% 1.58/1.78 211 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_x_2 != V_y_2 <-> 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)))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 212 (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].
% 1.58/1.78 213 (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].
% 1.58/1.78 214 (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].
% 1.58/1.78 215 (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].
% 1.58/1.78 216 (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].
% 1.58/1.78 217 (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_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 218 (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].
% 1.58/1.78 219 (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_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 220 (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_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.78 221 (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].
% 1.58/1.78 222 (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].
% 1.58/1.78 223 (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_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].
% 1.58/1.78 224 (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].
% 1.58/1.78 225 (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_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 226 (all V_y all V_x all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> ((all B_z (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z) -> (c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,B_z),V_x),V_y)))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 227 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v) -> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a)))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 228 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a)))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 229 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 230 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)))) # label(fact_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 231 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_one__le__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 232 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_sgn__1__pos) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 233 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 234 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) & -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 235 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a)) # label(fact_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 236 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a))) # label(fact_sgn__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 237 (all V_b_2 all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2) <-> V_a_2 = V_b_2))) # label(fact_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 238 (all V_b all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b) -> V_a = V_b))) # label(fact_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 239 (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].
% 1.58/1.79 240 (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].
% 1.58/1.79 241 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 242 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 243 (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].
% 1.58/1.79 244 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 245 (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].
% 1.58/1.79 246 (all V_ca_2 all V_b_2 all V_a_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2) <-> V_b_2 = V_ca_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 247 (all V_ca_2 all V_a_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2) <-> V_b_2 = V_ca_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 248 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 249 (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_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 250 (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_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 251 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_inverse__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 252 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 253 (all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_field__inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 254 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> V_a = V_b))))) # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 255 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 256 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a))) # label(fact_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 257 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 258 (all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 259 (all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 260 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 261 (all V_x_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a) <-> V_x_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 262 (all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_inverse__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 263 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a))) # label(fact_inverse__divide) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 264 (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].
% 1.58/1.79 265 (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].
% 1.58/1.79 266 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 267 (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].
% 1.58/1.79 268 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 269 (all V_a_2 all V_b_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 270 (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].
% 1.58/1.79 271 (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].
% 1.58/1.79 272 (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].
% 1.58/1.79 273 (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].
% 1.58/1.79 274 (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].
% 1.58/1.79 275 (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].
% 1.58/1.79 276 (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].
% 1.58/1.79 277 (all V_b_2 all V_a_2 all V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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].
% 1.58/1.79 278 (all V_b_2 all V_ca_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 279 (all V_b_2 all V_ca_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 280 (all V_b_2 all V_a_2 all V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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].
% 1.58/1.79 281 (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].
% 1.58/1.79 282 (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].
% 1.58/1.79 283 (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].
% 1.58/1.79 284 (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].
% 1.58/1.79 285 (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].
% 1.58/1.79 286 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 287 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 288 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_H),V_b)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 289 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_ya),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_ya)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 290 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),hAPP(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].
% 1.58/1.79 291 (all V_db_2 all V_ca_2 all V_b_2 all V_a_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_a_2 != V_b_2 & V_ca_2 != V_db_2 <-> c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 292 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 293 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_m)) = hAPP(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].
% 1.58/1.79 294 (all V_za_2 all V_x_2 all V_y_2 all V_wa_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2)) <-> V_wa_2 = V_x_2 | V_y_2 = V_za_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 295 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 296 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(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].
% 1.58/1.79 297 (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].
% 1.58/1.79 298 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 299 (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].
% 1.58/1.79 300 (all V_w all V_z2 all V_z1 hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_w))) # label(fact_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 301 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 302 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 303 (all T_a (class_Groups_Osgn__if(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 304 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sgn__0__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 305 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)))) # label(fact_sgn__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 306 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)))) # label(fact_sgn__times) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 307 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_sgn__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 308 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 309 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 310 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 311 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 312 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 313 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 314 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 315 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 316 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))))) # label(fact_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 317 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 318 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 319 (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),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 320 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 321 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = c_Groups_Oone__class_Oone(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b))) # label(fact_inverse__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 322 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_field__divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 323 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 324 (all V_a all T_a (class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a))) # label(fact_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 325 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a))) # label(fact_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 326 (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].
% 1.58/1.79 327 (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].
% 1.58/1.79 328 (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].
% 1.58/1.79 329 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2) -> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 330 (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].
% 1.58/1.79 331 (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_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 332 (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),c_Groups_Oplus__class_Oplus(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_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 333 (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].
% 1.58/1.79 334 (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].
% 1.58/1.79 335 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(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)) <-> c_Orderings_Oord__class_Oless(T_a,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].
% 1.58/1.79 336 (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].
% 1.58/1.79 337 (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].
% 1.58/1.79 338 (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].
% 1.58/1.79 339 (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].
% 1.58/1.79 340 (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) -> (V_r != c_Groups_Ozero__class_Ozero(T_a) -> (V_a = V_b & V_c != V_d -> c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 341 (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].
% 1.58/1.79 342 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),V_m) = hAPP(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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 343 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m)) = hAPP(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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 344 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 345 (all V_y all V_x c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y))) # label(fact_divide__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 346 (all V_S all V_R c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S))) # label(fact_real__divide__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 347 (all V_y_2 all V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),hAPP(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].
% 1.58/1.79 348 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_sgn__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 349 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))) # label(fact_sgn__greater) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 350 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a))))) # label(fact_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 351 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a))))) # label(fact_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 352 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 353 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 354 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)))) # label(fact_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 355 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_one__less__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 356 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 357 (all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_field__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 358 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_left__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 359 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_right__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 360 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)))) # label(fact_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 361 (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].
% 1.58/1.79 362 (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].
% 1.58/1.79 363 (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].
% 1.58/1.79 364 (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].
% 1.58/1.79 365 (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].
% 1.58/1.79 366 (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].
% 1.58/1.79 367 (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].
% 1.58/1.79 368 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_w),V_y)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_z)))))) # label(fact_add__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 369 (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_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_z)))) # label(fact_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 370 (all V_z all V_x all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_y != 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),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y)))) # label(fact_add__frac__num) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 371 (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_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,hAPP(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].
% 1.58/1.79 372 (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_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y)))) # label(fact_add__num__frac) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 373 (all V_x (V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 374 (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].
% 1.58/1.79 375 (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].
% 1.58/1.79 376 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 377 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(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].
% 1.58/1.79 378 (all V_y_2 all V_x_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),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 379 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(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) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 380 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 381 (all V_u all V_y all V_x1 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))))))) # label(fact_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 382 (all V_u all V_y all V_x1 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u)))))) # label(fact_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 383 (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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(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) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 384 (all V_a_2 all T_a (class_Rings_Olinordered__idom(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)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 385 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 386 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> ((all B_e (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_e) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e)))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 387 (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,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x))) # label(fact_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 388 (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) -> hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),hAPP(c_Transcendental_Oln,V_y))))) # label(fact_ln__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 389 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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),V_y_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2))))) # label(fact_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 390 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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),V_y_2) -> (hAPP(c_Transcendental_Oln,V_x_2) = hAPP(c_Transcendental_Oln,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_ln__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 391 (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,hAPP(c_Transcendental_Oln,V_x),V_x))) # label(fact_ln__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 392 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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),V_y_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))))) # label(fact_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 393 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)))) # label(fact_ln__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 394 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_Oone__class_Oone(tc_RealDef_Oreal),V_x)))) # label(fact_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 395 (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_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_ln__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 396 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 397 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> (hAPP(c_Transcendental_Oln,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 398 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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),hAPP(c_Transcendental_Oln,V_x_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)))) # label(fact_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 399 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)))) # label(fact_ln__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.79 400 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)))) # label(fact_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 401 (all V_x_2 (c_Orderings_Oord__class_Oless(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),hAPP(c_Transcendental_Oln,V_x_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)))) # label(fact_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 402 (all V_a_2 all V_wa_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))))) # label(fact_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 403 (all V_wa_2 all V_ca_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__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))))) # label(fact_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 404 (all V_ca_2 all V_b_2 all V_wa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 405 (all V_wa_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_wa_2))) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) & (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 406 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)))) # label(fact_DERIV__ln__divide) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 407 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z))) # label(fact_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 408 (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_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,V_v,V_w)))) # label(fact_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 409 (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].
% 1.58/1.80 410 (all V_y_2 all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2)))) # label(fact_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 411 (all V_y_2 all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Int_Oring__char__0(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 412 (all V_x_2 all V_wa_2 all T_a (class_Int_Onumber(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2 <-> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) # label(fact_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 413 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,hAPP(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].
% 1.58/1.80 414 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)))) # label(fact_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 415 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) = hAPP(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].
% 1.58/1.80 416 (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(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2)))) # label(fact_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 417 (all V_wa_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_wa_2)) <-> -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2))))) # label(fact_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 418 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> hAPP(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)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b,V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_b,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))))) # label(fact_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 419 (all V_c all V_b all V_v all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> hAPP(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)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)))) # label(fact_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 420 (all V_wa_2 all V_b_2 all V_a_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) <-> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_b_2) & (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 421 (all V_ca_2 all V_b_2 all V_wa_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) = V_b_2) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 422 (all V_wa_2 all V_ca_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 423 (all V_a_2 all V_wa_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_a_2 <-> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) & (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 424 (all V_w all T_b (class_Int_Onumber(T_b) & class_Rings_Odivision__ring(T_b) -> c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)) = c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)))) # label(fact_inverse__eq__divide__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 425 (all V_a_2 all V_wa_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))))) # label(fact_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 426 (all V_wa_2 all V_ca_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,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))))) # label(fact_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 427 (all V_ca_2 all V_b_2 all V_wa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 428 (all V_wa_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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))) & (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 429 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x_2)))) # label(fact_DERIV__ln) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 430 (all V_x_2 all V_ca_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Deriv_Oderiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_x_2,V_ca_2))) # label(fact_DERIV__cmult__Id) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 431 (all V_k all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k)))) # label(fact_number__of__succ) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 432 (all V_a ((V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) & (V_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),V_a) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) & (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_sgn__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 433 (all V_x ((V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) & (V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) & (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_real__sgn__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 434 (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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)))) # label(fact_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 435 (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,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)))) # label(fact_exp__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 436 (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].
% 1.58/1.80 437 (all V_l_2 all V_k_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)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 438 (all V_w all V_v hAPP(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)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))) # label(fact_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 439 (all V_z all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(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) = hAPP(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].
% 1.58/1.80 440 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 441 (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_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 442 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 443 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)))) # label(fact_sgn__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 444 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_exp__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 445 (all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) & class_SEQ_Obanach(T_a) -> hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)))) # label(fact_exp__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 446 (all V_y_2 all V_x_2 (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2) <-> V_x_2 = V_y_2)) # label(fact_exp__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 447 (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].
% 1.58/1.80 448 (all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) <-> c_Groups_Ozero__class_Ozero(T_a) = V_a_2))) # label(fact_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 449 (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].
% 1.58/1.80 450 (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) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 451 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2 <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 452 (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].
% 1.58/1.80 453 (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].
% 1.58/1.80 454 (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,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__eq(T_a,V_a_2,V_b_2)))) # label(fact_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 455 (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].
% 1.58/1.80 456 (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].
% 1.58/1.80 457 (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].
% 1.58/1.80 458 (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].
% 1.58/1.80 459 (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_a_2),V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)))) # label(fact_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 460 (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,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))) # label(fact_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 461 (all V_b_2 all V_a_2 all T_a (class_Rings_Oidom(T_a) -> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_b_2) <-> V_a_2 = V_b_2 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 462 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(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)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))) # label(fact_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 463 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 464 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 465 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(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].
% 1.58/1.80 466 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)))) # label(fact_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 467 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))) # label(fact_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 468 (all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x)))) # label(fact_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 469 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))) # label(fact_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 470 (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].
% 1.58/1.80 471 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b)) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 472 (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].
% 1.58/1.80 473 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 474 (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].
% 1.58/1.80 475 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(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,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 476 (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].
% 1.58/1.80 477 (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_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))) # label(fact_divide_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 478 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)))) # label(fact_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 479 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x)) # label(fact_double__compl) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 480 (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].
% 1.58/1.80 481 (all V_y_2 all V_x_2 all T_a (class_Lattices_Oboolean__algebra(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 482 (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].
% 1.58/1.80 483 (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) <-> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 484 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2 <-> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 485 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> V_a_2 = V_b_2))) # label(fact_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 486 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_exp__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 487 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y))) # label(fact_exp__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 488 (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].
% 1.58/1.80 489 (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].
% 1.58/1.80 490 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 491 (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].
% 1.58/1.80 492 (all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z) # label(fact_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 493 (all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z) # label(fact_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 494 (all V_z3 all V_z2 all V_z1 hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_z3))) # label(fact_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 495 (all V_w all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 496 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) | V_x = V_y | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 497 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_j))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 498 (all V_n_2 all V_ma_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2) -> (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 499 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 500 (all V_k c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_succ__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 501 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 502 (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].
% 1.58/1.80 503 (all V_za_2 all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) | V_wa_2 = V_za_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 504 (all V_za_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 505 (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].
% 1.58/1.80 506 (all V_w all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 507 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 508 (all V_z3 all V_z2 all V_z1 c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 509 (all V_w all V_z2 all V_z1 hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 510 (all V_z2 all V_z1 all V_w hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 511 (all V_za_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 512 (all V_za_2 all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 513 (all V_za_2 all V_wa_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 514 (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].
% 1.58/1.80 515 (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].
% 1.58/1.80 516 (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].
% 1.58/1.80 517 (all V_wa_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) & V_za_2 != V_wa_2)) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 518 (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].
% 1.58/1.80 519 (all V_x hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) = V_x) # label(fact_ln__exp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 520 (all V_x all V_u (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_u) = V_x -> hAPP(c_Transcendental_Oln,V_x) = V_u)) # label(fact_exp__ln__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 521 (all V_x all V_y (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y) = V_x -> hAPP(c_Transcendental_Oln,V_x) = V_y)) # label(fact_ln__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 522 (all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) & class_SEQ_Obanach(T_a) -> hAPP(c_Transcendental_Oexp(T_a),V_x) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_exp__not__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 523 (all V_x_2 all T_a (class_RealVector_Oreal__normed__field(T_a) & class_SEQ_Obanach(T_a) -> c_Deriv_Oderiv(T_a,c_Transcendental_Oexp(T_a),V_x_2,hAPP(c_Transcendental_Oexp(T_a),V_x_2)))) # label(fact_DERIV__exp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 524 (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].
% 1.58/1.80 525 (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].
% 1.58/1.80 526 (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_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 527 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 528 (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].
% 1.58/1.80 529 (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_a_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)))) # label(fact_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 530 (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].
% 1.58/1.80 531 (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].
% 1.58/1.80 532 (all V_y_2 all V_x_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)))) # label(fact_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 533 (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].
% 1.58/1.80 534 (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_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 535 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 536 (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),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 537 (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].
% 1.58/1.80 538 (all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 539 (all V_x_2 all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) <-> V_x_2 = c_Groups_Oone__class_Oone(T_a) | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 540 (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].
% 1.58/1.80 541 (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_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))))) # label(fact_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 542 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 543 (all V_x all V_u c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),V_u)),hAPP(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].
% 1.58/1.80 544 (all V_y_2 all V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))) # label(fact_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 545 (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].
% 1.58/1.80 546 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))) # label(fact_exp__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 547 (all V_x -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__exp__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 548 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))) # label(fact_exp__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 549 (all V_x -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__exp__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 550 (all V_x_2 (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_exp__eq__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 551 (all T_a (class_RealVector_Oreal__normed__field(T_a) & class_SEQ_Obanach(T_a) -> hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_exp__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 552 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) & class_SEQ_Obanach(T_a) -> hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)))) # label(fact_exp__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 553 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) & class_SEQ_Obanach(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)) = hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)))) # label(fact_mult__exp__exp) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 554 (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].
% 1.58/1.80 555 (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].
% 1.58/1.80 556 (all V_y_2 all 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)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)))) # label(fact_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 557 (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].
% 1.58/1.80 558 (all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_exp__le__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 559 (all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2))) # label(fact_one__le__exp__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 560 (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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)))) # label(fact_exp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 561 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_exp__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 562 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2))) # label(fact_one__less__exp__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 563 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) = V_x)) # label(fact_exp__ln) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 564 (all V_x_2 (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) = V_x_2 <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2))) # label(fact_exp__ln__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 565 (all V_E_2 all V_D_2 all V_x_2 all V_f_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2) -> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2) -> V_D_2 = V_E_2)))) # label(fact_DERIV__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 566 (all V_Y_2 all V_X_2 all V_x_2 all V_f_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_X_2) -> (V_X_2 = V_Y_2 -> c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_Y_2))))) # label(fact_DERIV__cong) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 567 (all V_E_2 all V_D_2 all V_x_2 all V_f_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2) -> (V_D_2 = V_E_2 -> c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2))))) # label(fact_Deriv_Olemma__DERIV__subst) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 568 (all V_x all T_a (class_Groups_Osgn__if(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(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_x) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))))) # label(fact_sgn__if) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 569 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 570 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_sgn__1__neg) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 571 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x)))) # label(fact_ln__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 572 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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,hAPP(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].
% 1.58/1.80 573 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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].
% 1.58/1.80 574 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_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,hAPP(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].
% 1.58/1.80 575 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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].
% 1.58/1.80 576 (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].
% 1.58/1.80 577 (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].
% 1.58/1.80 578 (all V_w all V_z hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w))) # label(fact_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 579 (all V_i ((V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i) -> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i) -> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) # label(fact_zsgn__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 580 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.80 581 (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].
% 1.58/1.80 582 (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].
% 1.58/1.80 583 (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,hAPP(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].
% 1.58/1.80 584 (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,hAPP(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].
% 1.58/1.80 585 (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,hAPP(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].
% 1.58/1.80 586 (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,hAPP(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].
% 1.58/1.80 587 (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),hAPP(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].
% 1.58/1.80 588 (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].
% 1.58/1.80 589 (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_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_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].
% 1.58/1.80 590 (all V_l_2 all V_x_2 all V_f_2 (c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2) -> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) & (all B_h (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,V_x_2),hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h))))))))))) # label(fact_DERIV__pos__inc__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 591 (all V_l_2 all V_x_2 all V_f_2 (c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) & (all B_h (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)),hAPP(V_f_2,V_x_2)))))))))) # label(fact_DERIV__neg__dec__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 592 (all V_za_2 all T_a (class_Rings_Osemiring__1(T_a) -> (c_Int_Oiszero(T_a,V_za_2) <-> V_za_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_iszero__def) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 593 (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].
% 1.58/1.81 594 (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].
% 1.58/1.81 595 (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].
% 1.58/1.81 596 (all V_y_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2) <-> 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].
% 1.58/1.81 597 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_Opred(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__pred) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 598 (all V_v_H_2 all V_v_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) <-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2))) # label(fact_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 599 (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].
% 1.58/1.81 600 (all V_v_2 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls))) # label(fact_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 601 (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__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 602 (all V_v_H_2 all V_v_2 (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)) <-> (-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)))) # label(fact_le__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 603 (all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k) # label(fact_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 604 (all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k) # label(fact_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 605 (all V_w hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),V_w) = c_Int_OPls) # label(fact_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 606 (all V_x c_Int_Osucc(c_Int_Opred(V_x)) = V_x) # label(fact_succ__pred) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 607 (all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))) # label(fact_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 608 (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].
% 1.58/1.81 609 (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].
% 1.58/1.81 610 (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].
% 1.58/1.81 611 (all V_v_H all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) -> c_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)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)))))) # label(fact_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 612 (all V_k all V_v_H all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))),V_k)))) # label(fact_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 613 (all V_v_H all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> hAPP(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)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))))) # label(fact_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 614 (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].
% 1.58/1.81 615 (all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))))) # label(fact_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 616 (all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (-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_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))))) # label(fact_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 617 (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_Opred(V_k_2),V_l_2))) # label(fact_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 618 (all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__Numeral0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 619 (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].
% 1.58/1.81 620 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls)))) # label(fact_le__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 621 (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_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2)))) # label(fact_less__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 622 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls)))) # label(fact_less__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 623 (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].
% 1.58/1.81 624 (all V_y_2 all T_a (class_Int_Onumber__ring(T_a) -> (c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2) <-> 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))))))) # label(fact_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 625 (all V_l c_Int_OPls != c_Int_OBit1(V_l)) # label(fact_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 626 (all V_k c_Int_OBit1(V_k) != c_Int_OPls) # label(fact_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 627 (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].
% 1.58/1.81 628 (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].
% 1.58/1.81 629 (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].
% 1.58/1.81 630 (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].
% 1.58/1.81 631 (all V_l_2 all V_k_2 (c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) <-> V_k_2 = V_l_2)) # label(fact_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 632 (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].
% 1.58/1.81 633 (all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 634 (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].
% 1.58/1.81 635 (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].
% 1.58/1.81 636 (all V_k c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)))) # label(fact_minus__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 637 (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].
% 1.58/1.81 638 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)))) # label(fact_number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 639 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a) = V_a)) # label(fact_mult__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 640 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a)) # label(fact_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 641 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 642 (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].
% 1.58/1.81 643 (all V_x all T_a (class_Fields_Ofield(T_a) & class_Int_Onumber__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x)) # label(fact_divide__Numeral1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 644 (all V_a all T_a (class_Fields_Ofield(T_a) & class_Int_Onumber__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a)) # label(fact_divide__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 645 (all T_a (class_Fields_Ofield(T_a) & class_Int_Onumber__ring(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))) # label(fact_inverse__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 646 (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].
% 1.58/1.81 647 (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].
% 1.58/1.81 648 (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].
% 1.58/1.81 649 (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_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)))) # label(fact_le__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 650 (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].
% 1.58/1.81 651 (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].
% 1.58/1.81 652 (all V_x_2 all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls))))) # label(fact_less__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 653 (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].
% 1.58/1.81 654 (all V_w all T_a (class_Int_Onumber__ring(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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)))) # label(fact_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 655 (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].
% 1.58/1.81 656 (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].
% 1.58/1.81 657 (all V_n_2 all V_ma_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(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__eq(tc_Nat_Onat,V_ma_2,V_n_2)))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 658 (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].
% 1.58/1.81 659 (all V_n_2 all V_ma_2 (V_ma_2 != V_n_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 660 (all V_y all V_x (V_x != V_y -> (-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].
% 1.58/1.81 661 (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].
% 1.58/1.81 662 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 663 (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].
% 1.58/1.81 664 (all V_P_2 all V_n_2 all V_ma_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))) -> ((V_ma_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))) -> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 665 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 666 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 667 (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].
% 1.58/1.81 668 (all V_n_2 all V_ma_2 all V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) <-> V_ma_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 669 (all V_n_2 all V_k_2 all V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_ma_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 670 (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].
% 1.58/1.81 671 (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].
% 1.58/1.81 672 (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].
% 1.58/1.81 673 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 674 (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].
% 1.58/1.81 675 (all V_k all V_n all V_m hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)),V_k) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 676 (all V_n all V_m hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 677 (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].
% 1.58/1.81 678 (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].
% 1.58/1.81 679 (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].
% 1.58/1.81 680 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 681 (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].
% 1.58/1.81 682 (all V_n all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 683 (all V_n_2 all V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 684 (all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 685 (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].
% 1.58/1.81 686 (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].
% 1.58/1.81 687 (all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(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].
% 1.58/1.81 688 (all V_n_2 all V_k_2 all V_ma_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2) <-> V_ma_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 689 (all V_n_2 all V_ma_2 all V_k_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2) <-> V_ma_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 690 (all V_n_2 all V_ma_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 691 (all V_m hAPP(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].
% 1.58/1.81 692 (all V_n hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 693 (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].
% 1.58/1.81 694 (all V_n all V_m all V_l all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 695 (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].
% 1.58/1.81 696 (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].
% 1.58/1.81 697 (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].
% 1.58/1.81 698 (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].
% 1.58/1.81 699 (all V_n_2 all V_ma_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 700 (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].
% 1.58/1.81 701 (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].
% 1.58/1.81 702 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) | 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].
% 1.58/1.81 703 (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].
% 1.58/1.81 704 (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].
% 1.58/1.81 705 (all V_n_2 all V_ma_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) | V_ma_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 706 (all V_n_2 all V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) & V_ma_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 707 (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].
% 1.58/1.81 708 (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].
% 1.58/1.81 709 (all V_n_2 all V_ma_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) <-> (exists B_k V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 710 (all V_n_2 all V_ma_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 711 (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].
% 1.58/1.81 712 (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].
% 1.58/1.81 713 (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].
% 1.58/1.81 714 (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].
% 1.58/1.81 715 (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].
% 1.58/1.81 716 (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].
% 1.58/1.81 717 (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].
% 1.58/1.81 718 (all V_k all V_n all V_m hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 719 (all V_n all V_m all V_k hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 720 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 721 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m)))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 722 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k)))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 723 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 724 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_l))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 725 (all V_n_2 all V_ma_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 726 (all V_n hAPP(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].
% 1.58/1.81 727 (all V_n_2 all V_ma_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2) <-> V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 728 (all V_n hAPP(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].
% 1.58/1.81 729 (all V_n_2 all V_ma_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_ma_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_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].
% 1.58/1.81 730 (all V_n_2 all V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 731 (all V_n_2 all V_ma_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(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_ma_2,V_n_2))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 732 (all V_n_2 all V_k_2 all V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 733 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 734 (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 735 (all V_n all V_m (V_m = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n) -> V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 736 (all V_n_2 all V_k_2 all V_ma_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 737 (all V_n_2 all V_ma_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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 738 (all V_n_2 all V_ma_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2) <-> V_ma_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 739 (all V_n_2 all V_ma_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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 740 (all V_n_2 all V_ma_2 all V_k_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_ma_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 741 (all V_k all V_j all V_u all V_i c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(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].
% 1.58/1.81 742 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 743 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 744 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 745 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 746 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 747 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) <-> (exists B_n V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 748 (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].
% 1.58/1.81 749 (all V_k_2 all V_P_2 all V_db_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_db_2) -> ((all B_x (hBOOL(hAPP(V_P_2,B_x)) -> hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_db_2))))) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (all B_x (hBOOL(hAPP(V_P_2,B_x)) -> hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_2)))))))))) # label(fact_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 750 (all V_wa_2 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_OBit0(V_wa_2))) <-> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))) # label(fact_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 751 (all V_k c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k)) # label(fact_pred__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 752 (all V_k c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k))) # label(fact_pred__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 753 (all V_k c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k)) # label(fact_succ__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 754 (all V_k c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k))) # label(fact_succ__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 755 (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].
% 1.58/1.81 756 (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_OBit0(V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 757 (all V_l all V_k hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l))) # label(fact_mult__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 758 (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].
% 1.58/1.81 759 (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].
% 1.58/1.81 760 (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].
% 1.58/1.81 761 (all V_l all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))) # label(fact_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 762 (all V_l all V_k c_Int_OBit1(V_k) != c_Int_OBit0(V_l)) # label(fact_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 763 (all V_l all V_k c_Int_OBit0(V_k) != c_Int_OBit1(V_l)) # label(fact_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 764 (all V_k c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))) # label(fact_minus__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 765 (all V_l_2 all V_k_2 (c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) <-> V_k_2 = V_l_2)) # label(fact_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 766 (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].
% 1.58/1.81 767 (all V_l_2 (c_Int_OPls = c_Int_OBit0(V_l_2) <-> c_Int_OPls = V_l_2)) # label(fact_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 768 (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].
% 1.58/1.81 769 (all V_l all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))) # label(fact_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 770 (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].
% 1.58/1.81 771 (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].
% 1.58/1.81 772 (all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 773 (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].
% 1.58/1.81 774 (all V_k2_2 all V_k1_2 (c_Orderings_Oord__class_Oless(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__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 775 (all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls))) # label(fact_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 776 (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].
% 1.58/1.81 777 (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_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_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 778 (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].
% 1.58/1.81 779 (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_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)))) # label(fact_number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 780 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2))) # label(fact_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 781 (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].
% 1.58/1.81 782 (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].
% 1.58/1.81 783 (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].
% 1.58/1.81 784 (all V_l all V_k hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),V_l)) # label(fact_mult__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 785 (all V_l all V_k c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_Osucc(V_l)))) # label(fact_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 786 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)))) # label(fact_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 787 (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].
% 1.58/1.81 788 (all V_za_2 all V_y_2 all V_x_2 (V_x_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2)) <-> hAPP(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) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2))) # label(fact_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 789 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> hAPP(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].
% 1.58/1.81 790 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> hAPP(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].
% 1.58/1.81 791 (all T_a (class_Int_Onumber__ring(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,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 792 (all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)) # label(fact_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 793 (all V_z hAPP(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) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)) # label(fact_nat__mult__2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 794 (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].
% 1.58/1.81 795 (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].
% 1.58/1.81 796 (all V_r 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),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].
% 1.58/1.81 797 (all V_r_2 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,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].
% 1.58/1.81 798 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_x = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 799 (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].
% 1.58/1.81 800 (all V_D_2 all V_x_2 (V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> V_D_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),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_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> V_D_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2))))) # label(fact_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 801 (all V_k_2 all V_v_2 all V_b_2 all V_a_2 (V_a_2 != V_b_2 -> ((all B_x c_Deriv_Oderiv(tc_RealDef_Oreal,V_v_2,B_x,V_k_2)) -> hAPP(V_v_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a_2,V_b_2),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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(V_v_2,V_a_2),hAPP(V_v_2,V_b_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_DERIV__const__average) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 802 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 803 (all V_y_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2))) # label(fact_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 804 (all V_y_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2))) # label(fact_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 805 (all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_real__sqrt__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 806 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)))) # label(fact_real__sqrt__ge__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 807 (all V_x_2 (hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 808 (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,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)))) # label(fact_real__sqrt__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 809 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_real__sqrt__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 810 (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,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)))) # label(fact_real__sqrt__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 811 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2))) # label(fact_real__sqrt__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 812 (all V_y all V_x hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),hAPP(c_NthRoot_Osqrt,V_y))) # label(fact_real__sqrt__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 813 (all V_x hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x))) # label(fact_real__sqrt__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 814 (all V_x hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x))) # label(fact_real__sqrt__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 815 (all V_y all V_x hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y))) # label(fact_real__sqrt__divide) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 816 (all V_y_2 all V_x_2 (hAPP(c_NthRoot_Osqrt,V_x_2) = hAPP(c_NthRoot_Osqrt,V_y_2) <-> V_x_2 = V_y_2)) # label(fact_real__sqrt__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 817 (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),hAPP(c_NthRoot_Osqrt,V_x)))) # label(fact_real__sqrt__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 818 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> hAPP(c_NthRoot_Osqrt,V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 819 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 820 (all V_y_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2))) # label(fact_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 821 (all V_y_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2))) # label(fact_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 822 (all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__sqrt__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 823 (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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)))) # label(fact_real__sqrt__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 824 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (hAPP(c_NthRoot_Osqrt,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 825 (all V_x_2 (hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 826 (all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y))))) # label(fact_le__real__sqrt__sumsq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 827 (all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y))))) # label(fact_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.81 828 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_x) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)))) # label(fact_sqrt__divide__self__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 829 (all V_u (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u))) # label(fact_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 830 (all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_DERIV__real__sqrt) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 831 (all V_y all V_x all V_u (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,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),V_x) -> (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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u))))))) # label(fact_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 832 (all V_ya all V_xa all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 833 (all V_k all V_x hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_k)) # label(fact_real__sqrt__power) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 834 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 835 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p)),c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 836 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q) = c_Power_Opower__class_Opower(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 837 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_q) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q)),c_Power_Opower__class_Opower(T_a,V_y,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 838 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 839 (all V_wa_2 all V_a_2 all T_a (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a) -> (c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_power__eq__0__iff__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 840 (all V_w all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a)) & (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power__0__left__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 841 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)),V_a))) # label(fact_power3__eq__cube) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 842 (all T_a (class_Rings_Osemiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_zero__power2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 843 (all V_a_2 all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__eq__power2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 844 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 845 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a))) # label(fact_power2__eq__square) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 846 (all T_a (class_Rings_Osemiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a))) # label(fact_one__power2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 847 (all V_a all T_a (class_Rings_Oring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_power2__minus) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 848 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_power__even__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 849 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_zero__le__power2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 850 (all V_y all V_x all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> (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_x,V_y))))) # label(fact_power2__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 851 (all V_y all V_x all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) -> (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) -> V_x = V_y))))) # label(fact_power2__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 852 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) <-> V_a_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__power2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 853 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power2__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 854 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 855 (all V_w all T_b (class_Groups_Omonoid__mult(T_b) & class_Int_Onumber(T_b) -> c_Power_Opower__class_Opower(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)))) # label(fact_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 856 (all V_a_2 all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) <-> V_a_2 = c_Groups_Oone__class_Oone(T_a) | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_power2__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 857 (all V_n all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,V_x,hAPP(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_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(T_a,V_x,V_n)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 858 (all V_n all V_a all T_a (class_Rings_Oring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),hAPP(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_n)) = c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_n)))) # label(fact_ring__1__class_Opower__minus__even) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 859 (all V_y_2 all V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = 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_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 860 (all V_x hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_four__x__squared) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 861 (all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))) # label(fact_two__realpow__ge__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 862 (all V_x all V_u c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_realpow__square__minus__le) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 863 (all V_y all V_x all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y))))) # label(fact_power2__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 864 (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),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_sum__power2__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 865 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__power2__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 866 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 867 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 868 (all V_y all V_x all T_a (class_Int_Onumber__ring(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(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_x)),V_y)))) # label(fact_power2__sum) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 869 (all V_k all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_k)),c_Groups_Ozero__class_Ozero(T_a)) -> V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_even__power__le__0__imp__0) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 870 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_n))))) # label(fact_zero__le__even__power_H) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 871 (all V_n all T_a (class_Rings_Oring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(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_n)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__minus1__even) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 872 (all V_x all V_y (c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> hAPP(c_NthRoot_Osqrt,V_x) = V_y))) # label(fact_real__sqrt__unique) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 873 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x)) # label(fact_real__sqrt__pow2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 874 (all V_x_2 (c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2 <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2))) # label(fact_real__sqrt__pow2__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 875 (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),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 876 (all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 877 (all V_x all V_y c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 878 (all V_d all V_b all V_c all V_a c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 879 (all V_y all V_x (hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_x -> V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 880 (all V_y all V_x (hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_y -> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 881 (all V_ya all V_xa all V_y all V_x c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 882 (all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 883 (all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))) # label(fact_real__inv__sqrt__pow2) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 884 (all V_y all V_x c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(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)),V_y))) # label(fact_real__sum__squared__expand) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 885 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))))))) # label(fact_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 886 (all V_n all V_m all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 887 (all V_n_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 888 (all V_n 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),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 889 (all V_z all V_y all V_x c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y)),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z))) # label(fact_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 890 (all V_z all V_y all V_x c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z) = c_Power_Opower__class_Opower(tc_Int_Oint,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y),V_z))) # label(fact_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 891 (all V_n_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,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_x_2))) # label(fact_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 892 (all V_wa_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2))) <-> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_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_x_2))) # label(fact_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 893 (all V_n all V_a all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_field__power__not__zero) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 894 (all V_n all V_b all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_b,V_n)))) # label(fact_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 895 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),V_a) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))) # label(fact_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 896 (all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__one) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 897 (all V_n all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)))) # label(fact_power__divide) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 898 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_n))) # label(fact_power__mult) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 899 (all V_n all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n))) # label(fact_power__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 900 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a)) # label(fact_power__one__right) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 901 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(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),c_Power_Opower__class_Opower(T_a,V_a,V_n))))) # label(fact_zero__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 902 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(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_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)))))) # label(fact_power__mono) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 903 (all V_n 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,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))))) # label(fact_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.58/1.82 904 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))))) # label(fact_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 905 (all V_n_2 all V_a_2 all T_a (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a) -> (c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 906 (all V_n_2 all V_ma_2 all V_a_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2) -> (c_Power_Opower__class_Opower(T_a,V_a_2,V_ma_2) = c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) <-> V_ma_2 = V_n_2)))) # label(fact_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 907 (all V_n all V_a all V_b all T_a (class_Fields_Ofield(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))))) # label(fact_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 908 (all V_a all T_a (class_Power_Opower(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__0) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 909 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m)),c_Power_Opower__class_Opower(T_a,V_a,V_n)))) # label(fact_power__add) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 910 (all V_n all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n))) # label(fact_power__one__over) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 911 (all V_n all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n)))) # label(fact_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 912 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 913 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))))) # label(fact_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 914 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))))) # label(fact_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 915 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 916 (all V_n all V_a all T_a (class_Rings_Oring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)))) # label(fact_power__minus) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 917 (all V_y_2 all V_x_2 all V_b_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2) -> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 918 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))))) # label(fact_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 919 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)))))) # label(fact_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 920 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)))))) # label(fact_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 921 (all V_n 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_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)))))) # label(fact_power__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 922 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n))))))) # label(fact_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 923 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Power_Opower__class_Opower(T_a,V_a,V_n) = c_Power_Opower__class_Opower(T_a,V_b,V_n) -> (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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> V_a = V_b)))))) # label(fact_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 924 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N) -> (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_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n))))))) # label(fact_power__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 925 (all V_y_2 all V_x_2 all V_b_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 926 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))))) # label(fact_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 927 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))))) # label(fact_one__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 928 (all V_z c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z) # label(fact_csqrt) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 929 (all V_x hAPP(c_Transcendental_Oarctan,V_x) = hAPP(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)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))))) # label(fact_arctan__half) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 930 (all V_x hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x))) # label(fact_arctan__minus) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 931 (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,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)))) # label(fact_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 932 (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,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)))) # label(fact_arctan__monotone) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 933 (all V_x_2 c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_DERIV__arctan) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 934 (all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_cos__x__y__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 935 (all V_y all V_u all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,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_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u)))) # label(fact_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 936 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)))) # label(fact_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 937 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n))) # label(fact_power__abs) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 938 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)) = c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)))) # label(fact_abs__power__minus) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 939 (all V_y all V_x all V_c (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y))) -> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 940 (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) -> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x))))) # label(fact_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 941 (all V_b all V_a all T_a (class_Rings_Oordered__ring__abs(T_a) -> ((c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_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,V_b,c_Groups_Ozero__class_Ozero(T_a))) -> c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 1.63/1.82 942 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 943 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 944 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_abs__of__neg) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 945 (all V_a all T_a (class_Groups_Oabs__if(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)) & (-c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a))) # label(fact_abs__if) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 946 (all V_x all V_y all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))) # label(fact_abs__div__pos) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 947 (all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_abs__one) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 948 (all V_x c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) # label(fact_real__sgn__eq) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 949 (all V_d all V_b all V_c all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d) -> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_d)))))) # label(fact_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.86/2.06 950 (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].
% 1.86/2.06 951 (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].
% 1.86/2.06 952 (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].
% 1.86/2.06 953 (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].
% 1.86/2.06 954 (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].
% 1.86/2.06
% 1.86/2.06 ============================== end of process non-clausal formulas ===
% 1.86/2.06
% 1.86/2.06 ============================== PROCESS INITIAL CLAUSES ===============
% 1.86/2.06
% 1.86/2.06 ============================== PREDICATE ELIMINATION =================
% 1.86/2.06 955 class_Rings_Ocomm__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.86/2.06 956 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),C) = hAPP(c_Groups_Otimes__class_Otimes(A,C),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(6)].
% 1.86/2.06 957 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(A,C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(8)].
% 1.86/2.06 958 -class_Rings_Ocomm__semiring__1(A) | hAPP(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(9)].
% 1.86/2.06 959 -class_Rings_Ocomm__semiring__1(A) | hAPP(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(10)].
% 1.86/2.06 960 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(11)].
% 1.86/2.06 961 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(12)].
% 1.86/2.06 962 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(19)].
% 1.86/2.06 963 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) = hAPP(c_Groups_Otimes__class_Otimes(A,D),hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(20)].
% 1.86/2.06 964 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(21)].
% 1.86/2.06 965 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(22)].
% 1.86/2.06 966 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D) = hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(23)].
% 1.86/2.06 967 -class_Rings_Ocomm__semiring__1(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D) = hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(24)].
% 1.86/2.06 968 -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(239)].
% 1.86/2.06 969 -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(240)].
% 1.86/2.06 970 -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(241)].
% 1.86/2.06 971 -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(242)].
% 1.86/2.06 972 -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(243)].
% 1.86/2.06 973 -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(244)].
% 1.86/2.06 974 -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(270)].
% 1.86/2.06 975 -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(271)].
% 1.86/2.06 976 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) = hAPP(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(290)].
% 1.86/2.06 977 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) = hAPP(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(292)].
% 1.86/2.06 978 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) = hAPP(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(293)].
% 1.86/2.06 979 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),C) = hAPP(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(342)].
% 1.86/2.06 980 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)) = hAPP(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(343)].
% 1.86/2.06 981 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oplus__class_Oplus(A,B,B) = hAPP(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(344)].
% 1.86/2.06 982 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(A) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom). [clausify(834)].
% 1.86/2.06 983 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,B,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(835)].
% 1.86/2.06 984 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,c_Power_Opower__class_Opower(A,B,C),D) = c_Power_Opower__class_Opower(A,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(836)].
% 1.86/2.06 985 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),D) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,D)),c_Power_Opower__class_Opower(A,C,D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(837)].
% 1.86/2.06 986 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(838)].
% 1.86/2.06 987 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(A,B),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(844)].
% 1.86/2.06 988 -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(A,B,hAPP(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)))),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,B,C)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(857)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),A). [resolve(955,a,956,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)). [resolve(955,a,957,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(955,a,958,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(955,a,959,a)].
% 1.86/2.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(955,a,960,a)].
% 1.86/2.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(955,a,961,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(955,a,962,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),D))). [resolve(955,a,964,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)),B). [resolve(955,a,965,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)). [resolve(955,a,966,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A). [resolve(955,a,968,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)). [resolve(955,a,969,a)].
% 1.86/2.06 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(955,a,970,a)].
% 1.86/2.06 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(955,a,972,a)].
% 1.86/2.06 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(955,a,973,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(955,a,974,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = A. [resolve(955,a,975,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)). [resolve(955,a,976,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)),B). [resolve(955,a,977,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),B) = hAPP(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(955,a,979,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),A)) = hAPP(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(955,a,980,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = hAPP(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(955,a,981,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(955,a,982,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B)),c_Power_Opower__class_Opower(tc_Int_Oint,A,C)). [resolve(955,a,983,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B),C) = c_Power_Opower__class_Opower(tc_Int_Oint,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(955,a,984,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,C)),c_Power_Opower__class_Opower(tc_Int_Oint,B,C)). [resolve(955,a,985,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(955,a,986,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A). [resolve(955,a,987,a)].
% 1.86/2.06 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,hAPP(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)))),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B)),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(955,a,988,a)].
% 1.86/2.06 989 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),A). [resolve(989,a,956,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)). [resolve(989,a,957,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(989,a,958,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(989,a,959,a)].
% 1.86/2.06 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(989,a,960,a)].
% 1.86/2.06 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(989,a,961,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(989,a,962,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),D))). [resolve(989,a,964,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)),B). [resolve(989,a,965,a)].
% 1.86/2.06 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(989,a,966,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A). [resolve(989,a,968,a)].
% 1.86/2.06 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(989,a,969,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(989,a,970,a)].
% 1.86/2.06 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(989,a,972,a)].
% 1.86/2.06 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(989,a,973,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(989,a,974,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = A. [resolve(989,a,975,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(989,a,976,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)),B). [resolve(989,a,977,a)].
% 1.86/2.06 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),B) = hAPP(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(989,a,979,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),A)) = hAPP(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(989,a,980,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,A) = hAPP(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(989,a,981,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(989,a,982,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)),c_Power_Opower__class_Opower(tc_Nat_Onat,A,C)). [resolve(989,a,983,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B),C) = c_Power_Opower__class_Opower(tc_Nat_Onat,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(989,a,984,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,C)),c_Power_Opower__class_Opower(tc_Nat_Onat,B,C)). [resolve(989,a,985,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(989,a,986,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),A). [resolve(989,a,987,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,hAPP(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)))),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)). [resolve(989,a,988,a)].
% 1.86/2.07 990 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A). [resolve(990,a,956,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)). [resolve(990,a,957,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(990,a,958,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A) = A. [resolve(990,a,959,a)].
% 1.86/2.07 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(990,a,960,a)].
% 1.86/2.07 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(990,a,961,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(990,a,962,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),D))). [resolve(990,a,964,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)),B). [resolve(990,a,965,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C)). [resolve(990,a,966,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,A). [resolve(990,a,968,a)].
% 1.86/2.07 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(990,a,969,a)].
% 1.86/2.07 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(990,a,970,a)].
% 1.86/2.07 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(990,a,972,a)].
% 1.86/2.07 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(990,a,973,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(990,a,974,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = A. [resolve(990,a,975,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)). [resolve(990,a,976,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)),B). [resolve(990,a,977,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),B) = hAPP(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(990,a,979,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)) = hAPP(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(990,a,980,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = hAPP(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(990,a,981,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(990,a,982,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C)). [resolve(990,a,983,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),C) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(990,a,984,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,C)). [resolve(990,a,985,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(990,a,986,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A). [resolve(990,a,987,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,hAPP(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)))),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(990,a,988,a)].
% 1.86/2.07 991 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),A). [resolve(991,a,956,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C)). [resolve(991,a,957,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(991,a,958,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(991,a,959,a)].
% 1.86/2.07 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(991,a,960,a)].
% 1.86/2.07 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(991,a,961,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C)),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),D)). [resolve(991,a,962,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),D))). [resolve(991,a,964,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C)),B). [resolve(991,a,965,a)].
% 1.86/2.07 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),C)). [resolve(991,a,966,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A). [resolve(991,a,968,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C)). [resolve(991,a,969,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)). [resolve(991,a,970,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),B). [resolve(991,a,972,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,D)). [resolve(991,a,973,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(991,a,974,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = A. [resolve(991,a,975,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)). [resolve(991,a,976,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C)),B). [resolve(991,a,977,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),B). [resolve(991,a,979,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),A)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(991,a,980,a)].
% 1.86/2.07 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(991,a,981,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(991,a,982,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)),c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,C)). [resolve(991,a,983,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B),C) = c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(991,a,984,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,C)),c_Power_Opower__class_Opower(tc_Complex_Ocomplex,B,C)). [resolve(991,a,985,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(991,a,986,a)].
% 1.86/2.07 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A). [resolve(991,a,987,a)].
% 1.88/2.08 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,hAPP(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)))),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)),c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)). [resolve(991,a,988,a)].
% 1.88/2.08 992 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),A). [resolve(992,a,956,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C)). [resolve(992,a,957,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(992,a,958,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A) = A. [resolve(992,a,959,a)].
% 1.88/2.08 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(992,a,960,a)].
% 1.88/2.08 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A). [resolve(992,a,961,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C)),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(992,a,962,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),D))). [resolve(992,a,964,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C)),B). [resolve(992,a,965,a)].
% 1.88/2.08 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),C)). [resolve(992,a,966,a)].
% 1.88/2.08 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(992,a,968,a)].
% 1.88/2.08 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(992,a,969,a)].
% 1.88/2.08 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(992,a,970,a)].
% 1.88/2.08 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(992,a,972,a)].
% 1.88/2.08 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(992,a,973,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(992,a,974,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) = A. [resolve(992,a,975,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(992,a,976,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,C)),B). [resolve(992,a,977,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),B) = hAPP(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(992,a,979,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),A)) = hAPP(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(992,a,980,a)].
% 1.88/2.08 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,A) = hAPP(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(992,a,981,a)].
% 1.88/2.08 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(992,a,982,a)].
% 1.88/2.08 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(992,a,983,a)].
% 1.88/2.08 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),C) = c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(992,a,984,a)].
% 1.88/2.08 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C)),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(992,a,985,a)].
% 1.94/2.19 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(992,a,986,a)].
% 1.94/2.19 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),A). [resolve(992,a,987,a)].
% 1.94/2.19 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,hAPP(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)))),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(992,a,988,a)].
% 1.94/2.19 993 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption].
% 1.94/2.19 994 -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),hAPP(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(27)].
% 1.94/2.19 995 -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),hAPP(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(28)].
% 1.94/2.19 996 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(29)].
% 1.94/2.19 997 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(29)].
% 1.94/2.19 998 -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_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)) # label(fact_neg__less__divide__eq) # label(axiom). [clausify(30)].
% 1.94/2.19 999 -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_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)) # label(fact_neg__less__divide__eq) # label(axiom). [clausify(30)].
% 1.94/2.19 1000 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,hAPP(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(31)].
% 1.94/2.19 1001 -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,hAPP(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(32)].
% 1.94/2.19 1002 -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_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) # label(fact_pos__divide__less__eq) # label(axiom). [clausify(33)].
% 1.94/2.19 1003 -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_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) # label(fact_pos__divide__less__eq) # label(axiom). [clausify(33)].
% 1.94/2.19 1004 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(34)].
% 1.94/2.19 1005 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(34)].
% 1.94/2.19 1006 -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(38)].
% 1.94/2.19 1007 -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(39)].
% 1.94/2.19 1008 -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(40)].
% 1.94/2.19 1009 -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(41)].
% 1.94/2.19 1010 -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(42)].
% 1.94/2.19 1011 -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(43)].
% 1.94/2.19 1012 -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(145)].
% 1.94/2.19 1013 -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(146)].
% 1.94/2.19 1014 -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(147)].
% 1.94/2.19 1015 -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(148)].
% 1.94/2.19 1016 -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(149)].
% 1.94/2.19 1017 -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(150)].
% 1.94/2.19 1018 -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(151)].
% 1.94/2.19 1019 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(159)].
% 1.94/2.19 1020 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(159)].
% 1.94/2.19 1021 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(160)].
% 1.94/2.19 1022 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(160)].
% 1.94/2.19 1023 -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,hAPP(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(161)].
% 1.94/2.19 1024 -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,hAPP(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(162)].
% 1.94/2.19 1025 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)) # label(fact_neg__le__divide__eq) # label(axiom). [clausify(163)].
% 1.94/2.19 1026 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)) # label(fact_neg__le__divide__eq) # label(axiom). [clausify(163)].
% 1.94/2.19 1027 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C) # label(fact_neg__divide__le__eq) # label(axiom). [clausify(164)].
% 1.94/2.19 1028 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C) # label(fact_neg__divide__le__eq) # label(axiom). [clausify(164)].
% 1.94/2.19 1029 -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),hAPP(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(165)].
% 1.94/2.19 1030 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__le__inverse) # label(axiom). [clausify(231)].
% 1.94/2.19 1031 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_inverse__less__imp__less__neg) # label(axiom). [clausify(310)].
% 1.94/2.19 1032 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_inverse__less__imp__less) # label(axiom). [clausify(311)].
% 1.94/2.19 1033 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__negative__imp__negative) # label(axiom). [clausify(312)].
% 1.94/2.19 1034 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_less__imp__inverse__less__neg) # label(axiom). [clausify(313)].
% 1.94/2.19 1035 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_less__imp__inverse__less) # label(axiom). [clausify(314)].
% 1.94/2.19 1036 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_negative__imp__inverse__negative) # label(axiom). [clausify(315)].
% 1.94/2.19 1037 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__positive__imp__positive) # label(axiom). [clausify(316)].
% 1.94/2.19 1038 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_positive__imp__inverse__positive) # label(axiom). [clausify(317)].
% 1.94/2.19 1039 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_inverse__le__imp__le__neg) # label(axiom). [clausify(350)].
% 1.94/2.19 1040 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_inverse__le__imp__le) # label(axiom). [clausify(351)].
% 1.94/2.19 1041 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_le__imp__inverse__le__neg) # label(axiom). [clausify(352)].
% 1.94/2.19 1042 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_le__imp__inverse__le) # label(axiom). [clausify(353)].
% 1.94/2.19 1043 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_one__less__inverse) # label(axiom). [clausify(355)].
% 1.94/2.19 1044 -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(374)].
% 1.94/2.19 1045 -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(375)].
% 1.94/2.19 1046 -class_Fields_Olinordered__field(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),f4(B,C,A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__epsilon) # label(axiom). [clausify(386)].
% 1.94/2.19 1047 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oplus__class_Oplus(A,C,f4(C,B,A))) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_field__le__epsilon) # label(axiom). [clausify(386)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(993,a,994,a)].
% 1.94/2.19 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),hAPP(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(993,a,995,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A),B). [resolve(993,a,996,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A),B). [resolve(993,a,997,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)). [resolve(993,a,998,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)). [resolve(993,a,999,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(993,a,1000,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(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(993,a,1001,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)). [resolve(993,a,1002,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),C). [resolve(993,a,1004,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(993,a,1006,a)].
% 1.94/2.19 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(993,a,1007,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)). [resolve(993,a,1008,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(993,a,1009,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_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(993,a,1010,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(993,a,1011,a)].
% 1.94/2.19 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(993,a,1012,a)].
% 1.94/2.19 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(993,a,1013,a)].
% 1.94/2.19 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(993,a,1014,a)].
% 1.94/2.19 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(993,a,1015,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(993,a,1016,a)].
% 1.94/2.19 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(993,a,1017,a)].
% 1.94/2.19 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(993,a,1018,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),C). [resolve(993,a,1019,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),C). [resolve(993,a,1020,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)). [resolve(993,a,1021,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)). [resolve(993,a,1022,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)). [resolve(993,a,1025,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)). [resolve(993,a,1026,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A),B). [resolve(993,a,1027,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A),B). [resolve(993,a,1028,a)].
% 1.94/2.19 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),hAPP(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(993,a,1029,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1030,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(993,a,1031,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(993,a,1032,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_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)). [resolve(993,a,1033,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1034,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1035,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(993,a,1036,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | 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),A). [resolve(993,a,1037,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1038,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(993,a,1039,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(993,a,1040,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1041,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1042,a)].
% 1.94/2.19 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(993,a,1043,a)].
% 2.09/2.30 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(993,a,1044,a)].
% 2.09/2.30 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(993,a,1045,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f4(A,B,tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(993,a,1046,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,f4(B,A,tc_RealDef_Oreal))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(993,a,1047,a)].
% 2.09/2.30 1048 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 2.09/2.30 1049 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1050 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1051 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1052 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1053 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1054 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1055 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1056 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1057 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1058 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom). [clausify(35)].
% 2.09/2.30 1059 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1060 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1061 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1062 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1063 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1064 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1065 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1066 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1067 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1068 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom). [clausify(36)].
% 2.09/2.30 1069 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(44)].
% 2.09/2.30 1070 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__less__0__iff) # label(axiom). [clausify(44)].
% 2.09/2.30 1071 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),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,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(44)].
% 2.09/2.30 1072 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),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) # label(fact_divide__less__0__iff) # label(axiom). [clausify(44)].
% 2.09/2.30 1073 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__0__iff) # label(axiom). [clausify(44)].
% 2.09/2.30 1074 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(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) # label(fact_divide__less__0__iff) # label(axiom). [clausify(44)].
% 2.09/2.30 1075 -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)) | 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)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(45)].
% 2.09/2.30 1076 -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)) | 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)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(45)].
% 2.09/2.30 1077 -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)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(45)].
% 2.09/2.30 1078 -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)) | 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)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(45)].
% 2.09/2.30 1079 -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)) | -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__divide__iff) # label(axiom). [clausify(45)].
% 2.09/2.30 1080 -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)) | -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)) # label(fact_zero__less__divide__iff) # label(axiom). [clausify(45)].
% 2.09/2.30 1081 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,D),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_divide__right__mono__neg) # label(axiom). [clausify(126)].
% 2.09/2.30 1082 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide__right__mono) # label(axiom). [clausify(127)].
% 2.09/2.30 1083 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom). [clausify(128)].
% 2.09/2.30 1084 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom). [clausify(128)].
% 2.09/2.30 1085 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom). [clausify(128)].
% 2.09/2.30 1086 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom). [clausify(128)].
% 2.09/2.30 1087 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom). [clausify(128)].
% 2.09/2.30 1088 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom). [clausify(128)].
% 2.09/2.30 1089 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(129)].
% 2.09/2.30 1090 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(129)].
% 2.09/2.30 1091 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(129)].
% 2.09/2.30 1092 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(129)].
% 2.09/2.30 1093 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(129)].
% 2.09/2.30 1094 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom). [clausify(129)].
% 2.09/2.30 1095 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1096 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1097 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1098 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1099 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1100 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1101 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1102 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1103 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1104 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom). [clausify(157)].
% 2.09/2.30 1105 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1106 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1107 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1108 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1109 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1110 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1111 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1112 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1113 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1114 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom). [clausify(158)].
% 2.09/2.30 1115 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_divide__left__mono__neg) # label(axiom). [clausify(166)].
% 2.09/2.30 1116 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),f3(B,C,A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__mult__one__interval) # label(axiom). [clausify(226)].
% 2.09/2.30 1117 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,f3(B,C,A),c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__mult__one__interval) # label(axiom). [clausify(226)].
% 2.09/2.30 1118 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,f3(B,C,A)),C),B) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__mult__one__interval) # label(axiom). [clausify(226)].
% 2.09/2.30 1119 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(229)].
% 2.09/2.30 1120 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oone__class_Oone(A)) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(229)].
% 2.09/2.30 1121 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oone__class_Oone(A)) # label(fact_one__le__inverse__iff) # label(axiom). [clausify(229)].
% 2.09/2.30 1122 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(230)].
% 2.09/2.30 1123 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(230)].
% 2.09/2.30 1124 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__less__1__iff) # label(axiom). [clausify(230)].
% 2.09/2.30 1125 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(308)].
% 2.09/2.30 1126 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(308)].
% 2.09/2.30 1127 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(309)].
% 2.09/2.30 1128 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(309)].
% 2.09/2.30 1129 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__negative__iff__negative) # label(axiom). [clausify(318)].
% 2.09/2.30 1130 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__negative__iff__negative) # label(axiom). [clausify(318)].
% 2.09/2.30 1131 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__positive__iff__positive) # label(axiom). [clausify(319)].
% 2.09/2.30 1132 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_inverse__positive__iff__positive) # label(axiom). [clausify(319)].
% 2.09/2.30 1133 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(354)].
% 2.09/2.30 1134 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(354)].
% 2.09/2.30 1135 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__le__1__iff) # label(axiom). [clausify(354)].
% 2.09/2.30 1136 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(356)].
% 2.09/2.30 1137 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(356)].
% 2.09/2.30 1138 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) # label(fact_one__less__inverse__iff) # label(axiom). [clausify(356)].
% 2.09/2.30 1139 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(402)].
% 2.09/2.30 1140 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(402)].
% 2.09/2.30 1141 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(402)].
% 2.09/2.30 1142 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(402)].
% 2.09/2.30 1143 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B) | -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(402)].
% 2.09/2.30 1144 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(402)].
% 2.09/2.30 1145 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(402)].
% 2.09/2.30 1146 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(402)].
% 2.09/2.30 1147 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B) | -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(402)].
% 2.09/2.30 1148 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq__number__of1) # label(axiom). [clausify(402)].
% 2.09/2.30 1149 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(403)].
% 2.09/2.30 1150 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(403)].
% 2.09/2.30 1151 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(403)].
% 2.09/2.30 1152 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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(403)].
% 2.09/2.30 1153 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(403)].
% 2.09/2.30 1154 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(403)].
% 2.09/2.30 1155 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(403)].
% 2.09/2.30 1156 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(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(403)].
% 2.09/2.30 1157 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(403)].
% 2.09/2.30 1158 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(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,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(403)].
% 2.09/2.30 1159 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_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__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1160 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_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__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1161 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_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__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1162 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_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__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1163 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_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__eq(A,C,hAPP(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_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1164 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_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__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1165 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1166 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1167 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(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_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1168 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq__number__of) # label(axiom). [clausify(404)].
% 2.09/2.30 1169 -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,hAPP(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(405)].
% 2.09/2.30 1170 -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,hAPP(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(405)].
% 2.09/2.30 1171 -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(405)].
% 2.09/2.30 1172 -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(405)].
% 2.09/2.30 1173 -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,hAPP(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(405)].
% 2.09/2.30 1174 -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,hAPP(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(405)].
% 2.09/2.30 1175 -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,hAPP(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(405)].
% 2.09/2.30 1176 -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,hAPP(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(405)].
% 2.09/2.30 1177 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(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(405)].
% 2.09/2.30 1178 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(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(405)].
% 2.09/2.30 1179 -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,hAPP(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(425)].
% 2.09/2.30 1180 -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,hAPP(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(425)].
% 2.09/2.30 1181 -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(425)].
% 2.09/2.30 1182 -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(425)].
% 2.09/2.30 1183 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(425)].
% 2.09/2.30 1184 -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,hAPP(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),D) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(425)].
% 2.09/2.30 1185 -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,B,hAPP(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__less__eq__number__of1) # label(axiom). [clausify(425)].
% 2.09/2.30 1186 -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,B,hAPP(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(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(425)].
% 2.09/2.30 1187 -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,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(425)].
% 2.09/2.30 1188 -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,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))) | -c_Orderings_Oord__class_Oless(A,hAPP(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),D) # label(fact_divide__less__eq__number__of1) # label(axiom). [clausify(425)].
% 2.09/2.30 1189 -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),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,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1190 -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),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(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1191 -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),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(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1192 -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),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(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1193 -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),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,hAPP(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__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1194 -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),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,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1195 -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),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless(A,B,hAPP(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__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1196 -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),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless(A,B,hAPP(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(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1197 -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),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(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__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1198 -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),c_Int_Onumber__class_Onumber__of(A,D)) | -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)) # label(fact_divide__less__eq__number__of) # label(axiom). [clausify(426)].
% 2.09/2.30 1199 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_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,hAPP(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(427)].
% 2.09/2.30 1200 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_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,hAPP(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(427)].
% 2.09/2.30 1201 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_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(427)].
% 2.09/2.30 1202 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_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(427)].
% 2.09/2.30 1203 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_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,hAPP(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(427)].
% 2.09/2.30 1204 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_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,hAPP(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(427)].
% 2.09/2.30 1205 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(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(427)].
% 2.09/2.30 1206 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(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(427)].
% 2.09/2.30 1207 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(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(427)].
% 2.09/2.30 1208 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(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(427)].
% 2.09/2.30 1209 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(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,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1210 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(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(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1211 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | -c_Orderings_Oord__class_Oless(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(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1212 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(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(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1213 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(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,hAPP(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_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1214 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(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,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1215 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,hAPP(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_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1216 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,hAPP(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(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1217 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(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_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1218 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber(A) | c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq__number__of1) # label(axiom). [clausify(428)].
% 2.09/2.30 1219 -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(748)].
% 2.09/2.30 1220 -class_Fields_Olinordered__field__inverse__zero(A) | -class_Int_Onumber__ring(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(796)].
% 2.09/2.30 1221 -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,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(797)].
% 2.09/2.30 1222 -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,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(797)].
% 2.09/2.30 1223 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),B) # label(fact_abs__div__pos) # label(axiom). [clausify(946)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1051,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1052,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1054,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1056,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1058,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1061,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1062,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1064,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1066,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1068,a)].
% 2.09/2.30 Derived: -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)) | 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)). [resolve(1048,a,1069,a)].
% 2.09/2.30 Derived: -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)) | 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(1048,a,1070,a)].
% 2.09/2.30 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1071,a)].
% 2.09/2.30 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1048,a,1072,a)].
% 2.09/2.30 Derived: -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)) | 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)). [resolve(1048,a,1075,a)].
% 2.09/2.30 Derived: -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)) | 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)). [resolve(1048,a,1076,a)].
% 2.09/2.30 Derived: -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)) | 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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1077,a)].
% 2.09/2.30 Derived: -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)) | 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)). [resolve(1048,a,1078,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)). [resolve(1048,a,1081,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1048,a,1082,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1083,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1048,a,1084,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1085,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1048,a,1086,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1087,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1048,a,1088,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1089,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1090,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1091,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1092,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1048,a,1093,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1094,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1097,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1098,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1100,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1102,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1104,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1107,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1108,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1110,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1112,a)].
% 2.09/2.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1048,a,1114,a)].
% 2.09/2.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)). [resolve(1048,a,1115,a)].
% 2.09/2.31 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f3(A,B,tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1048,a,1116,a)].
% 2.09/2.31 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,f3(A,B,tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1048,a,1117,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,f3(A,B,tc_RealDef_Oreal)),B),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1048,a,1118,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1048,a,1119,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1048,a,1120,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | 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_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1048,a,1122,a)].
% 2.09/2.31 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1123,a)].
% 2.09/2.31 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1048,a,1124,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1125,a)].
% 2.09/2.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1126,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1048,a,1127,a)].
% 2.09/2.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1048,a,1128,a)].
% 2.09/2.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1129,a)].
% 2.21/2.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1048,a,1131,a)].
% 2.21/2.40 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1048,a,1133,a)].
% 2.21/2.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1048,a,1134,a)].
% 2.21/2.40 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1048,a,1135,a)].
% 2.21/2.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1048,a,1136,a)].
% 2.21/2.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1048,a,1137,a)].
% 2.21/2.40 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(1048,a,1219,a)].
% 2.21/2.40 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_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))))). [resolve(1048,a,1220,a)].
% 2.21/2.40 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1048,a,1221,a)].
% 2.21/2.40 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B),A). [resolve(1048,a,1223,a)].
% 2.21/2.40 1224 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 2.21/2.40 1225 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Odivide(A,B,D)),c_Rings_Oinverse__class_Odivide(A,C,E)) # label(fact_times__divide__times__eq) # label(axiom). [clausify(37)].
% 2.21/2.40 1226 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) = c_Rings_Oinverse__class_Odivide(A,C,D) # label(fact_mult__divide__mult__cancel__left) # label(axiom). [clausify(47)].
% 2.21/2.40 1227 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) = c_Rings_Oinverse__class_Odivide(A,C,D) # label(fact_mult__divide__mult__cancel__right) # label(axiom). [clausify(48)].
% 2.21/2.40 1228 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) = C | hAPP(c_Groups_Otimes__class_Otimes(A,D),C) = B # label(fact_divide__eq__eq) # label(axiom). [clausify(49)].
% 2.21/2.40 1229 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_divide__eq__eq) # label(axiom). [clausify(49)].
% 2.21/2.40 1230 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq) # label(axiom). [clausify(49)].
% 2.21/2.40 1231 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divide__eq__eq) # label(axiom). [clausify(49)].
% 2.21/2.40 1232 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),C) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq) # label(axiom). [clausify(49)].
% 2.21/2.40 1233 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) = C | hAPP(c_Groups_Otimes__class_Otimes(A,D),C) = B # label(fact_eq__divide__eq) # label(axiom). [clausify(50)].
% 2.21/2.40 1234 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_eq__divide__eq) # label(axiom). [clausify(50)].
% 2.21/2.40 1235 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq) # label(axiom). [clausify(50)].
% 2.21/2.40 1236 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_eq__divide__eq) # label(axiom). [clausify(50)].
% 2.21/2.40 1237 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),C) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq) # label(axiom). [clausify(50)].
% 2.21/2.40 1238 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_field__inverse__zero) # label(axiom). [clausify(253)].
% 2.21/2.40 1239 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_inverse__mult__distrib) # label(axiom). [clausify(260)].
% 2.21/2.40 1240 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) = B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(261)].
% 2.21/2.40 1241 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) != B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(261)].
% 2.21/2.40 1242 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Odivide(A,B,C)) = c_Rings_Oinverse__class_Odivide(A,C,B) # label(fact_inverse__divide) # label(axiom). [clausify(263)].
% 2.21/2.40 1243 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)),B) # label(fact_add__frac__num) # label(axiom). [clausify(370)].
% 2.21/2.40 1244 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)),B) # label(fact_add__num__frac) # label(axiom). [clausify(372)].
% 2.21/2.40 1245 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(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) | hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)) = B # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(420)].
% 2.21/2.40 1246 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(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_eq__divide__eq__number__of1) # label(axiom). [clausify(420)].
% 2.21/2.40 1247 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(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_eq__divide__eq__number__of1) # label(axiom). [clausify(420)].
% 2.21/2.40 1248 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)) != B | c_Int_Onumber__class_Onumber__of(A,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(420)].
% 2.21/2.40 1249 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq__number__of1) # label(axiom). [clausify(420)].
% 2.21/2.40 1250 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Rings_Oinverse__class_Odivide(A,C,D) | c_Groups_Ozero__class_Ozero(A) = D | hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D) = C # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(421)].
% 2.21/2.40 1251 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Rings_Oinverse__class_Odivide(A,C,D) | c_Groups_Ozero__class_Ozero(A) != D | c_Int_Onumber__class_Onumber__of(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(421)].
% 2.21/2.40 1252 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Rings_Oinverse__class_Odivide(A,C,D) | c_Groups_Ozero__class_Ozero(A) != D | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(421)].
% 2.21/2.40 1253 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Rings_Oinverse__class_Odivide(A,C,D) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(421)].
% 2.21/2.40 1254 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Rings_Oinverse__class_Odivide(A,C,D) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D) != C | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_eq__divide__eq__number__of) # label(axiom). [clausify(421)].
% 2.21/2.40 1255 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Rings_Oinverse__class_Odivide(A,C,D) | c_Groups_Ozero__class_Ozero(A) = D | hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D) = C # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(422)].
% 2.21/2.40 1256 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) != c_Rings_Oinverse__class_Odivide(A,C,D) | c_Groups_Ozero__class_Ozero(A) != D | c_Int_Onumber__class_Onumber__of(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(422)].
% 2.21/2.40 1257 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Rings_Oinverse__class_Odivide(A,C,D) | c_Groups_Ozero__class_Ozero(A) != D | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(422)].
% 2.21/2.40 1258 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Rings_Oinverse__class_Odivide(A,C,D) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(422)].
% 2.21/2.40 1259 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(A,B) = c_Rings_Oinverse__class_Odivide(A,C,D) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D) != C | c_Int_Onumber__class_Onumber__of(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of) # label(axiom). [clausify(422)].
% 2.21/2.40 1260 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(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) | hAPP(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(423)].
% 2.21/2.40 1261 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(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(423)].
% 2.21/2.40 1262 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(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(423)].
% 2.21/2.40 1263 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)) != B | c_Int_Onumber__class_Onumber__of(A,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(423)].
% 2.21/2.40 1264 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq__number__of1) # label(axiom). [clausify(423)].
% 2.21/2.40 1265 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) = c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__divide__right) # label(axiom). [clausify(475)].
% 2.21/2.40 1266 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) = c_Rings_Oinverse__class_Odivide(A,B,C) # label(fact_minus__divide__divide) # label(axiom). [clausify(476)].
% 2.21/2.40 1267 -class_Fields_Ofield__inverse__zero(A) | -class_Int_Onumber__ring(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(618)].
% 2.21/2.40 1268 -class_Fields_Ofield__inverse__zero(A) | c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) = c_Rings_Oinverse__class_Odivide(A,c_Power_Opower__class_Opower(A,B,D),c_Power_Opower__class_Opower(A,C,D)) # label(fact_power__divide) # label(axiom). [clausify(897)].
% 2.21/2.40 1269 -class_Fields_Ofield__inverse__zero(A) | c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B),C) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Power_Opower__class_Opower(A,B,C)) # label(fact_power__one__over) # label(axiom). [clausify(910)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,D)). [resolve(1224,a,1225,a)].
% 2.21/2.40 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C). [resolve(1224,a,1226,a)].
% 2.21/2.40 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C). [resolve(1224,a,1227,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) != C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B) = A. [resolve(1224,a,1228,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) != C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = C. [resolve(1224,a,1229,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C. [resolve(1224,a,1230,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1224,a,1231,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C. [resolve(1224,a,1232,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1224,a,1238,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1224,a,1239,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = A. [resolve(1224,a,1240,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A. [resolve(1224,a,1241,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A). [resolve(1224,a,1242,a)].
% 2.21/2.40 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)),A). [resolve(1224,a,1243,a)].
% 2.21/2.40 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)),A). [resolve(1224,a,1244,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(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) | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = A. [resolve(1224,a,1245,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = C. [resolve(1224,a,1246,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C. [resolve(1224,a,1247,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) != A | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1224,a,1248,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C) = B. [resolve(1224,a,1250,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1224,a,1251,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1224,a,1252,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C) | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = C. [resolve(1224,a,1253,a)].
% 2.21/2.40 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C) | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)),C) != B | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1224,a,1254,a)].
% 2.21/2.40 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)). [resolve(1224,a,1265,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B). [resolve(1224,a,1266,a)].
% 2.21/2.40 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1224,a,1267,a)].
% 2.21/2.40 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,C)). [resolve(1224,a,1268,a)].
% 2.21/2.40 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A),B) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1224,a,1269,a)].
% 2.21/2.40 1270 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),D)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,D)). [resolve(1270,a,1225,a)].
% 2.21/2.40 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C). [resolve(1270,a,1226,a)].
% 2.21/2.40 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C). [resolve(1270,a,1227,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),B) = A. [resolve(1270,a,1228,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C. [resolve(1270,a,1229,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C. [resolve(1270,a,1230,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1270,a,1231,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C. [resolve(1270,a,1232,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1270,a,1238,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1270,a,1239,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A. [resolve(1270,a,1240,a)].
% 2.21/2.40 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1270,a,1241,a)].
% 2.21/2.41 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A). [resolve(1270,a,1242,a)].
% 2.21/2.41 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),A)),A). [resolve(1270,a,1243,a)].
% 2.21/2.41 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),A)),A). [resolve(1270,a,1244,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)) != C | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)) = A. [resolve(1270,a,1245,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)) != C | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C. [resolve(1270,a,1246,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)) = C | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C. [resolve(1270,a,1247,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B)) != A | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1270,a,1248,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)),C) = B. [resolve(1270,a,1250,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1270,a,1251,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1270,a,1252,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C) | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)),C) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C. [resolve(1270,a,1253,a)].
% 2.21/2.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C) | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)),C) != B | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1270,a,1254,a)].
% 2.24/2.49 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1270,a,1265,a)].
% 2.24/2.49 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B). [resolve(1270,a,1266,a)].
% 2.24/2.49 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1270,a,1267,a)].
% 2.24/2.49 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B),C) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,C),c_Power_Opower__class_Opower(tc_Complex_Ocomplex,B,C)). [resolve(1270,a,1268,a)].
% 2.24/2.49 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A),B) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)). [resolve(1270,a,1269,a)].
% 2.24/2.49 1271 class_Fields_Ofield(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield) # label(axiom). [assumption].
% 2.24/2.49 1272 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) != c_Rings_Oinverse__class_Odivide(A,E,B) | hAPP(c_Groups_Otimes__class_Otimes(A,D),B) = hAPP(c_Groups_Otimes__class_Otimes(A,E),C) # label(fact_frac__eq__eq) # label(axiom). [clausify(46)].
% 2.24/2.49 1273 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) = c_Rings_Oinverse__class_Odivide(A,E,B) | hAPP(c_Groups_Otimes__class_Otimes(A,D),B) != hAPP(c_Groups_Otimes__class_Otimes(A,E),C) # label(fact_frac__eq__eq) # label(axiom). [clausify(46)].
% 2.24/2.49 1274 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,B))),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_inverse__add) # label(axiom). [clausify(251)].
% 2.24/2.49 1275 -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_field__divide__inverse) # label(axiom). [clausify(322)].
% 2.24/2.49 1276 -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_field__class_Onormalizing__field__rules_I2_J) # label(axiom). [clausify(324)].
% 2.24/2.49 1277 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),B) # label(fact_field__inverse) # label(axiom). [clausify(357)].
% 2.24/2.49 1278 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,E),B)),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_add__frac__eq) # label(axiom). [clausify(368)].
% 2.24/2.49 1279 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)),B) # label(fact_divide__add__eq__iff) # label(axiom). [clausify(369)].
% 2.24/2.49 1280 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oplus__class_Oplus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),D),B) # label(fact_add__divide__eq__iff) # label(axiom). [clausify(371)].
% 2.24/2.49 1281 -class_Fields_Ofield(A) | -class_Int_Onumber__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) = B # label(fact_divide__Numeral1) # label(axiom). [clausify(643)].
% 2.24/2.49 1282 -class_Fields_Ofield(A) | -class_Int_Onumber__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) = B # label(fact_divide__numeral__1) # label(axiom). [clausify(644)].
% 2.24/2.49 1283 -class_Fields_Ofield(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))) # label(fact_inverse__numeral__1) # label(axiom). [clausify(645)].
% 2.24/2.49 1284 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) = c_Rings_Oinverse__class_Odivide(A,c_Power_Opower__class_Opower(A,C,D),c_Power_Opower__class_Opower(A,B,D)) # label(fact_nonzero__power__divide) # label(axiom). [clausify(907)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,A) | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),B). [resolve(1271,a,1272,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,A) | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),B). [resolve(1271,a,1273,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1271,a,1274,a)].
% 2.24/2.49 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1271,a,1275,a)].
% 2.24/2.49 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). [resolve(1271,a,1276,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),A). [resolve(1271,a,1277,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),A)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)). [resolve(1271,a,1278,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)),A). [resolve(1271,a,1279,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),C),A). [resolve(1271,a,1280,a)].
% 2.24/2.49 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls))) = A. [resolve(1271,a,1281,a)].
% 2.24/2.49 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OPls))). [resolve(1271,a,1283,a)].
% 2.24/2.49 1285 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom). [assumption].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,A) | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D),B). [resolve(1285,a,1272,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,A) | hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),A) != hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D),B). [resolve(1285,a,1273,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A))),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1285,a,1274,a)].
% 2.24/2.49 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1285,a,1275,a)].
% 2.24/2.49 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A). [resolve(1285,a,1276,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),A). [resolve(1285,a,1277,a)].
% 2.24/2.49 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D),A)),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)). [resolve(1285,a,1278,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C)),A). [resolve(1285,a,1279,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),C),A). [resolve(1285,a,1280,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(c_Int_OPls))) = A. [resolve(1285,a,1281,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(c_Int_OPls))). [resolve(1285,a,1283,a)].
% 2.31/2.57 1286 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom). [assumption].
% 2.31/2.57 1287 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) != c_Rings_Oinverse__class_Odivide(A,C,B) | C = B # label(fact_right__inverse__eq) # label(axiom). [clausify(52)].
% 2.31/2.57 1288 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Odivide(A,C,B) | C != B # label(fact_right__inverse__eq) # label(axiom). [clausify(52)].
% 2.31/2.57 1289 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Odivide(A,B,B) # label(fact_divide__self) # label(axiom). [clausify(53)].
% 2.31/2.57 1290 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(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(55)].
% 2.31/2.57 1291 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(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(56)].
% 2.31/2.57 1292 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | hAPP(c_Groups_Otimes__class_Otimes(A,D),B) = C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(57)].
% 2.31/2.57 1293 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),B) != C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(57)].
% 2.31/2.57 1294 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | hAPP(c_Groups_Otimes__class_Otimes(A,D),B) = C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(58)].
% 2.31/2.57 1295 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | hAPP(c_Groups_Otimes__class_Otimes(A,D),B) != C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(58)].
% 2.31/2.57 1296 -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(70)].
% 2.31/2.57 1297 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),D) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_times__divide__eq__right) # label(axiom). [clausify(72)].
% 2.31/2.57 1298 -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(73)].
% 2.31/2.57 1299 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oplus__class_Oplus(A,B,C))),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__add) # label(axiom). [clausify(252)].
% 2.31/2.57 1300 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ozero__class_Ozero(A) = B | B = C # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(254)].
% 2.31/2.57 1301 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__zero__imp__zero) # label(axiom). [clausify(255)].
% 2.31/2.57 1302 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B)) = B # label(fact_nonzero__inverse__inverse__eq) # label(axiom). [clausify(256)].
% 2.31/2.57 1303 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom). [clausify(257)].
% 2.31/2.57 1304 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_inverse__1) # label(axiom). [clausify(262)].
% 2.31/2.57 1305 -class_Rings_Odivision__ring(A) | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Rings_Oinverse__class_Odivide(A,D,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_add__divide__distrib) # label(axiom). [clausify(298)].
% 2.31/2.57 1306 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_nonzero__inverse__mult__distrib) # label(axiom). [clausify(320)].
% 2.31/2.57 1307 -class_Rings_Odivision__ring(A) | c_Groups_Oone__class_Oone(A) != hAPP(c_Groups_Otimes__class_Otimes(A,B),C) | c_Rings_Oinverse__class_Oinverse(A,B) = C # label(fact_inverse__unique) # label(axiom). [clausify(321)].
% 2.31/2.57 1308 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_divide__inverse) # label(axiom). [clausify(323)].
% 2.31/2.57 1309 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__eq__divide) # label(axiom). [clausify(325)].
% 2.31/2.57 1310 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),B) # label(fact_left__inverse) # label(axiom). [clausify(358)].
% 2.31/2.57 1311 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_right__inverse) # label(axiom). [clausify(359)].
% 2.31/2.57 1312 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_nonzero__inverse__eq__divide) # label(axiom). [clausify(360)].
% 2.31/2.57 1313 -class_Int_Onumber(A) | -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,c_Int_Onumber__class_Onumber__of(A,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_inverse__eq__divide__number__of) # label(axiom). [clausify(424)].
% 2.31/2.57 1314 -class_Rings_Odivision__ring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_minus__divide__left) # label(axiom). [clausify(474)].
% 2.31/2.57 1315 -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(540)].
% 2.31/2.57 1316 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,C,B)) = c_Rings_Oinverse__class_Odivide(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_nonzero__minus__divide__right) # label(axiom). [clausify(541)].
% 2.31/2.57 1317 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)) = c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_nonzero__inverse__minus__eq) # label(axiom). [clausify(542)].
% 2.31/2.57 1318 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Oinverse(A,B),C) = c_Rings_Oinverse__class_Oinverse(A,c_Power_Opower__class_Opower(A,B,C)) # label(fact_nonzero__power__inverse) # label(axiom). [clausify(911)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A) | B = A. [resolve(1286,a,1287,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A) | B != A. [resolve(1286,a,1288,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,A). [resolve(1286,a,1289,a)].
% 2.31/2.57 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(1286,a,1296,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)). [resolve(1286,a,1297,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1286,a,1298,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)). [resolve(1286,a,1299,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | A = B. [resolve(1286,a,1300,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1286,a,1301,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = A. [resolve(1286,a,1302,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1286,a,1304,a)].
% 2.31/2.57 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),B). [resolve(1286,a,1305,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1286,a,1306,a)].
% 2.31/2.57 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = B. [resolve(1286,a,1307,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)). [resolve(1286,a,1311,a)].
% 2.31/2.57 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B). [resolve(1286,a,1314,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1286,a,1317,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),B) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1286,a,1318,a)].
% 2.31/2.57 1319 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom). [assumption].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) | B = A. [resolve(1319,a,1287,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) | B != A. [resolve(1319,a,1288,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A). [resolve(1319,a,1289,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1319,a,1296,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B),C) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)). [resolve(1319,a,1297,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1319,a,1298,a)].
% 2.31/2.57 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B))),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1319,a,1299,a)].
% 2.31/2.57 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | A = B. [resolve(1319,a,1300,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1319,a,1301,a)].
% 2.39/2.66 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1319,a,1302,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1319,a,1304,a)].
% 2.39/2.66 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C),B). [resolve(1319,a,1305,a)].
% 2.39/2.66 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1319,a,1306,a)].
% 2.39/2.66 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B) | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = B. [resolve(1319,a,1307,a)].
% 2.39/2.66 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1319,a,1311,a)].
% 2.39/2.66 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B). [resolve(1319,a,1314,a)].
% 2.39/2.66 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1319,a,1317,a)].
% 2.39/2.66 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),B) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)). [resolve(1319,a,1318,a)].
% 2.39/2.66 1320 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 2.39/2.66 1321 -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(54)].
% 2.39/2.66 1322 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Odivide(A,B,B) # label(fact_divide__self__if) # label(axiom). [clausify(54)].
% 2.39/2.66 1323 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__zero) # label(axiom). [clausify(71)].
% 2.39/2.66 1324 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B)) = B # label(fact_inverse__inverse__eq) # label(axiom). [clausify(235)].
% 2.39/2.66 1325 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | B = C # label(fact_inverse__eq__iff__eq) # label(axiom). [clausify(237)].
% 2.39/2.66 1326 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Oinverse(A,C) | B != C # label(fact_inverse__eq__iff__eq) # label(axiom). [clausify(237)].
% 2.39/2.66 1327 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | B = C # label(fact_inverse__eq__imp__eq) # label(axiom). [clausify(238)].
% 2.39/2.66 1328 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(258)].
% 2.39/2.66 1329 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(258)].
% 2.39/2.66 1330 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_inverse__zero) # label(axiom). [clausify(259)].
% 2.39/2.66 1331 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)) = c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_inverse__minus__eq) # label(axiom). [clausify(478)].
% 2.39/2.66 1332 -class_Rings_Odivision__ring__inverse__zero(A) | c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Oinverse(A,B),C) = c_Rings_Oinverse__class_Oinverse(A,c_Power_Opower__class_Opower(A,B,C)) # label(fact_power__inverse) # label(axiom). [clausify(899)].
% 2.39/2.66 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(1320,a,1321,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1320,a,1323,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = A. [resolve(1320,a,1324,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) != c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | A = B. [resolve(1320,a,1325,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B) | A != B. [resolve(1320,a,1326,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1320,a,1329,a)].
% 2.39/2.66 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1320,a,1331,a)].
% 2.39/2.66 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A),B) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1320,a,1332,a)].
% 2.39/2.66 1333 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 2.39/2.66 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1333,a,1321,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1333,a,1323,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1333,a,1324,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | A = B. [resolve(1333,a,1325,a)].
% 2.39/2.66 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | A != B. [resolve(1333,a,1326,a)].
% 2.54/2.74 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1333,a,1329,a)].
% 2.54/2.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1333,a,1331,a)].
% 2.54/2.74 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),B) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)). [resolve(1333,a,1332,a)].
% 2.54/2.74 1334 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.54/2.74 1335 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_less__1__mult) # label(axiom). [clausify(59)].
% 2.54/2.74 1336 -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(60)].
% 2.54/2.74 1337 -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(61)].
% 2.54/2.74 1338 -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(124)].
% 2.54/2.74 1339 -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(125)].
% 2.54/2.74 1340 -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(337)].
% 2.54/2.74 1341 -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(341)].
% 2.54/2.74 1342 -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(367)].
% 2.54/2.74 1343 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_power2__le__imp__le) # label(axiom). [clausify(850)].
% 2.54/2.74 1344 -class_Rings_Olinordered__semidom(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | B = C # label(fact_power2__eq__imp__eq) # label(axiom). [clausify(851)].
% 2.54/2.74 1345 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_power2__less__imp__less) # label(axiom). [clausify(863)].
% 2.54/2.74 1346 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D) | c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,D),c_Power_Opower__class_Opower(A,C,D)) # label(fact_power__strict__mono) # label(axiom). [clausify(885)].
% 2.54/2.74 1347 -class_Rings_Olinordered__semidom(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_Power_Opower__class_Opower(A,B,C)) # label(fact_zero__le__power) # label(axiom). [clausify(901)].
% 2.54/2.74 1348 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(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_Power_Opower__class_Opower(A,B,D),c_Power_Opower__class_Opower(A,C,D)) # label(fact_power__mono) # label(axiom). [clausify(902)].
% 2.54/2.74 1349 -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_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C)) # label(fact_zero__less__power) # label(axiom). [clausify(903)].
% 2.54/2.74 1350 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Power_Opower__class_Opower(A,B,C)) # label(fact_one__le__power) # label(axiom). [clausify(904)].
% 2.54/2.74 1351 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Power_Opower__class_Opower(A,B,C) != c_Power_Opower__class_Opower(A,B,D) | C = D # label(fact_power__inject__exp) # label(axiom). [clausify(906)].
% 2.54/2.74 1352 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Power_Opower__class_Opower(A,B,C) = c_Power_Opower__class_Opower(A,B,D) | C != D # label(fact_power__inject__exp) # label(axiom). [clausify(906)].
% 2.54/2.74 1353 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_power__less__imp__less__base) # label(axiom). [clausify(912)].
% 2.54/2.74 1354 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Power_Opower__class_Opower(A,B,C))) # label(fact_power__gt1__lemma) # label(axiom). [clausify(913)].
% 2.54/2.74 1355 -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_Power_Opower__class_Opower(A,B,C),hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Power_Opower__class_Opower(A,B,C))) # label(fact_power__less__power__Suc) # label(axiom). [clausify(914)].
% 2.54/2.74 1356 -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_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(917)].
% 2.54/2.74 1357 -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_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(917)].
% 2.54/2.74 1358 -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_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) # label(fact_power__less__imp__less__exp) # label(axiom). [clausify(918)].
% 2.54/2.74 1359 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),D) | c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,D,B),c_Power_Opower__class_Opower(A,D,C)) # label(fact_power__strict__increasing) # label(axiom). [clausify(919)].
% 2.54/2.74 1360 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,D,B),c_Power_Opower__class_Opower(A,D,C)) # label(fact_power__increasing) # label(axiom). [clausify(920)].
% 2.54/2.74 1361 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,B,C)) # label(fact_power__Suc__less) # label(axiom). [clausify(921)].
% 2.54/2.74 1362 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,D,C),c_Power_Opower__class_Opower(A,D,B)) # label(fact_power__strict__decreasing) # label(axiom). [clausify(922)].
% 2.54/2.74 1363 -class_Rings_Olinordered__semidom(A) | c_Power_Opower__class_Opower(A,B,C) != c_Power_Opower__class_Opower(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | B = D # label(fact_power__eq__imp__eq__base) # label(axiom). [clausify(923)].
% 2.54/2.74 1364 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,D,C),c_Power_Opower__class_Opower(A,D,B)) # label(fact_power__decreasing) # label(axiom). [clausify(924)].
% 2.54/2.74 1365 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) # label(fact_power__increasing__iff) # label(axiom). [clausify(925)].
% 2.54/2.74 1366 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) # label(fact_power__increasing__iff) # label(axiom). [clausify(925)].
% 2.54/2.74 1367 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) # label(fact_power__le__imp__le__exp) # label(axiom). [clausify(926)].
% 2.54/2.74 1368 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Power_Opower__class_Opower(A,B,C)) # label(fact_one__less__power) # label(axiom). [clausify(927)].
% 2.54/2.74 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)). [resolve(1334,a,1335,a)].
% 2.54/2.74 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(1334,a,1336,a)].
% 2.54/2.74 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(1334,a,1337,a)].
% 2.54/2.74 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(1334,a,1338,a)].
% 2.54/2.74 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(1334,a,1339,a)].
% 2.54/2.74 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(1334,a,1340,a)].
% 2.54/2.74 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(1334,a,1341,a)].
% 2.54/2.74 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(1334,a,1342,a)].
% 2.54/2.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1334,a,1343,a)].
% 2.54/2.74 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | A = B. [resolve(1334,a,1344,a)].
% 2.54/2.74 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -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,B). [resolve(1334,a,1345,a)].
% 2.54/2.74 Derived: -c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,C),c_Power_Opower__class_Opower(tc_Int_Oint,B,C)). [resolve(1334,a,1346,a)].
% 2.54/2.74 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_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1334,a,1347,a)].
% 2.54/2.74 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),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,C),c_Power_Opower__class_Opower(tc_Int_Oint,B,C)). [resolve(1334,a,1348,a)].
% 2.54/2.74 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),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1334,a,1349,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1334,a,1350,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Power_Opower__class_Opower(tc_Int_Oint,A,B) != c_Power_Opower__class_Opower(tc_Int_Oint,A,C) | B = C. [resolve(1334,a,1351,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Power_Opower__class_Opower(tc_Int_Oint,A,B) = c_Power_Opower__class_Opower(tc_Int_Oint,A,C) | B != C. [resolve(1334,a,1352,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Power_Opower__class_Opower(tc_Int_Oint,C,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,A,C). [resolve(1334,a,1353,a)].
% 2.54/2.75 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Power_Opower__class_Opower(tc_Int_Oint,A,B))). [resolve(1334,a,1354,a)].
% 2.54/2.75 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_Power_Opower__class_Opower(tc_Int_Oint,A,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Power_Opower__class_Opower(tc_Int_Oint,A,B))). [resolve(1334,a,1355,a)].
% 2.54/2.75 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_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Power_Opower__class_Opower(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1334,a,1356,a)].
% 2.54/2.75 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_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Power_Opower__class_Opower(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1334,a,1357,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,C,A),c_Power_Opower__class_Opower(tc_Int_Oint,C,B)). [resolve(1334,a,1360,a)].
% 2.54/2.75 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_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1334,a,1361,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,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,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,C,B),c_Power_Opower__class_Opower(tc_Int_Oint,C,A)). [resolve(1334,a,1362,a)].
% 2.54/2.75 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,B) != c_Power_Opower__class_Opower(tc_Int_Oint,C,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_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1334,a,1363,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,C,B),c_Power_Opower__class_Opower(tc_Int_Oint,C,A)). [resolve(1334,a,1364,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Power_Opower__class_Opower(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1334,a,1365,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Power_Opower__class_Opower(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1334,a,1366,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1334,a,1368,a)].
% 2.54/2.75 1369 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.54/2.75 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)). [resolve(1369,a,1335,a)].
% 2.54/2.75 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(1369,a,1336,a)].
% 2.54/2.75 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(1369,a,1337,a)].
% 2.54/2.75 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1369,a,1338,a)].
% 2.54/2.75 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(1369,a,1339,a)].
% 2.54/2.75 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(1369,a,1340,a)].
% 2.54/2.75 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(1369,a,1341,a)].
% 2.54/2.75 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(1369,a,1342,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -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,A,B). [resolve(1369,a,1343,a)].
% 2.54/2.75 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -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),A) | A = B. [resolve(1369,a,1344,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Nat_Onat,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(1369,a,1345,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -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_Power_Opower__class_Opower(tc_Nat_Onat,A,C),c_Power_Opower__class_Opower(tc_Nat_Onat,B,C)). [resolve(1369,a,1346,a)].
% 2.54/2.75 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),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)). [resolve(1369,a,1347,a)].
% 2.54/2.75 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),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,C),c_Power_Opower__class_Opower(tc_Nat_Onat,B,C)). [resolve(1369,a,1348,a)].
% 2.54/2.75 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),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)). [resolve(1369,a,1349,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)). [resolve(1369,a,1350,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,B) != c_Power_Opower__class_Opower(tc_Nat_Onat,A,C) | B = C. [resolve(1369,a,1351,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,B) = c_Power_Opower__class_Opower(tc_Nat_Onat,A,C) | B != C. [resolve(1369,a,1352,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Power_Opower__class_Opower(tc_Nat_Onat,C,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,A,C). [resolve(1369,a,1353,a)].
% 2.54/2.75 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))). [resolve(1369,a,1354,a)].
% 2.54/2.75 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_Power_Opower__class_Opower(tc_Nat_Onat,A,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))). [resolve(1369,a,1355,a)].
% 2.54/2.75 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_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Power_Opower__class_Opower(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1369,a,1356,a)].
% 2.54/2.75 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_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Power_Opower__class_Opower(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1369,a,1357,a)].
% 2.54/2.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,C,A),c_Power_Opower__class_Opower(tc_Nat_Onat,C,B)). [resolve(1369,a,1360,a)].
% 2.54/2.76 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,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)). [resolve(1369,a,1361,a)].
% 2.54/2.76 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,c_Groups_Oone__class_Oone(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,C,B),c_Power_Opower__class_Opower(tc_Nat_Onat,C,A)). [resolve(1369,a,1362,a)].
% 2.54/2.76 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,B) != c_Power_Opower__class_Opower(tc_Nat_Onat,C,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_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1369,a,1363,a)].
% 2.54/2.76 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,c_Groups_Oone__class_Oone(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,C,B),c_Power_Opower__class_Opower(tc_Nat_Onat,C,A)). [resolve(1369,a,1364,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Power_Opower__class_Opower(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1369,a,1365,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Power_Opower__class_Opower(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1369,a,1366,a)].
% 2.54/2.76 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_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B)). [resolve(1369,a,1368,a)].
% 2.54/2.76 1370 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.54/2.76 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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)). [resolve(1370,a,1335,a)].
% 2.54/2.76 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(1370,a,1336,a)].
% 2.54/2.76 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(1370,a,1337,a)].
% 2.54/2.76 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(1370,a,1338,a)].
% 2.54/2.76 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(1370,a,1339,a)].
% 2.54/2.76 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(1370,a,1340,a)].
% 2.54/2.76 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(1370,a,1341,a)].
% 2.54/2.76 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(1370,a,1342,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1370,a,1343,a)].
% 2.54/2.76 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | A = B. [resolve(1370,a,1344,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1370,a,1345,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,C)). [resolve(1370,a,1346,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1370,a,1347,a)].
% 2.54/2.76 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),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,C)). [resolve(1370,a,1348,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1370,a,1349,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1370,a,1350,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C) | B = C. [resolve(1370,a,1351,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C) | B != C. [resolve(1370,a,1352,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1370,a,1353,a)].
% 2.54/2.76 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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B))). [resolve(1370,a,1354,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B))). [resolve(1370,a,1355,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1370,a,1356,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1370,a,1357,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,A),c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,B)). [resolve(1370,a,1360,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1370,a,1361,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,A)). [resolve(1370,a,1362,a)].
% 2.54/2.76 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1370,a,1363,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,A)). [resolve(1370,a,1364,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1370,a,1365,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1370,a,1366,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1370,a,1368,a)].
% 2.54/2.76 1371 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.54/2.76 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)). [resolve(1371,a,1335,a)].
% 2.54/2.76 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(1371,a,1336,a)].
% 2.54/2.76 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(1371,a,1337,a)].
% 2.54/2.76 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(1371,a,1338,a)].
% 2.54/2.76 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(1371,a,1339,a)].
% 2.54/2.76 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(1371,a,1340,a)].
% 2.54/2.76 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(1371,a,1341,a)].
% 2.54/2.76 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(1371,a,1342,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -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,A,B). [resolve(1371,a,1343,a)].
% 2.54/2.76 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -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),A) | A = B. [resolve(1371,a,1344,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | -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,B). [resolve(1371,a,1345,a)].
% 2.54/2.76 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_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1371,a,1346,a)].
% 2.54/2.76 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),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1371,a,1347,a)].
% 2.54/2.76 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),A) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(1371,a,1348,a)].
% 2.54/2.76 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),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1371,a,1349,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1371,a,1350,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B) != c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C) | B = C. [resolve(1371,a,1351,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B) = c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C) | B != C. [resolve(1371,a,1352,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),c_Power_Opower__class_Opower(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),C) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(1371,a,1353,a)].
% 2.54/2.76 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B))). [resolve(1371,a,1354,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B))). [resolve(1371,a,1355,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1371,a,1356,a)].
% 2.54/2.76 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_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1371,a,1357,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),C) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,C,A),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,C,B)). [resolve(1371,a,1360,a)].
% 2.54/2.76 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,A,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1371,a,1361,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,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,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,C,B),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,C,A)). [resolve(1371,a,1362,a)].
% 2.54/2.76 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B) != c_Power_Opower__class_Opower(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),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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1371,a,1363,a)].
% 2.54/2.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) | c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,C,B),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,C,A)). [resolve(1371,a,1364,a)].
% 2.63/2.85 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__eq(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1371,a,1365,a)].
% 2.63/2.85 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__eq(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1371,a,1366,a)].
% 2.63/2.85 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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(1371,a,1368,a)].
% 2.63/2.85 1372 class_Rings_Olinordered__idom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__idom) # label(axiom). [assumption].
% 2.63/2.85 1373 -class_Rings_Olinordered__idom(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neqE__linordered__idom) # label(axiom). [clausify(62)].
% 2.63/2.85 1374 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),B) # label(fact_mult__left__le__one__le) # label(axiom). [clausify(143)].
% 2.63/2.85 1375 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),B) # label(fact_mult__right__le__one__le) # label(axiom). [clausify(144)].
% 2.63/2.85 1376 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Oone__class_Oone(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_sgn__1__pos) # label(axiom). [clausify(232)].
% 2.63/2.85 1377 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_sgn__1__pos) # label(axiom). [clausify(232)].
% 2.63/2.85 1378 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__pos) # label(axiom). [clausify(233)].
% 2.63/2.85 1379 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Osgn__class_Osgn(A,B)) = c_Groups_Osgn__class_Osgn(A,B) # label(fact_sgn__sgn) # label(axiom). [clausify(236)].
% 2.63/2.85 1380 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sgn__0__0) # label(axiom). [clausify(304)].
% 2.63/2.85 1381 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sgn__0__0) # label(axiom). [clausify(304)].
% 2.63/2.85 1382 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C)) # label(fact_sgn__times) # label(axiom). [clausify(306)].
% 2.63/2.85 1383 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_sgn__less) # label(axiom). [clausify(348)].
% 2.63/2.85 1384 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_sgn__less) # label(axiom). [clausify(348)].
% 2.63/2.85 1385 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_sgn__greater) # label(axiom). [clausify(349)].
% 2.63/2.85 1386 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_sgn__greater) # label(axiom). [clausify(349)].
% 2.63/2.85 1387 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_even__less__0__iff) # label(axiom). [clausify(384)].
% 2.63/2.85 1388 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_even__less__0__iff) # label(axiom). [clausify(384)].
% 2.63/2.85 1389 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) # label(fact_less__number__of) # label(axiom). [clausify(410)].
% 2.63/2.85 1390 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) # label(fact_less__number__of) # label(axiom). [clausify(410)].
% 2.63/2.85 1391 -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_Int_Onumber__class_Onumber__of(A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) # label(fact_le__number__of) # label(axiom). [clausify(416)].
% 2.63/2.85 1392 -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_Int_Onumber__class_Onumber__of(A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) # label(fact_le__number__of) # label(axiom). [clausify(416)].
% 2.63/2.85 1393 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__minus__self__iff) # label(axiom). [clausify(531)].
% 2.63/2.85 1394 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__minus__self__iff) # label(axiom). [clausify(531)].
% 2.63/2.85 1395 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Osgn__class_Osgn(A,B) # label(fact_sgn__neg) # label(axiom). [clausify(569)].
% 2.63/2.85 1396 -class_Rings_Olinordered__idom(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != c_Groups_Osgn__class_Osgn(A,B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_sgn__1__neg) # label(axiom). [clausify(570)].
% 2.63/2.85 1397 -class_Rings_Olinordered__idom(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Osgn__class_Osgn(A,B) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_sgn__1__neg) # label(axiom). [clausify(570)].
% 2.63/2.85 1398 -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(619)].
% 2.63/2.85 1399 -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(619)].
% 2.63/2.85 1400 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OPls) # label(fact_le__special_I3_J) # label(axiom). [clausify(620)].
% 2.63/2.85 1401 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Int_OPls) # label(fact_le__special_I3_J) # label(axiom). [clausify(620)].
% 2.63/2.85 1402 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B) # label(fact_less__special_I1_J) # label(axiom). [clausify(621)].
% 2.63/2.85 1403 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B) # label(fact_less__special_I1_J) # label(axiom). [clausify(621)].
% 2.63/2.85 1404 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls) # label(fact_less__special_I3_J) # label(axiom). [clausify(622)].
% 2.63/2.85 1405 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls) # label(fact_less__special_I3_J) # label(axiom). [clausify(622)].
% 2.63/2.85 1406 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) # label(fact_le__special_I2_J) # label(axiom). [clausify(649)].
% 2.63/2.85 1407 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B) # label(fact_le__special_I2_J) # label(axiom). [clausify(649)].
% 2.63/2.85 1408 -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(650)].
% 2.63/2.85 1409 -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(650)].
% 2.63/2.85 1410 -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(651)].
% 2.63/2.85 1411 -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(651)].
% 2.63/2.85 1412 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) # label(fact_less__special_I4_J) # label(axiom). [clausify(652)].
% 2.63/2.85 1413 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)) # label(fact_less__special_I4_J) # label(axiom). [clausify(652)].
% 2.63/2.85 1414 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_zero__le__power2) # label(axiom). [clausify(849)].
% 2.63/2.85 1415 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__power2) # label(axiom). [clausify(852)].
% 2.63/2.85 1416 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__power2) # label(axiom). [clausify(852)].
% 2.63/2.85 1417 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(A)) # label(fact_power2__less__0) # label(axiom). [clausify(853)].
% 2.63/2.85 1418 -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__power2__eq__zero__iff) # label(axiom). [clausify(854)].
% 2.63/2.85 1419 -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__power2__eq__zero__iff) # label(axiom). [clausify(854)].
% 2.63/2.85 1420 -class_Rings_Olinordered__idom(A) | c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__power2__eq__zero__iff) # label(axiom). [clausify(854)].
% 2.63/2.85 1421 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_sum__power2__ge__zero) # label(axiom). [clausify(864)].
% 2.63/2.85 1422 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__power2__le__zero__iff) # label(axiom). [clausify(865)].
% 2.63/2.85 1423 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__power2__le__zero__iff) # label(axiom). [clausify(865)].
% 2.63/2.85 1424 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__power2__le__zero__iff) # label(axiom). [clausify(865)].
% 2.63/2.85 1425 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__sum__power2__lt__zero) # label(axiom). [clausify(866)].
% 2.63/2.85 1426 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__power2__gt__zero__iff) # label(axiom). [clausify(867)].
% 2.63/2.85 1427 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__power2__gt__zero__iff) # label(axiom). [clausify(867)].
% 2.63/2.85 1428 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__power2__gt__zero__iff) # label(axiom). [clausify(867)].
% 2.63/2.85 1429 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,hAPP(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)))),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_even__power__le__0__imp__0) # label(axiom). [clausify(869)].
% 2.63/2.85 1430 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,hAPP(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)))),C))) # label(fact_zero__le__even__power_H) # label(axiom). [clausify(870)].
% 2.63/2.85 1431 -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,c_Groups_Oabs__class_Oabs(A,B),C)) # label(fact_zero__le__power__abs) # label(axiom). [clausify(936)].
% 2.63/2.85 1432 -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(A,c_Power_Opower__class_Opower(A,B,C)) = c_Power_Opower__class_Opower(A,c_Groups_Oabs__class_Oabs(A,B),C) # label(fact_power__abs) # label(axiom). [clausify(937)].
% 2.63/2.85 1433 -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(A,c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,B),C)) = c_Groups_Oabs__class_Oabs(A,c_Power_Opower__class_Opower(A,B,C)) # label(fact_abs__power__minus) # label(axiom). [clausify(938)].
% 2.63/2.85 1434 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,C)),B) # label(fact_abs__mult__pos) # label(axiom). [clausify(940)].
% 2.63/2.85 1435 -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_abs__one) # label(axiom). [clausify(947)].
% 2.63/2.85 1436 -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,D),E) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,D)),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_abs__mult__less) # label(axiom). [clausify(949)].
% 2.63/2.85 Derived: A = B | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1372,a,1373,a)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),A),A). [resolve(1372,a,1374,a)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),A). [resolve(1372,a,1375,a)].
% 2.63/2.85 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) != c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1372,a,1376,a)].
% 2.63/2.85 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Oone__class_Oone(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1372,a,1377,a)].
% 2.63/2.85 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,A). [resolve(1372,a,1379,a)].
% 2.63/2.85 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1372,a,1380,a)].
% 2.63/2.85 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1372,a,1381,a)].
% 2.63/2.85 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,B)). [resolve(1372,a,1382,a)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Osgn__class_Osgn(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1383,a)].
% 2.63/2.85 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Osgn__class_Osgn(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1384,a)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1372,a,1385,a)].
% 2.63/2.85 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1372,a,1386,a)].
% 2.63/2.85 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1387,a)].
% 2.63/2.85 Derived: 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)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1388,a)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1372,a,1389,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1372,a,1390,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1372,a,1391,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1372,a,1392,b)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,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(1372,a,1393,a)].
% 2.63/2.85 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,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(1372,a,1394,a)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,A). [resolve(1372,a,1395,a)].
% 2.63/2.85 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) != c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1396,a)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(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(1372,a,1398,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(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(1372,a,1399,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1372,a,1400,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1372,a,1401,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1372,a,1402,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1372,a,1403,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). [resolve(1372,a,1404,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). [resolve(1372,a,1405,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1372,a,1406,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1372,a,1407,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1372,a,1408,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1372,a,1409,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(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(1372,a,1410,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(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(1372,a,1411,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1372,a,1412,b)].
% 2.63/2.85 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1372,a,1413,b)].
% 2.63/2.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(1372,a,1414,a)].
% 2.63/2.85 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1372,a,1415,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1372,a,1416,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1417,a)].
% 2.63/2.86 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1372,a,1418,a)].
% 2.63/2.86 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1372,a,1419,a)].
% 2.63/2.86 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1372,a,1420,a)].
% 2.63/2.86 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_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). [resolve(1372,a,1421,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1372,a,1422,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1372,a,1423,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1372,a,1424,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1372,a,1425,a)].
% 2.63/2.86 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_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1372,a,1426,a)].
% 2.63/2.86 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_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1372,a,1427,a)].
% 2.63/2.86 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_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_Int_Oint,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1372,a,1428,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,hAPP(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)))),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1372,a,1429,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,hAPP(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)))),B))). [resolve(1372,a,1430,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B)). [resolve(1372,a,1431,a)].
% 2.63/2.86 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B)) = c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B). [resolve(1372,a,1432,a)].
% 2.63/2.86 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1372,a,1433,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),A)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)),A). [resolve(1372,a,1434,a)].
% 2.63/2.86 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1372,a,1435,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,C),D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,C)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1372,a,1436,a)].
% 2.63/2.86 1437 class_Rings_Olinordered__idom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__idom) # label(axiom). [assumption].
% 2.63/2.86 Derived: A = B | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1437,a,1373,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),A). [resolve(1437,a,1374,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),A). [resolve(1437,a,1375,a)].
% 2.63/2.86 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1437,a,1376,a)].
% 2.63/2.86 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1437,a,1377,a)].
% 2.63/2.86 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A). [resolve(1437,a,1379,a)].
% 2.63/2.86 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1437,a,1380,a)].
% 2.63/2.86 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1437,a,1381,a)].
% 2.63/2.86 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,B)). [resolve(1437,a,1382,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1383,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1384,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1437,a,1385,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1437,a,1386,a)].
% 2.63/2.86 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1387,a)].
% 2.63/2.86 Derived: 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)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1388,a)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1437,a,1389,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1437,a,1390,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1437,a,1391,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1437,a,1392,b)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,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(1437,a,1393,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,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(1437,a,1394,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A). [resolve(1437,a,1395,a)].
% 2.63/2.86 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1396,a)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(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(1437,a,1398,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(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(1437,a,1399,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1437,a,1400,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OPls). [resolve(1437,a,1401,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1437,a,1402,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). [resolve(1437,a,1403,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). [resolve(1437,a,1404,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). [resolve(1437,a,1405,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1437,a,1406,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),A). [resolve(1437,a,1407,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1437,a,1408,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1437,a,1409,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(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(1437,a,1410,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(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(1437,a,1411,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1437,a,1412,b)].
% 2.63/2.86 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OBit1(c_Int_OPls)). [resolve(1437,a,1413,b)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(1437,a,1414,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1437,a,1415,a)].
% 2.63/2.86 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1437,a,1416,a)].
% 2.63/2.86 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1417,a)].
% 2.63/2.86 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1437,a,1418,a)].
% 2.63/2.87 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1437,a,1419,a)].
% 2.63/2.87 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1437,a,1420,a)].
% 2.63/2.87 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). [resolve(1437,a,1421,a)].
% 2.63/2.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1437,a,1422,a)].
% 2.63/2.87 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1437,a,1423,a)].
% 2.63/2.87 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1437,a,1424,a)].
% 2.63/2.87 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1437,a,1425,a)].
% 2.63/2.87 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1437,a,1426,a)].
% 2.71/2.96 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1437,a,1427,a)].
% 2.71/2.96 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_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1437,a,1428,a)].
% 2.71/2.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,hAPP(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)))),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1437,a,1429,a)].
% 2.71/2.96 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,hAPP(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)))),B))). [resolve(1437,a,1430,a)].
% 2.71/2.96 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)). [resolve(1437,a,1431,a)].
% 2.71/2.96 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B). [resolve(1437,a,1432,a)].
% 2.71/2.96 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1437,a,1433,a)].
% 2.71/2.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)),A). [resolve(1437,a,1434,a)].
% 2.71/2.96 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1437,a,1435,a)].
% 2.71/2.96 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,C)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1437,a,1436,a)].
% 2.71/2.96 1438 class_Rings_Ono__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.71/2.96 1439 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Otimes__class_Otimes(A,B),C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divisors__zero) # label(axiom). [clausify(63)].
% 2.71/2.96 1440 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Otimes__class_Otimes(A,B),C) # label(fact_no__zero__divisors) # label(axiom). [clausify(64)].
% 2.71/2.96 1441 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_power__eq__0__iff__number__of) # label(axiom). [clausify(839)].
% 2.71/2.96 1442 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) != c_Groups_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) # label(fact_power__eq__0__iff__number__of) # label(axiom). [clausify(839)].
% 2.71/2.96 1443 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) # label(fact_power__eq__0__iff__number__of) # label(axiom). [clausify(839)].
% 2.71/2.96 1444 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Power_Opower__class_Opower(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_power__eq__0__iff) # label(axiom). [clausify(905)].
% 2.71/2.96 1445 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Power_Opower__class_Opower(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C # label(fact_power__eq__0__iff) # label(axiom). [clausify(905)].
% 2.71/2.96 1446 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Power_Opower__class_Opower(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C # label(fact_power__eq__0__iff) # label(axiom). [clausify(905)].
% 2.71/2.96 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1438,a,1439,a)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1438,a,1441,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1438,a,1442,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1438,a,1443,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Power_Opower__class_Opower(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1438,a,1444,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Power_Opower__class_Opower(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1438,a,1445,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Power_Opower__class_Opower(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1438,a,1446,c)].
% 2.71/2.96 1447 class_Rings_Ono__zero__divisors(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.71/2.96 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1447,a,1439,a)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1447,a,1441,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1447,a,1442,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1447,a,1443,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1447,a,1444,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1447,a,1445,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,A,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1447,a,1446,c)].
% 2.71/2.96 1448 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.71/2.96 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1448,a,1439,a)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1448,a,1441,c)].
% 2.71/2.96 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1448,a,1442,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1448,a,1443,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1448,a,1444,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1448,a,1445,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1448,a,1446,c)].
% 2.71/2.97 1449 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.71/2.97 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1449,a,1439,a)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1449,a,1441,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1449,a,1442,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1449,a,1443,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1449,a,1444,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1449,a,1445,c)].
% 2.71/2.97 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1449,a,1446,c)].
% 2.83/3.06 1450 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.83/3.06 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B. [resolve(1450,a,1439,a)].
% 2.83/3.06 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(1450,a,1441,c)].
% 2.83/3.06 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1450,a,1442,c)].
% 2.83/3.06 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1450,a,1443,c)].
% 2.83/3.06 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(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) = A. [resolve(1450,a,1444,c)].
% 2.83/3.06 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1450,a,1445,c)].
% 2.83/3.06 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(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) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1450,a,1446,c)].
% 2.83/3.06 1451 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.83/3.06 1452 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Otimes__class_Otimes(A,B),C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(65)].
% 2.83/3.06 1453 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),C) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(65)].
% 2.83/3.06 1454 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),C) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(65)].
% 2.92/3.15 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1451,a,1453,a)].
% 2.92/3.15 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1451,a,1454,a)].
% 2.92/3.15 1455 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.92/3.15 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1455,a,1453,a)].
% 2.92/3.15 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1455,a,1454,a)].
% 2.92/3.15 1456 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.92/3.15 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1456,a,1453,a)].
% 2.92/3.15 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1456,a,1454,a)].
% 2.92/3.15 1457 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 2.92/3.15 1458 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(75)].
% 2.92/3.15 1459 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),D),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(76)].
% 2.92/3.15 1460 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_mult__neg__neg) # label(axiom). [clausify(80)].
% 2.92/3.15 1461 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(82)].
% 2.92/3.15 1462 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(82)].
% 2.92/3.15 1463 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(88)].
% 2.92/3.15 1464 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(88)].
% 2.92/3.15 1465 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(89)].
% 2.92/3.15 1466 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(89)].
% 2.92/3.15 1467 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(89)].
% 2.92/3.15 1468 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(89)].
% 2.92/3.15 1469 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(A,C,D) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(89)].
% 2.92/3.15 1470 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(89)].
% 2.92/3.15 1471 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(90)].
% 2.92/3.15 1472 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(A,D,B) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(90)].
% 2.92/3.15 1473 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | c_Orderings_Oord__class_Oless(A,B,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(90)].
% 2.92/3.15 1474 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | c_Orderings_Oord__class_Oless(A,B,D) | c_Orderings_Oord__class_Oless(A,D,B) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(90)].
% 2.92/3.15 1475 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(A,B,D) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(90)].
% 2.92/3.15 1476 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,B) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(90)].
% 2.92/3.15 1477 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(121)].
% 2.92/3.15 1478 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(121)].
% 2.92/3.15 1479 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(121)].
% 2.92/3.15 1480 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(121)].
% 2.92/3.15 1481 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(121)].
% 2.92/3.15 1482 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(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(121)].
% 2.92/3.15 1483 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(122)].
% 2.92/3.15 1484 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(122)].
% 2.92/3.15 1485 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(122)].
% 2.92/3.15 1486 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(122)].
% 2.92/3.15 1487 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(122)].
% 2.92/3.15 1488 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(122)].
% 2.92/3.15 1489 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(131)].
% 2.92/3.15 1490 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(131)].
% 2.92/3.15 1491 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(132)].
% 2.92/3.15 1492 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(132)].
% 2.92/3.15 1493 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(378)].
% 2.92/3.15 1494 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(378)].
% 2.92/3.15 1495 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(378)].
% 2.92/3.15 1496 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(379)].
% 2.92/3.15 1497 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(379)].
% 2.92/3.15 1498 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(379)].
% 2.92/3.15 1499 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(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(383)].
% 2.92/3.15 1500 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(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(383)].
% 2.92/3.15 1501 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(383)].
% 2.92/3.15 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A)). [resolve(1457,a,1458,a)].
% 2.92/3.15 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)). [resolve(1457,a,1459,a)].
% 2.92/3.15 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)). [resolve(1457,a,1460,a)].
% 2.92/3.15 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B). [resolve(1457,a,1461,a)].
% 2.92/3.15 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1457,a,1463,a)].
% 2.92/3.15 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1457,a,1464,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | 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)). [resolve(1457,a,1465,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | 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,B). [resolve(1457,a,1466,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1467,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B). [resolve(1457,a,1468,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(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(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1471,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(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(tc_Int_Oint,C,A). [resolve(1457,a,1472,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1473,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A). [resolve(1457,a,1474,a)].
% 2.92/3.15 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(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(tc_Int_Oint,A,C). [resolve(1457,a,1475,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1477,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1457,a,1478,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1457,a,1479,a)].
% 2.92/3.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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),B). [resolve(1457,a,1480,a)].
% 2.92/3.15 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1481,a)].
% 2.92/3.15 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1457,a,1482,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1483,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1484,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1485,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1486,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1457,a,1487,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1457,a,1488,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1457,a,1489,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1457,a,1490,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B). [resolve(1457,a,1491,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B). [resolve(1457,a,1492,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1457,a,1493,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1457,a,1494,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1457,a,1495,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(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(1457,a,1496,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(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(1457,a,1497,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1457,a,1498,a)].
% 2.92/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(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(1457,a,1499,a)].
% 2.92/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(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(1457,a,1500,a)].
% 2.92/3.16 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1457,a,1501,a)].
% 2.92/3.16 1502 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)). [resolve(1502,a,1458,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)). [resolve(1502,a,1459,a)].
% 2.92/3.16 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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)). [resolve(1502,a,1460,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B). [resolve(1502,a,1461,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1502,a,1463,a)].
% 2.92/3.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1502,a,1464,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1465,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B). [resolve(1502,a,1466,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1467,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B). [resolve(1502,a,1468,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1471,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,A). [resolve(1502,a,1472,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1473,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,A). [resolve(1502,a,1474,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1502,a,1475,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1477,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1502,a,1478,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1502,a,1479,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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),B). [resolve(1502,a,1480,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1481,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1502,a,1482,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1483,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1484,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1485,a)].
% 2.92/3.16 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1486,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1502,a,1487,a)].
% 2.92/3.16 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1502,a,1488,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1502,a,1489,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1502,a,1490,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B). [resolve(1502,a,1491,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B). [resolve(1502,a,1492,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1502,a,1493,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1502,a,1494,a)].
% 2.92/3.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1502,a,1495,a)].
% 2.92/3.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(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(1502,a,1496,a)].
% 2.92/3.17 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(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(1502,a,1497,a)].
% 2.92/3.17 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(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 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1502,a,1498,a)].
% 2.92/3.17 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(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(1502,a,1499,a)].
% 3.14/3.36 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(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(1502,a,1500,a)].
% 3.14/3.36 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(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 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1502,a,1501,a)].
% 3.14/3.36 1503 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.14/3.36 1504 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(77)].
% 3.14/3.36 1505 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)). [resolve(1505,a,1504,a)].
% 3.14/3.36 1506 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.14/3.36 1507 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].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),B)). [resolve(1507,a,1504,a)].
% 3.14/3.36 1508 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.14/3.36 1509 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(78)].
% 3.14/3.36 1510 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(79)].
% 3.14/3.36 1511 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__neg__pos) # label(axiom). [clausify(81)].
% 3.14/3.36 1512 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(83)].
% 3.14/3.36 1513 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(84)].
% 3.14/3.36 1514 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg2) # label(axiom). [clausify(85)].
% 3.14/3.36 1515 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg) # label(axiom). [clausify(86)].
% 3.14/3.36 1516 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_mult__pos__pos) # label(axiom). [clausify(87)].
% 3.14/3.36 1517 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_mult__strict__mono) # label(axiom). [clausify(133)].
% 3.14/3.36 1518 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_mult__strict__mono_H) # label(axiom). [clausify(134)].
% 3.14/3.36 1519 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_mult__less__le__imp__less) # label(axiom). [clausify(135)].
% 3.14/3.36 1520 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_mult__le__less__imp__less) # label(axiom). [clausify(136)].
% 3.14/3.36 1521 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(138)].
% 3.14/3.36 1522 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(140)].
% 3.14/3.36 1523 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(141)].
% 3.14/3.36 1524 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(142)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1508,a,1511,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1508,a,1512,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1508,a,1513,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1508,a,1515,a)].
% 3.14/3.36 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)). [resolve(1508,a,1516,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1508,a,1517,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1508,a,1518,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1508,a,1519,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1508,a,1520,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(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(1508,a,1521,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(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(1508,a,1522,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),hAPP(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(1508,a,1523,a)].
% 3.14/3.36 1525 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(1525,a,1510,a)].
% 3.14/3.36 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1525,a,1511,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). [resolve(1525,a,1512,a)].
% 3.14/3.36 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(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(1525,a,1513,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1525,a,1515,a)].
% 3.14/3.36 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)). [resolve(1525,a,1516,a)].
% 3.14/3.36 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(1525,a,1517,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(1525,a,1518,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(1525,a,1519,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(1525,a,1520,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1525,a,1521,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1525,a,1522,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(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(1525,a,1523,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)) | -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). [resolve(1525,a,1524,a)].
% 3.14/3.37 1526 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1526,a,1511,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1526,a,1512,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1526,a,1513,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1526,a,1515,a)].
% 3.14/3.37 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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)). [resolve(1526,a,1516,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1526,a,1517,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1526,a,1518,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1526,a,1519,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1526,a,1520,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(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(1526,a,1521,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(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(1526,a,1522,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1526,a,1523,a)].
% 3.14/3.37 1527 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),C)). [resolve(1527,a,1510,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1527,a,1511,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),hAPP(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(1527,a,1512,a)].
% 3.14/3.37 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),hAPP(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(1527,a,1513,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1527,a,1515,a)].
% 3.14/3.37 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)). [resolve(1527,a,1516,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(1527,a,1517,a)].
% 3.14/3.37 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(1527,a,1518,a)].
% 3.24/3.47 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(1527,a,1519,a)].
% 3.24/3.47 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(1527,a,1520,a)].
% 3.24/3.47 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),hAPP(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(1527,a,1521,a)].
% 3.24/3.47 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),hAPP(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(1527,a,1522,a)].
% 3.24/3.47 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),hAPP(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(1527,a,1523,a)].
% 3.24/3.47 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),hAPP(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(1527,a,1524,a)].
% 3.24/3.47 1528 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 3.24/3.47 1529 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__square__less__zero) # label(axiom). [clausify(91)].
% 3.24/3.47 1530 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),B)) # label(fact_zero__le__square) # label(axiom). [clausify(123)].
% 3.24/3.47 1531 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__sum__squares__lt__zero) # label(axiom). [clausify(377)].
% 3.24/3.47 1532 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))) # label(fact_sum__squares__ge__zero) # label(axiom). [clausify(380)].
% 3.33/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1528,a,1529,a)].
% 3.33/3.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A)). [resolve(1528,a,1530,a)].
% 3.33/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1528,a,1531,a)].
% 3.33/3.57 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B))). [resolve(1528,a,1532,a)].
% 3.33/3.57 1533 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom). [assumption].
% 3.33/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1533,a,1529,a)].
% 3.33/3.57 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A)). [resolve(1533,a,1530,a)].
% 3.33/3.57 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1533,a,1531,a)].
% 3.33/3.57 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))). [resolve(1533,a,1532,a)].
% 3.33/3.57 1534 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 3.33/3.57 1535 -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(92)].
% 3.33/3.57 1536 -class_RealVector_Oreal__normed__field(A) | c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Rings_Oinverse__class_Odivide(A,D,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_divide_Oadd) # label(axiom). [clausify(297)].
% 3.33/3.57 1537 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(A,c_Groups_Otimes__class_Otimes(A,B),C,B) # label(fact_DERIV__cmult__Id) # label(axiom). [clausify(430)].
% 3.33/3.57 1538 -class_RealVector_Oreal__normed__field(A) | -class_SEQ_Obanach(A) | c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Transcendental_Oexp(A),B)) = hAPP(c_Transcendental_Oexp(A),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_exp__minus) # label(axiom). [clausify(445)].
% 3.33/3.57 1539 -class_RealVector_Oreal__normed__field(A) | c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_divide_Ominus) # label(axiom). [clausify(477)].
% 3.33/3.57 1540 -class_RealVector_Oreal__normed__field(A) | -class_SEQ_Obanach(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Transcendental_Oexp(A),B) # label(fact_exp__not__eq__zero) # label(axiom). [clausify(522)].
% 3.33/3.57 1541 -class_RealVector_Oreal__normed__field(A) | -class_SEQ_Obanach(A) | c_Deriv_Oderiv(A,c_Transcendental_Oexp(A),B,hAPP(c_Transcendental_Oexp(A),B)) # label(fact_DERIV__exp) # label(axiom). [clausify(523)].
% 3.33/3.57 1542 -class_RealVector_Oreal__normed__field(A) | -class_SEQ_Obanach(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Transcendental_Oexp(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_exp__zero) # label(axiom). [clausify(551)].
% 3.33/3.57 1543 -class_RealVector_Oreal__normed__field(A) | -class_SEQ_Obanach(A) | hAPP(c_Transcendental_Oexp(A),c_Groups_Oplus__class_Oplus(A,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Transcendental_Oexp(A),B)),hAPP(c_Transcendental_Oexp(A),C)) # label(fact_exp__add) # label(axiom). [clausify(552)].
% 3.33/3.57 1544 -class_RealVector_Oreal__normed__field(A) | -class_SEQ_Obanach(A) | hAPP(c_Transcendental_Oexp(A),c_Groups_Oplus__class_Oplus(A,B,C)) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Transcendental_Oexp(A),B)),hAPP(c_Transcendental_Oexp(A),C)) # label(fact_mult__exp__exp) # label(axiom). [clausify(553)].
% 3.33/3.57 1545 -class_RealVector_Oreal__normed__field(A) | -c_Deriv_Oderiv(A,B,C,D) | -c_Deriv_Oderiv(A,B,C,E) | D = E # label(fact_DERIV__unique) # label(axiom). [clausify(565)].
% 3.33/3.57 1546 -class_RealVector_Oreal__normed__field(A) | -c_Deriv_Oderiv(A,B,C,D) | D != E | c_Deriv_Oderiv(A,B,C,E) # label(fact_DERIV__cong) # label(axiom). [clausify(566)].
% 3.33/3.57 1547 -class_RealVector_Oreal__normed__field(A) | -c_Deriv_Oderiv(A,B,C,D) | D != E | c_Deriv_Oderiv(A,B,C,E) # label(fact_Deriv_Olemma__DERIV__subst) # label(axiom). [clausify(567)].
% 3.33/3.57 Derived: c_Deriv_Oderiv(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B,A). [resolve(1534,a,1537,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1534,a,1538,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A). [resolve(1534,a,1540,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oexp(tc_RealDef_Oreal),A,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)). [resolve(1534,a,1541,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1534,a,1542,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B)). [resolve(1534,a,1543,a)].
% 3.33/3.57 Derived: -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,C) | -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,D) | C = D. [resolve(1534,a,1545,a)].
% 3.33/3.57 Derived: -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,C) | C != D | c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,D). [resolve(1534,a,1546,a)].
% 3.33/3.57 1548 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 3.33/3.57 Derived: c_Deriv_Oderiv(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B,A). [resolve(1548,a,1537,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),A)) = hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1548,a,1538,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),A). [resolve(1548,a,1540,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Deriv_Oderiv(tc_Complex_Ocomplex,c_Transcendental_Oexp(tc_Complex_Ocomplex),A,hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),A)). [resolve(1548,a,1541,a)].
% 3.33/3.57 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1548,a,1542,a)].
% 3.54/3.76 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),A)),hAPP(c_Transcendental_Oexp(tc_Complex_Ocomplex),B)). [resolve(1548,a,1543,a)].
% 3.54/3.76 Derived: -c_Deriv_Oderiv(tc_Complex_Ocomplex,A,B,C) | -c_Deriv_Oderiv(tc_Complex_Ocomplex,A,B,D) | C = D. [resolve(1548,a,1545,a)].
% 3.54/3.76 Derived: -c_Deriv_Oderiv(tc_Complex_Ocomplex,A,B,C) | C != D | c_Deriv_Oderiv(tc_Complex_Ocomplex,A,B,D). [resolve(1548,a,1546,a)].
% 3.54/3.76 1549 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.54/3.76 1550 -class_Groups_Ocomm__monoid__mult(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom). [clausify(93)].
% 3.54/3.76 1551 -class_Groups_Ocomm__monoid__mult(A) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1) # label(axiom). [clausify(95)].
% 3.54/3.76 1552 -class_Groups_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),D) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,D)),c_Power_Opower__class_Opower(A,C,D)) # label(fact_power__mult__distrib) # label(axiom). [clausify(894)].
% 3.54/3.76 1553 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.54/3.76 1554 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.54/3.76 1555 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.54/3.76 1556 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.54/3.76 1557 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 3.54/3.76 1558 -class_Groups_Omonoid__mult(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(94)].
% 3.54/3.76 1559 -class_Groups_Omonoid__mult(A) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(96)].
% 3.54/3.76 1560 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B)),B) # label(fact_power3__eq__cube) # label(axiom). [clausify(841)].
% 3.54/3.76 1561 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(A,B),B) # label(fact_power2__eq__square) # label(axiom). [clausify(845)].
% 3.54/3.76 1562 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,c_Power_Opower__class_Opower(A,B,C),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(A,B,hAPP(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)))),C)) # label(fact_power__even__eq) # label(axiom). [clausify(848)].
% 3.54/3.76 1563 -class_Groups_Omonoid__mult(A) | -class_Int_Onumber(A) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,B)) # label(fact_power2__eq__square__number__of) # label(axiom). [clausify(855)].
% 3.54/3.76 1564 -class_Groups_Omonoid__mult(A) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),B) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Power_Opower__class_Opower(A,B,C)) # label(fact_power__commutes) # label(axiom). [clausify(895)].
% 3.54/3.77 1565 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,c_Groups_Oone__class_Oone(A),B) = c_Groups_Oone__class_Oone(A) # label(fact_power__one) # label(axiom). [clausify(896)].
% 3.54/3.77 1566 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,c_Power_Opower__class_Opower(A,B,C),D) = c_Power_Opower__class_Opower(A,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),D)) # label(fact_power__mult) # label(axiom). [clausify(898)].
% 3.54/3.77 1567 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_power__one__right) # label(axiom). [clausify(900)].
% 3.54/3.77 1568 -class_Groups_Omonoid__mult(A) | c_Power_Opower__class_Opower(A,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,B,D)) # label(fact_power__add) # label(axiom). [clausify(909)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A)),A). [resolve(1557,a,1560,a)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_Int_Oint,A,hAPP(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)))),B)). [resolve(1557,a,1562,a)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1557,a,1565,a)].
% 3.54/3.77 1569 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),A)),A). [resolve(1569,a,1560,a)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_Nat_Onat,A,hAPP(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)))),B)). [resolve(1569,a,1562,a)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1569,a,1565,a)].
% 3.54/3.77 1570 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A)),A). [resolve(1570,a,1560,a)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,hAPP(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)))),B)). [resolve(1570,a,1562,a)].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1570,a,1565,a)].
% 3.54/3.77 1571 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom). [assumption].
% 3.54/3.77 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A)),A). [resolve(1571,a,1560,a)].
% 3.63/3.87 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,hAPP(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)))),B)). [resolve(1571,a,1562,a)].
% 3.63/3.87 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1571,a,1565,a)].
% 3.63/3.87 1572 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) # label(axiom). [assumption].
% 3.63/3.87 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),A)),A). [resolve(1572,a,1560,a)].
% 3.63/3.87 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,A,hAPP(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)))),B)). [resolve(1572,a,1562,a)].
% 3.63/3.87 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(1572,a,1565,a)].
% 3.63/3.87 1573 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.63/3.87 1574 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__right_Ozero) # label(axiom). [clausify(97)].
% 3.63/3.87 1575 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult_Ozero__right) # label(axiom). [clausify(98)].
% 3.63/3.87 1576 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__left_Ozero) # label(axiom). [clausify(99)].
% 3.63/3.87 1577 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult_Ozero__left) # label(axiom). [clausify(100)].
% 3.63/3.87 1578 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_mult_Oadd__right) # label(axiom). [clausify(286)].
% 3.63/3.87 1579 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_mult__right_Oadd) # label(axiom). [clausify(287)].
% 3.63/3.87 1580 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D)),C) # label(fact_mult_Oadd__left) # label(axiom). [clausify(288)].
% 3.63/3.87 1581 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D)),C) # label(fact_mult__left_Oadd) # label(axiom). [clausify(289)].
% 3.71/3.96 1582 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C) # label(fact_mult__left_Ominus) # label(axiom). [clausify(466)].
% 3.71/3.96 1583 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C) # label(fact_mult_Ominus__left) # label(axiom). [clausify(467)].
% 3.71/3.96 1584 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_mult__right_Ominus) # label(axiom). [clausify(468)].
% 3.71/3.96 1585 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_mult_Ominus__right) # label(axiom). [clausify(469)].
% 3.71/3.96 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)),B). [resolve(1573,a,1582,a)].
% 3.71/3.96 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)). [resolve(1573,a,1584,a)].
% 3.71/3.96 1586 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.71/3.96 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)),B). [resolve(1586,a,1582,a)].
% 3.71/3.96 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1586,a,1584,a)].
% 3.71/3.96 1587 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 3.71/3.96 1588 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(107)].
% 3.71/3.96 1589 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(107)].
% 3.71/3.96 1590 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonpos__nonneg) # label(axiom). [clausify(117)].
% 3.71/3.96 1591 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos2) # label(axiom). [clausify(118)].
% 3.71/3.96 1592 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos) # label(axiom). [clausify(119)].
% 3.85/4.06 1593 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_mult__nonneg__nonneg) # label(axiom). [clausify(120)].
% 3.85/4.06 1594 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 3.85/4.06 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1594,a,1588,a)].
% 3.85/4.06 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1594,a,1589,a)].
% 3.85/4.06 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)). [resolve(1594,a,1593,a)].
% 3.85/4.06 1595 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 3.85/4.06 1596 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 3.85/4.06 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1596,a,1588,a)].
% 3.85/4.06 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1596,a,1589,a)].
% 3.85/4.06 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),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),B)). [resolve(1596,a,1593,a)].
% 3.85/4.06 1597 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 3.85/4.06 1598 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(108)].
% 3.93/4.16 1599 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(108)].
% 3.93/4.16 1600 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),B)) # label(fact_mult__left__mono__neg) # label(axiom). [clausify(111)].
% 3.93/4.16 1601 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),D),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)) # label(fact_mult__right__mono__neg) # label(axiom). [clausify(112)].
% 3.93/4.16 1602 -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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) # label(fact_mult__nonpos__nonpos) # label(axiom). [clausify(116)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A)). [resolve(1597,a,1600,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C)). [resolve(1597,a,1601,a)].
% 3.93/4.16 1603 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom). [assumption].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)). [resolve(1603,a,1600,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)). [resolve(1603,a,1601,a)].
% 3.93/4.16 1604 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 3.93/4.16 1605 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_mult__mono) # label(axiom). [clausify(109)].
% 3.93/4.16 1606 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) # label(fact_mult__mono_H) # label(axiom). [clausify(110)].
% 3.93/4.16 1607 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) # label(fact_mult__left__mono) # label(axiom). [clausify(114)].
% 3.93/4.16 1608 -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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_mult__right__mono) # label(axiom). [clausify(115)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1604,a,1605,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)). [resolve(1604,a,1606,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B)). [resolve(1604,a,1607,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)). [resolve(1604,a,1608,a)].
% 3.93/4.16 1609 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(1609,a,1605,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)). [resolve(1609,a,1606,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)). [resolve(1609,a,1607,a)].
% 3.93/4.16 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(1609,a,1608,a)].
% 3.99/4.17 1610 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom). [assumption].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1610,a,1605,a)].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)). [resolve(1610,a,1606,a)].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B)). [resolve(1610,a,1607,a)].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C)). [resolve(1610,a,1608,a)].
% 3.99/4.17 1611 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) # label(axiom). [assumption].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(1611,a,1605,a)].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(1611,a,1606,a)].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,C),B)). [resolve(1611,a,1607,a)].
% 3.99/4.17 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),C)). [resolve(1611,a,1608,a)].
% 4.29/4.55 1612 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.29/4.55 1613 -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) # label(fact_comm__mult__left__mono) # label(axiom). [clausify(113)].
% 4.29/4.55 1614 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.29/4.55 1615 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.29/4.55 1616 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.29/4.55 1617 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 4.29/4.55 1618 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(137)].
% 4.29/4.55 1619 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(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(139)].
% 4.29/4.55 1620 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 4.29/4.55 1621 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 4.29/4.55 1622 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 4.29/4.55 1623 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.29/4.55 1624 -class_Groups_Oab__semigroup__mult(A) | hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D) = hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(155)].
% 4.29/4.55 1625 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.29/4.55 1626 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.29/4.55 1627 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.29/4.55 1628 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.29/4.55 1629 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 4.29/4.55 1630 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(168)].
% 4.29/4.55 1631 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(168)].
% 4.29/4.55 1632 -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(169)].
% 4.29/4.55 1633 -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(169)].
% 4.29/4.55 1634 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(170)].
% 4.29/4.55 1635 -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(174)].
% 4.29/4.55 1636 -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(175)].
% 4.29/4.55 1637 -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(177)].
% 4.29/4.55 1638 -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(191)].
% 4.29/4.55 1639 -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(192)].
% 4.29/4.55 1640 -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(207)].
% 4.29/4.55 1641 -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__antisym__conv3) # label(axiom). [clausify(208)].
% 4.29/4.55 1642 -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__antisym__conv3) # label(axiom). [clausify(208)].
% 4.29/4.55 1643 -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(209)].
% 4.29/4.55 1644 -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(210)].
% 4.29/4.55 1645 -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(210)].
% 4.29/4.55 1646 -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(210)].
% 4.29/4.55 1647 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(211)].
% 4.29/4.55 1648 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom). [clausify(211)].
% 4.29/4.55 1649 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(211)].
% 4.29/4.55 1650 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,B,C) | B = C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(220)].
% 4.29/4.55 1651 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,C) | B != C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(220)].
% 4.29/4.55 1652 -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(222)].
% 4.29/4.55 1653 -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(225)].
% 4.29/4.56 1654 -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(225)].
% 4.29/4.56 1655 -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(417)].
% 4.29/4.56 1656 -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(417)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1629,a,1630,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1629,a,1631,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1629,a,1637,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | B != A. [resolve(1629,a,1642,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1629,a,1645,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | A != B. [resolve(1629,a,1646,a)].
% 4.29/4.56 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1629,a,1649,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | A = B. [resolve(1629,a,1650,a)].
% 4.29/4.56 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(1629,a,1654,a)].
% 4.29/4.56 1657 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1657,a,1630,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1657,a,1631,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1657,a,1637,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B = A | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1657,a,1639,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A) | B != A. [resolve(1657,a,1642,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1657,a,1645,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | A != B. [resolve(1657,a,1646,a)].
% 4.29/4.56 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1657,a,1649,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | A = B. [resolve(1657,a,1650,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | A != B. [resolve(1657,a,1654,a)].
% 4.29/4.56 1658 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1658,a,1630,a)].
% 4.29/4.56 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1658,a,1631,a)].
% 4.29/4.56 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1658,a,1637,a)].
% 4.46/4.67 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | B != A. [resolve(1658,a,1642,a)].
% 4.46/4.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1658,a,1645,a)].
% 4.46/4.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | A != B. [resolve(1658,a,1646,a)].
% 4.46/4.67 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1658,a,1649,a)].
% 4.46/4.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | A = B. [resolve(1658,a,1650,a)].
% 4.46/4.67 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(1658,a,1654,a)].
% 4.46/4.67 1659 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) # label(axiom). [assumption].
% 4.46/4.67 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(1659,a,1630,a)].
% 4.46/4.67 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(1659,a,1631,a)].
% 4.46/4.67 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,B,A). [resolve(1659,a,1637,a)].
% 4.46/4.67 Derived: c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | B = A | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1659,a,1639,a)].
% 4.46/4.67 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(1659,a,1642,a)].
% 4.46/4.67 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(1659,a,1645,a)].
% 4.46/4.67 Derived: -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | A != B. [resolve(1659,a,1646,a)].
% 4.46/4.67 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(1659,a,1649,a)].
% 4.46/4.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral,A,B) | c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral,A,B) | A = B. [resolve(1659,a,1650,a)].
% 4.46/4.67 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(1659,a,1654,a)].
% 4.46/4.67 1660 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 4.46/4.67 1661 -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,hAPP(c_Groups_Otimes__class_Otimes(A,E),B),hAPP(c_Groups_Otimes__class_Otimes(A,F),D)),C) # label(fact_convex__bound__lt) # label(axiom). [clausify(227)].
% 4.46/4.67 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,E),C)),B). [resolve(1660,a,1661,a)].
% 4.46/4.67 1662 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 4.76/4.95 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,E),C)),B). [resolve(1662,a,1661,a)].
% 4.76/4.95 1663 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 4.76/4.95 1664 -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,hAPP(c_Groups_Otimes__class_Otimes(A,E),B),hAPP(c_Groups_Otimes__class_Otimes(A,F),D)),C) # label(fact_convex__bound__le) # label(axiom). [clausify(228)].
% 4.76/4.95 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,E),C)),B). [resolve(1663,a,1664,a)].
% 4.76/4.95 1665 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 4.76/4.95 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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,E),C)),B). [resolve(1665,a,1664,a)].
% 4.76/4.95 1666 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 4.76/4.95 1667 -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(245)].
% 4.76/4.95 1668 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 4.76/4.95 1669 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 4.76/4.95 1670 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 4.76/4.95 1671 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 4.76/4.95 1672 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.76/4.95 1673 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(246)].
% 4.76/4.96 1674 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,B,D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(246)].
% 4.76/4.96 1675 -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__cancel) # label(axiom). [clausify(247)].
% 4.76/4.96 1676 -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__cancel) # label(axiom). [clausify(247)].
% 4.76/4.96 1677 -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(248)].
% 4.76/4.96 1678 -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(250)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B = C. [resolve(1672,a,1673,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B != C. [resolve(1672,a,1674,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A = C. [resolve(1672,a,1675,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A != C. [resolve(1672,a,1676,a)].
% 4.76/4.96 1679 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B = C. [resolve(1679,a,1673,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B != C. [resolve(1679,a,1674,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A = C. [resolve(1679,a,1675,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A != C. [resolve(1679,a,1676,a)].
% 4.76/4.96 1680 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B = C. [resolve(1680,a,1673,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B != C. [resolve(1680,a,1674,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A = C. [resolve(1680,a,1675,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A != C. [resolve(1680,a,1676,a)].
% 4.76/4.96 1681 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B = C. [resolve(1681,a,1673,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B != C. [resolve(1681,a,1674,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,B) | A = C. [resolve(1681,a,1675,a)].
% 4.76/4.96 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,B) | A != C. [resolve(1681,a,1676,a)].
% 4.76/4.96 1682 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.76/4.96 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(1682,a,1673,a)].
% 5.14/5.33 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(1682,a,1674,a)].
% 5.14/5.33 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(1682,a,1675,a)].
% 5.14/5.33 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(1682,a,1676,a)].
% 5.14/5.33 1683 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.14/5.33 1684 -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(249)].
% 5.14/5.33 1685 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.14/5.33 1686 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.14/5.33 1687 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.14/5.33 1688 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].
% 5.14/5.33 1689 class_Groups_Ocomm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.14/5.33 1690 -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(264)].
% 5.14/5.33 1691 -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(267)].
% 5.14/5.33 1692 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.14/5.33 1693 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.14/5.33 1694 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.14/5.33 1695 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.14/5.33 1696 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.14/5.33 1697 -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(265)].
% 5.14/5.33 1698 -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(268)].
% 5.14/5.33 1699 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.14/5.33 1700 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.14/5.33 1701 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.14/5.33 1702 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) # label(axiom). [assumption].
% 5.14/5.33 1703 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 5.14/5.33 1704 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom). [clausify(266)].
% 5.14/5.33 1705 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom). [clausify(266)].
% 5.14/5.33 1706 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(331)].
% 5.14/5.33 1707 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(331)].
% 5.14/5.33 1708 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(332)].
% 5.14/5.33 1709 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(332)].
% 5.14/5.33 1710 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(335)].
% 5.14/5.33 1711 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(335)].
% 5.14/5.33 1712 -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(336)].
% 5.14/5.33 1713 -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(336)].
% 5.14/5.33 1714 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom). [clausify(385)].
% 5.14/5.33 1715 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Oplus__class_Oplus(A,B,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom). [clausify(385)].
% 5.14/5.33 1716 -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(449)].
% 5.14/5.33 1717 -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(449)].
% 5.14/5.33 1718 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__zero) # label(axiom). [clausify(451)].
% 5.14/5.33 1719 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__zero) # label(axiom). [clausify(451)].
% 5.14/5.34 1720 -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(524)].
% 5.14/5.34 1721 -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(524)].
% 5.14/5.34 1722 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__minus__self__iff) # label(axiom). [clausify(526)].
% 5.14/5.34 1723 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__minus__self__iff) # label(axiom). [clausify(526)].
% 5.14/5.34 1724 -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(528)].
% 5.14/5.34 1725 -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(528)].
% 5.14/5.34 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1703,a,1704,a)].
% 5.14/5.34 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1703,a,1705,a)].
% 5.14/5.34 Derived: -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)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1703,a,1706,a)].
% 5.14/5.34 Derived: 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)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1703,a,1707,a)].
% 5.14/5.34 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,A,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1703,a,1708,a)].
% 5.14/5.34 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,A,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1703,a,1709,a)].
% 5.14/5.34 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(1703,a,1712,a)].
% 5.14/5.34 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1703,a,1716,a)].
% 5.14/5.34 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1703,a,1717,a)].
% 5.14/5.34 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(1703,a,1720,a)].
% 5.14/5.34 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(1703,a,1721,a)].
% 5.14/5.34 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1703,a,1722,a)].
% 5.14/5.34 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1703,a,1723,a)].
% 5.14/5.34 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(1703,a,1724,a)].
% 5.14/5.34 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(1703,a,1725,a)].
% 5.14/5.34 1726 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 5.14/5.34 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1726,a,1704,a)].
% 5.14/5.34 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1726,a,1705,a)].
% 5.14/5.34 Derived: -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)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1726,a,1706,a)].
% 5.14/5.34 Derived: 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)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1726,a,1707,a)].
% 5.14/5.34 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,A,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1726,a,1708,a)].
% 5.14/5.34 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,A,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1726,a,1709,a)].
% 5.14/5.34 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(1726,a,1712,a)].
% 5.14/5.34 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1726,a,1716,a)].
% 5.14/5.34 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1726,a,1717,a)].
% 5.14/5.34 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(1726,a,1720,a)].
% 5.14/5.34 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(1726,a,1721,a)].
% 5.14/5.34 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1726,a,1722,a)].
% 5.14/5.34 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1726,a,1723,a)].
% 5.14/5.34 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(1726,a,1724,a)].
% 5.19/5.44 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(1726,a,1725,a)].
% 5.19/5.44 1727 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].
% 5.19/5.44 1728 -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(269)].
% 5.19/5.44 1729 -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(269)].
% 5.19/5.44 1730 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) != c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(291)].
% 5.19/5.44 1731 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(291)].
% 5.19/5.44 1732 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,E),C)) = c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,E),B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(291)].
% 5.19/5.44 1733 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) != c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom). [clausify(294)].
% 5.19/5.44 1734 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | B != D # label(fact_crossproduct__eq) # label(axiom). [clausify(294)].
% 5.19/5.44 1735 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) | C != E # label(fact_crossproduct__eq) # label(axiom). [clausify(294)].
% 5.19/5.44 1736 -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,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),E)) != c_Groups_Oplus__class_Oplus(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,B),F)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(340)].
% 5.19/5.44 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1727,a,1728,a)].
% 5.19/5.44 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1727,a,1729,a)].
% 5.19/5.44 Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)). [resolve(1727,a,1730,a)].
% 5.19/5.44 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)). [resolve(1727,a,1731,a)].
% 5.19/5.44 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),B)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),A)). [resolve(1727,a,1732,a)].
% 5.19/5.44 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),D)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),E)). [resolve(1727,a,1736,a)].
% 5.19/5.44 1737 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].
% 5.19/5.44 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1737,a,1728,a)].
% 5.19/5.44 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1737,a,1729,a)].
% 5.19/5.44 Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(1737,a,1730,a)].
% 5.19/5.44 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)). [resolve(1737,a,1731,a)].
% 5.19/5.44 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,D),B)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,D),A)). [resolve(1737,a,1732,a)].
% 5.19/5.44 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),E)). [resolve(1737,a,1736,a)].
% 5.19/5.44 1738 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].
% 5.19/5.44 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1738,a,1728,a)].
% 5.19/5.44 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1738,a,1729,a)].
% 5.19/5.44 Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C)). [resolve(1738,a,1730,a)].
% 5.19/5.44 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C)). [resolve(1738,a,1731,a)].
% 5.34/5.54 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),B)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),A)). [resolve(1738,a,1732,a)].
% 5.34/5.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),D)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),E)). [resolve(1738,a,1736,a)].
% 5.34/5.54 1739 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 5.34/5.54 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1739,a,1728,a)].
% 5.34/5.54 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1739,a,1729,a)].
% 5.34/5.54 Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),D)) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),C)). [resolve(1739,a,1730,a)].
% 5.34/5.54 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),D),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),C)). [resolve(1739,a,1731,a)].
% 5.34/5.54 Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D),B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D),A)). [resolve(1739,a,1732,a)].
% 5.34/5.54 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),D)) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),E)). [resolve(1739,a,1736,a)].
% 5.34/5.54 1740 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].
% 5.34/5.54 1741 -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(272)].
% 5.34/5.54 1742 -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(273)].
% 5.34/5.54 1743 -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(277)].
% 5.34/5.54 1744 -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(277)].
% 5.36/5.54 1745 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(278)].
% 5.36/5.54 1746 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(278)].
% 5.36/5.54 1747 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(279)].
% 5.36/5.54 1748 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(279)].
% 5.36/5.54 1749 -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(280)].
% 5.36/5.54 1750 -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(280)].
% 5.36/5.54 1751 -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(284)].
% 5.36/5.54 1752 -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(285)].
% 5.36/5.54 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(1740,a,1741,a)].
% 5.36/5.54 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(1740,a,1742,a)].
% 5.36/5.54 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(1740,a,1744,a)].
% 5.36/5.54 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(1740,a,1746,a)].
% 5.36/5.54 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(1740,a,1747,a)].
% 5.36/5.54 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(1740,a,1748,a)].
% 5.36/5.54 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(1740,a,1749,a)].
% 5.36/5.54 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(1740,a,1750,a)].
% 5.36/5.55 1753 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].
% 5.36/5.55 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(1753,a,1741,a)].
% 5.36/5.55 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(1753,a,1742,a)].
% 5.36/5.55 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(1753,a,1744,a)].
% 5.36/5.55 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(1753,a,1746,a)].
% 5.36/5.55 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(1753,a,1747,a)].
% 5.36/5.55 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(1753,a,1748,a)].
% 5.36/5.55 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(1753,a,1749,a)].
% 5.36/5.55 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(1753,a,1750,a)].
% 5.36/5.55 1754 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].
% 5.36/5.55 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(1754,a,1741,a)].
% 5.36/5.55 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(1754,a,1742,a)].
% 5.36/5.55 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(1754,a,1744,a)].
% 5.36/5.55 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(1754,a,1746,a)].
% 5.36/5.55 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(1754,a,1747,a)].
% 5.36/5.55 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(1754,a,1748,a)].
% 5.36/5.55 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(1754,a,1749,a)].
% 5.36/5.55 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(1754,a,1750,a)].
% 5.44/5.64 1755 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].
% 5.44/5.64 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(1755,a,1741,a)].
% 5.44/5.64 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(1755,a,1742,a)].
% 5.44/5.64 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(1755,a,1744,a)].
% 5.44/5.64 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(1755,a,1746,a)].
% 5.44/5.64 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(1755,a,1747,a)].
% 5.44/5.64 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(1755,a,1748,a)].
% 5.44/5.64 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(1755,a,1749,a)].
% 5.44/5.64 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(1755,a,1750,a)].
% 5.44/5.64 1756 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.44/5.64 1757 -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(274)].
% 5.44/5.64 1758 -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(275)].
% 5.44/5.64 1759 -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(276)].
% 5.44/5.64 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(1756,a,1757,a)].
% 5.51/5.74 1760 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.51/5.74 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1760,a,1757,a)].
% 5.51/5.74 1761 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.51/5.74 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(1761,a,1757,a)].
% 5.51/5.74 1762 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].
% 5.51/5.74 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(1762,a,1757,a)].
% 5.51/5.74 1763 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.51/5.74 1764 -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(281)].
% 5.51/5.74 1765 -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(282)].
% 5.51/5.74 1766 -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(283)].
% 5.51/5.74 1767 -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(338)].
% 5.51/5.74 1768 -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(339)].
% 5.51/5.74 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(1763,a,1766,a)].
% 5.51/5.74 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). [resolve(1763,a,1767,a)].
% 5.51/5.74 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(1763,a,1768,a)].
% 5.51/5.74 1769 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.64/5.85 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_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1769,a,1766,a)].
% 5.64/5.85 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(1769,a,1767,a)].
% 5.64/5.85 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(1769,a,1768,a)].
% 5.64/5.85 1770 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.64/5.85 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(1770,a,1766,a)].
% 5.64/5.85 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(1770,a,1767,a)].
% 5.64/5.85 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(1770,a,1768,a)].
% 5.64/5.85 1771 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].
% 5.64/5.85 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(1771,a,1766,a)].
% 5.64/5.85 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(1771,a,1767,a)].
% 5.64/5.85 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(1771,a,1768,a)].
% 5.64/5.85 1772 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.64/5.85 1773 -class_Rings_Ocomm__semiring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D)),C) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(295)].
% 5.64/5.85 1774 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.64/5.85 1775 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.64/5.85 1776 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.72/5.94 1777 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.72/5.94 1778 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 5.72/5.94 1779 -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),D),E) = c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),D),E)) # label(fact_combine__common__factor) # label(axiom). [clausify(296)].
% 5.72/5.94 1780 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))) = hAPP(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(418)].
% 5.72/5.94 1781 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),C),hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)) = hAPP(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(419)].
% 5.72/5.94 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C),D)). [resolve(1778,a,1779,a)].
% 5.72/5.94 1782 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 5.72/5.94 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C),D)). [resolve(1782,a,1779,a)].
% 5.72/5.94 1783 class_Rings_Osemiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring) # label(axiom). [assumption].
% 5.72/5.94 Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C),D)). [resolve(1783,a,1779,a)].
% 5.72/5.94 1784 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom). [assumption].
% 5.72/5.94 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),C),D)). [resolve(1784,a,1779,a)].
% 5.72/5.94 1785 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) # label(axiom). [assumption].
% 5.72/5.94 Derived: c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,A),C),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral,hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral,B),C),D)). [resolve(1785,a,1779,a)].
% 5.94/6.13 1786 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 5.94/6.13 1787 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sgn__zero__iff) # label(axiom). [clausify(301)].
% 5.94/6.13 1788 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sgn__zero__iff) # label(axiom). [clausify(301)].
% 5.94/6.13 1789 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__zero) # label(axiom). [clausify(302)].
% 5.94/6.13 1790 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Osgn__class_Osgn(A,B)) = c_Groups_Osgn__class_Osgn(A,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_sgn__minus) # label(axiom). [clausify(443)].
% 5.94/6.13 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1786,a,1789,a)].
% 5.94/6.13 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1786,a,1790,a)].
% 5.94/6.13 1791 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 5.94/6.13 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1791,a,1787,a)].
% 5.94/6.13 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1791,a,1788,a)].
% 5.94/6.13 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1791,a,1789,a)].
% 5.94/6.13 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A)) = c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1791,a,1790,a)].
% 5.94/6.13 1792 class_Groups_Osgn__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Osgn__if) # label(axiom). [assumption].
% 5.94/6.13 1793 -class_Groups_Osgn__if(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn0) # label(axiom). [clausify(303)].
% 5.94/6.13 1794 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__if) # label(axiom). [clausify(568)].
% 5.94/6.13 1795 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__if) # label(axiom). [clausify(568)].
% 5.94/6.13 1796 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Osgn__class_Osgn(A,B) # label(fact_sgn__if) # label(axiom). [clausify(568)].
% 5.94/6.13 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1792,a,1793,a)].
% 5.94/6.13 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),A) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,A). [resolve(1792,a,1796,a)].
% 5.94/6.13 1797 class_Groups_Osgn__if(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Osgn__if) # label(axiom). [assumption].
% 5.94/6.13 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),A) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A). [resolve(1797,a,1796,a)].
% 6.23/6.41 1798 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 6.23/6.41 1799 -class_RealVector_Oreal__normed__div__algebra(A) | c_Groups_Osgn__class_Osgn(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C)) # label(fact_sgn__mult) # label(axiom). [clausify(305)].
% 6.23/6.41 1800 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 6.23/6.41 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A)),c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,B)). [resolve(1800,a,1799,a)].
% 6.23/6.41 1801 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 6.23/6.41 1802 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__one) # label(axiom). [clausify(307)].
% 6.23/6.41 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1801,a,1802,a)].
% 6.23/6.41 1803 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 6.23/6.41 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1803,a,1802,a)].
% 6.23/6.41 1804 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.23/6.41 1805 -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(326)].
% 6.23/6.41 1806 -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(327)].
% 6.23/6.41 1807 -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(328)].
% 6.23/6.41 1808 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(329)].
% 6.23/6.41 1809 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(329)].
% 6.23/6.41 1810 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(329)].
% 6.23/6.42 1811 -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(330)].
% 6.23/6.42 1812 -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(333)].
% 6.23/6.42 1813 -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(334)].
% 6.23/6.42 1814 -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(361)].
% 6.23/6.42 1815 -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(362)].
% 6.23/6.42 1816 -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(363)].
% 6.23/6.42 1817 -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(364)].
% 6.23/6.42 1818 -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(365)].
% 6.23/6.42 1819 -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(366)].
% 6.23/6.42 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(1804,a,1805,a)].
% 6.23/6.42 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(1804,a,1806,a)].
% 6.23/6.42 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(1804,a,1807,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1804,a,1808,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1804,a,1809,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1804,a,1810,a)].
% 6.23/6.42 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(1804,a,1812,a)].
% 6.23/6.42 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(1804,a,1814,a)].
% 6.23/6.42 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(1804,a,1815,a)].
% 6.23/6.42 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(1804,a,1816,a)].
% 6.23/6.42 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(1804,a,1817,a)].
% 6.23/6.42 1820 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.23/6.42 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(1820,a,1805,a)].
% 6.23/6.42 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(1820,a,1806,a)].
% 6.23/6.42 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,A,C)). [resolve(1820,a,1807,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1820,a,1808,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1820,a,1809,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1820,a,1810,a)].
% 6.23/6.42 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(1820,a,1812,a)].
% 6.23/6.42 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(1820,a,1814,a)].
% 6.23/6.42 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(1820,a,1815,a)].
% 6.23/6.42 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(1820,a,1816,a)].
% 6.23/6.42 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(1820,a,1817,a)].
% 6.23/6.42 1821 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.23/6.42 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(1821,a,1805,a)].
% 6.23/6.42 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(1821,a,1806,a)].
% 6.23/6.42 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(1821,a,1807,a)].
% 6.23/6.42 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1821,a,1808,a)].
% 6.23/6.43 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1821,a,1809,a)].
% 6.23/6.43 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1821,a,1810,a)].
% 6.23/6.43 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(1821,a,1812,a)].
% 6.23/6.43 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(1821,a,1814,a)].
% 6.23/6.43 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(1821,a,1815,a)].
% 6.23/6.43 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(1821,a,1816,a)].
% 6.23/6.43 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(1821,a,1817,a)].
% 6.23/6.43 1822 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].
% 6.23/6.43 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(1822,a,1805,a)].
% 6.23/6.43 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(1822,a,1806,a)].
% 6.23/6.43 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(1822,a,1807,a)].
% 6.32/6.53 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_Oplus__class_Oplus(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) = A. [resolve(1822,a,1808,a)].
% 6.32/6.53 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_Oplus__class_Oplus(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. [resolve(1822,a,1809,a)].
% 6.32/6.53 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_Oplus__class_Oplus(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) != A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != B. [resolve(1822,a,1810,a)].
% 6.32/6.53 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(1822,a,1812,a)].
% 6.32/6.53 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(1822,a,1814,a)].
% 6.32/6.53 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(1822,a,1815,a)].
% 6.32/6.53 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(1822,a,1816,a)].
% 6.32/6.53 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(1822,a,1817,a)].
% 6.32/6.53 1823 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 6.32/6.53 1824 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(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(411)].
% 6.32/6.53 1825 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(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(411)].
% 6.32/6.53 1826 -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(637)].
% 6.32/6.53 1827 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(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(750)].
% 6.32/6.53 1828 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(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(750)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1823,a,1824,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1823,a,1825,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(A))). [resolve(1823,a,1826,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1823,a,1827,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1823,a,1828,b)].
% 6.32/6.53 1829 class_Int_Oring__char__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Oring__char__0) # label(axiom). [assumption].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1829,a,1824,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1829,a,1825,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | -c_Int_Oiszero(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(A))). [resolve(1829,a,1826,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1829,a,1827,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(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(1829,a,1828,b)].
% 6.32/6.53 1830 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B) | A = B. [resolve(1830,a,1824,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,B) | A != B. [resolve(1830,a,1825,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | -c_Int_Oiszero(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit1(A))). [resolve(1830,a,1826,b)].
% 6.32/6.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | -c_Int_Oiszero(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit0(A))) | c_Int_Oiszero(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)). [resolve(1830,a,1827,b)].
% 6.41/6.63 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Oiszero(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OBit0(A))) | -c_Int_Oiszero(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)). [resolve(1830,a,1828,b)].
% 6.41/6.63 1831 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 6.41/6.63 1832 -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(447)].
% 6.41/6.63 1833 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(448)].
% 6.41/6.63 1834 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(448)].
% 6.41/6.63 1835 -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(450)].
% 6.41/6.63 1836 -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(450)].
% 6.41/6.63 1837 -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(470)].
% 6.41/6.63 1838 -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(471)].
% 6.41/6.63 1839 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_minus__add) # label(axiom). [clausify(472)].
% 6.41/6.63 1840 -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(482)].
% 6.41/6.63 1841 -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(483)].
% 6.41/6.63 1842 -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(483)].
% 6.41/6.63 1843 -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(484)].
% 6.41/6.63 1844 -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(484)].
% 6.41/6.63 1845 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ouminus__class_Ouminus(A,C) | B = C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(485)].
% 6.41/6.63 1846 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ouminus__class_Ouminus(A,C) | B != C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(485)].
% 6.41/6.63 1847 -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_add__eq__0__iff) # label(axiom). [clausify(532)].
% 6.41/6.63 1848 -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_add__eq__0__iff) # label(axiom). [clausify(532)].
% 6.41/6.63 1849 -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(533)].
% 6.41/6.63 1850 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Oplus__class_Oplus(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(534)].
% 6.41/6.63 1851 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Oplus__class_Oplus(A,C,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(534)].
% 6.41/6.63 1852 -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(535)].
% 6.41/6.63 1853 -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(537)].
% 6.41/6.63 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(1831,a,1832,a)].
% 6.41/6.63 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(1831,a,1833,a)].
% 6.41/6.63 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(1831,a,1834,a)].
% 6.41/6.63 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(1831,a,1837,a)].
% 6.41/6.63 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(1831,a,1838,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1831,a,1839,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) = A. [resolve(1831,a,1840,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A. [resolve(1831,a,1841,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) | A = B. [resolve(1831,a,1845,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) | A != B. [resolve(1831,a,1846,a)].
% 6.41/6.63 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = B. [resolve(1831,a,1847,a)].
% 6.41/6.63 Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B. [resolve(1831,a,1848,a)].
% 6.41/6.63 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(1831,a,1849,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1831,a,1850,a)].
% 6.41/6.63 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1831,a,1851,a)].
% 6.41/6.63 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(1831,a,1852,a)].
% 6.41/6.63 1854 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom). [assumption].
% 6.41/6.63 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(1854,a,1832,a)].
% 6.41/6.63 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(1854,a,1833,a)].
% 6.41/6.64 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(1854,a,1834,a)].
% 6.41/6.64 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(1854,a,1837,a)].
% 6.41/6.64 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(1854,a,1838,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)). [resolve(1854,a,1839,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) = A. [resolve(1854,a,1840,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) = A. [resolve(1854,a,1841,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) | A = B. [resolve(1854,a,1845,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) | A != B. [resolve(1854,a,1846,a)].
% 6.41/6.64 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,A) = B. [resolve(1854,a,1847,a)].
% 6.41/6.64 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,A) != B. [resolve(1854,a,1848,a)].
% 6.41/6.64 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(1854,a,1849,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1854,a,1850,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1854,a,1851,a)].
% 6.41/6.64 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(1854,a,1852,a)].
% 6.41/6.64 1855 class_Groups_Ogroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ogroup__add) # label(axiom). [assumption].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1855,a,1832,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1855,a,1833,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1855,a,1834,a)].
% 6.41/6.64 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = B. [resolve(1855,a,1837,a)].
% 6.41/6.64 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B)) = B. [resolve(1855,a,1838,a)].
% 6.41/6.64 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1855,a,1839,a)].
% 6.55/6.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = A. [resolve(1855,a,1840,a)].
% 6.55/6.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) = A. [resolve(1855,a,1841,a)].
% 6.55/6.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) | A = B. [resolve(1855,a,1845,a)].
% 6.55/6.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) | A != B. [resolve(1855,a,1846,a)].
% 6.55/6.74 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = B. [resolve(1855,a,1847,a)].
% 6.55/6.74 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B. [resolve(1855,a,1848,a)].
% 6.55/6.74 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1855,a,1849,a)].
% 6.55/6.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1855,a,1850,a)].
% 6.55/6.74 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1855,a,1851,a)].
% 6.55/6.74 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1855,a,1852,a)].
% 6.55/6.74 1856 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 6.55/6.74 1857 -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(452)].
% 6.55/6.74 1858 -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(452)].
% 6.55/6.74 1859 -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(453)].
% 6.55/6.74 1860 -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(453)].
% 6.55/6.74 1861 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_neg__le__iff__le) # label(axiom). [clausify(454)].
% 6.55/6.74 1862 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_neg__le__iff__le) # label(axiom). [clausify(454)].
% 6.55/6.74 1863 -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(455)].
% 6.55/6.74 1864 -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(458)].
% 6.55/6.74 1865 -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(458)].
% 6.55/6.74 1866 -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(459)].
% 6.55/6.74 1867 -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(459)].
% 6.55/6.74 1868 -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(460)].
% 6.55/6.74 1869 -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(460)].
% 6.55/6.74 1870 -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(525)].
% 6.55/6.74 1871 -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(525)].
% 6.55/6.74 1872 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(527)].
% 6.55/6.74 1873 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(527)].
% 6.55/6.74 1874 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(529)].
% 6.55/6.74 1875 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(529)].
% 6.55/6.74 1876 -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(530)].
% 6.55/6.74 1877 -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(530)].
% 6.55/6.74 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(1856,a,1857,a)].
% 6.55/6.74 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(1856,a,1859,a)].
% 6.55/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_Int_Oint,B,A). [resolve(1856,a,1861,a)].
% 6.55/6.75 Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_Int_Oint,B,A). [resolve(1856,a,1862,a)].
% 6.55/6.75 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(1856,a,1864,a)].
% 6.55/6.75 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(1856,a,1865,a)].
% 6.55/6.75 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(1856,a,1866,a)].
% 6.55/6.75 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(1856,a,1868,a)].
% 6.55/6.75 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(1856,a,1870,a)].
% 6.55/6.75 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(1856,a,1871,a)].
% 6.55/6.75 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1856,a,1872,a)].
% 6.55/6.75 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1856,a,1873,a)].
% 6.55/6.75 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1856,a,1874,a)].
% 6.55/6.75 Derived: 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)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). [resolve(1856,a,1875,a)].
% 6.55/6.75 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(1856,a,1876,a)].
% 6.55/6.75 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(1856,a,1877,a)].
% 6.55/6.75 1878 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 6.55/6.75 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(1878,a,1857,a)].
% 6.55/6.75 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(1878,a,1859,a)].
% 6.64/6.85 Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,B,A). [resolve(1878,a,1861,a)].
% 6.64/6.85 Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,B,A). [resolve(1878,a,1862,a)].
% 6.64/6.85 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(1878,a,1864,a)].
% 6.64/6.85 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(1878,a,1865,a)].
% 6.64/6.85 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(1878,a,1866,a)].
% 6.64/6.85 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(1878,a,1868,a)].
% 6.64/6.85 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(1878,a,1870,a)].
% 6.64/6.85 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(1878,a,1871,a)].
% 6.64/6.85 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1878,a,1872,a)].
% 6.64/6.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1878,a,1873,a)].
% 6.64/6.85 Derived: -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)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1878,a,1874,a)].
% 6.64/6.85 Derived: 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)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). [resolve(1878,a,1875,a)].
% 6.64/6.85 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(1878,a,1876,a)].
% 6.64/6.85 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(1878,a,1877,a)].
% 6.64/6.85 1879 class_Rings_Oidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oidom) # label(axiom). [assumption].
% 6.64/6.85 1880 -class_Rings_Oidom(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),B) != hAPP(c_Groups_Otimes__class_Otimes(A,C),C) | B = C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_square__eq__iff) # label(axiom). [clausify(461)].
% 6.73/6.95 1881 -class_Rings_Oidom(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),B) = hAPP(c_Groups_Otimes__class_Otimes(A,C),C) | B != C # label(fact_square__eq__iff) # label(axiom). [clausify(461)].
% 6.73/6.95 1882 -class_Rings_Oidom(A) | hAPP(c_Groups_Otimes__class_Otimes(A,B),B) = hAPP(c_Groups_Otimes__class_Otimes(A,C),C) | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_square__eq__iff) # label(axiom). [clausify(461)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A) != hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B) | A = B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A. [resolve(1879,a,1880,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B) | A != B. [resolve(1879,a,1881,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),B) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) != A. [resolve(1879,a,1882,a)].
% 6.73/6.95 1883 class_Rings_Oidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oidom) # label(axiom). [assumption].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B) | A = B | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) = A. [resolve(1883,a,1880,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B) | A != B. [resolve(1883,a,1881,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B) != A. [resolve(1883,a,1882,a)].
% 6.73/6.95 1884 class_Rings_Oidom(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oidom) # label(axiom). [assumption].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A) != hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),B) | A = B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) = A. [resolve(1884,a,1880,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),B) | A != B. [resolve(1884,a,1881,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B),B) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) != A. [resolve(1884,a,1882,a)].
% 6.73/6.95 1885 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption].
% 6.73/6.95 1886 -class_Rings_Oring(A) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),C) # label(fact_minus__mult__minus) # label(axiom). [clausify(462)].
% 6.73/6.95 1887 -class_Rings_Oring(A) | hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__commute) # label(axiom). [clausify(463)].
% 6.73/6.95 1888 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C) # label(fact_minus__mult__left) # label(axiom). [clausify(464)].
% 6.73/6.95 1889 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__right) # label(axiom). [clausify(465)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B). [resolve(1885,a,1886,a)].
% 6.73/6.95 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1885,a,1887,a)].
% 6.94/7.16 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B). [resolve(1885,a,1888,a)].
% 6.94/7.16 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1885,a,1889,a)].
% 6.94/7.16 1890 class_Rings_Oring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring) # label(axiom). [assumption].
% 6.94/7.16 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B). [resolve(1890,a,1886,a)].
% 6.94/7.16 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B)). [resolve(1890,a,1887,a)].
% 6.94/7.16 1891 class_Rings_Oring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring) # label(axiom). [assumption].
% 6.94/7.16 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),B). [resolve(1891,a,1886,a)].
% 6.94/7.16 Derived: hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1891,a,1887,a)].
% 6.94/7.16 1892 class_Groups_Oab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__group__add) # label(axiom). [assumption].
% 6.94/7.16 1893 -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__add__distrib) # label(axiom). [clausify(473)].
% 6.94/7.16 1894 -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(536)].
% 6.94/7.16 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)) = 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)). [resolve(1892,a,1893,a)].
% 6.94/7.16 1895 class_Groups_Oab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__group__add) # label(axiom). [assumption].
% 6.94/7.16 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)) = 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)). [resolve(1895,a,1893,a)].
% 6.94/7.16 1896 class_Groups_Oab__group__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__group__add) # label(axiom). [assumption].
% 6.94/7.16 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1896,a,1893,a)].
% 6.94/7.16 1897 class_Rings_Ocomm__ring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__ring__1) # label(axiom). [assumption].
% 6.94/7.16 1898 -class_Rings_Ocomm__ring__1(A) | c_Groups_Ouminus__class_Ouminus(A,B) = hAPP(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(538)].
% 6.94/7.16 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = hAPP(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(1897,a,1898,a)].
% 7.03/7.26 1899 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__ring__1) # label(axiom). [assumption].
% 7.03/7.26 Derived: c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A) = hAPP(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(1899,a,1898,a)].
% 7.03/7.26 1900 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__ring__1) # label(axiom). [assumption].
% 7.03/7.26 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(1900,a,1898,a)].
% 7.03/7.26 1901 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 7.03/7.26 1902 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) != hAPP(c_Groups_Otimes__class_Otimes(A,B),B) | c_Groups_Oone__class_Oone(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B # label(fact_square__eq__1__iff) # label(axiom). [clausify(539)].
% 7.03/7.26 1903 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),B) | c_Groups_Oone__class_Oone(A) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(539)].
% 7.03/7.26 1904 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Otimes__class_Otimes(A,B),B) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(539)].
% 7.03/7.26 1905 -class_Rings_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__eq__power2) # label(axiom). [clausify(843)].
% 7.03/7.26 1906 -class_Rings_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__eq__power2) # label(axiom). [clausify(843)].
% 7.03/7.26 1907 -class_Rings_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B # label(fact_power2__eq__1__iff) # label(axiom). [clausify(856)].
% 7.03/7.26 1908 -class_Rings_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) != B # label(fact_power2__eq__1__iff) # label(axiom). [clausify(856)].
% 7.03/7.26 1909 -class_Rings_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B # label(fact_power2__eq__1__iff) # label(axiom). [clausify(856)].
% 7.03/7.26 1910 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Power_Opower__class_Opower(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_field__power__not__zero) # label(axiom). [clausify(893)].
% 7.03/7.26 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A) | c_Groups_Oone__class_Oone(tc_Int_Oint) = A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1901,a,1902,a)].
% 7.03/7.26 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A) | c_Groups_Oone__class_Oone(tc_Int_Oint) != A. [resolve(1901,a,1903,a)].
% 7.03/7.27 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),A) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) != A. [resolve(1901,a,1904,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1901,a,1905,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1901,a,1906,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Groups_Oone__class_Oone(tc_Int_Oint) = A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1901,a,1907,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) | c_Groups_Oone__class_Oone(tc_Int_Oint) != A. [resolve(1901,a,1908,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = 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(1901,a,1909,a)].
% 7.03/7.27 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Power_Opower__class_Opower(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1901,a,1910,a)].
% 7.03/7.27 1911 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 7.03/7.27 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1911,a,1902,a)].
% 7.03/7.27 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A. [resolve(1911,a,1903,a)].
% 7.03/7.27 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != A. [resolve(1911,a,1904,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1911,a,1905,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1911,a,1906,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = A | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1911,a,1907,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A. [resolve(1911,a,1908,a)].
% 7.03/7.27 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = 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(1911,a,1909,a)].
% 7.12/7.37 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1911,a,1910,a)].
% 7.12/7.37 1912 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 7.12/7.37 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1912,a,1902,a)].
% 7.12/7.37 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1912,a,1903,a)].
% 7.12/7.37 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A),A) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) != A. [resolve(1912,a,1904,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1912,a,1905,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1912,a,1906,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1912,a,1907,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1912,a,1908,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) != A. [resolve(1912,a,1909,a)].
% 7.12/7.37 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1912,a,1910,a)].
% 7.12/7.37 1913 class_Rings_Osemiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__1) # label(axiom). [assumption].
% 7.12/7.37 1914 -class_Rings_Osemiring__1(A) | -c_Int_Oiszero(A,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_iszero__def) # label(axiom). [clausify(592)].
% 7.12/7.37 1915 -class_Rings_Osemiring__1(A) | c_Int_Oiszero(A,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_iszero__def) # label(axiom). [clausify(592)].
% 7.12/7.37 1916 -class_Rings_Osemiring__1(A) | c_Int_Oiszero(A,c_Groups_Ozero__class_Ozero(A)) # label(fact_iszero__0) # label(axiom). [clausify(593)].
% 7.12/7.37 1917 -class_Rings_Osemiring__1(A) | -c_Int_Oiszero(A,c_Groups_Oone__class_Oone(A)) # label(fact_not__iszero__1) # label(axiom). [clausify(594)].
% 7.12/7.37 1918 -class_Rings_Osemiring__1(A) | c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(A) # label(fact_zero__power2) # label(axiom). [clausify(842)].
% 7.12/7.37 1919 -class_Rings_Osemiring__1(A) | c_Power_Opower__class_Opower(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(A) # label(fact_one__power2) # label(axiom). [clausify(846)].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1913,a,1914,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1913,a,1915,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1913,a,1916,a)].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1913,a,1917,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1913,a,1918,a)].
% 7.12/7.37 1920 class_Rings_Osemiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__1) # label(axiom). [assumption].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Nat_Onat,A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1920,a,1914,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Nat_Onat,A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A. [resolve(1920,a,1915,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1920,a,1916,a)].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1920,a,1917,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1920,a,1918,a)].
% 7.12/7.37 1921 class_Rings_Osemiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__1) # label(axiom). [assumption].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1921,a,1914,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_RealDef_Oreal,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1921,a,1915,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1921,a,1916,a)].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1921,a,1917,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1921,a,1918,a)].
% 7.12/7.37 1922 class_Rings_Osemiring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring__1) # label(axiom). [assumption].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Complex_Ocomplex,A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1922,a,1914,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Complex_Ocomplex,A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1922,a,1915,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1922,a,1916,a)].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1922,a,1917,a)].
% 7.12/7.37 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1922,a,1918,a)].
% 7.12/7.37 1923 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) # label(axiom). [assumption].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,A) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(1923,a,1914,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,A) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A. [resolve(1923,a,1915,a)].
% 7.12/7.37 Derived: c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(1923,a,1916,a)].
% 7.12/7.37 Derived: -c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(1923,a,1917,a)].
% 7.27/7.48 Derived: c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1923,a,1918,a)].
% 7.27/7.48 1924 class_Rings_Osemiring__0(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.27/7.48 1925 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Oone__class_Oone(A) # label(fact_power__0__left__number__of) # label(axiom). [clausify(840)].
% 7.27/7.48 1926 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)) = c_Groups_Ozero__class_Ozero(A) # label(fact_power__0__left__number__of) # label(axiom). [clausify(840)].
% 7.27/7.48 1927 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Oone__class_Oone(A) # label(fact_power__0__left) # label(axiom). [clausify(915)].
% 7.27/7.48 1928 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_power__0__left) # label(axiom). [clausify(915)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1924,a,1925,b)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1924,a,1926,b)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1924,a,1927,b)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1924,a,1928,b)].
% 7.27/7.48 1929 class_Rings_Osemiring__0(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1929,a,1925,b)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1929,a,1926,b)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1929,a,1927,b)].
% 7.27/7.48 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1929,a,1928,b)].
% 7.27/7.49 1930 class_Rings_Osemiring__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.27/7.49 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1930,a,1925,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1930,a,1926,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1930,a,1927,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1930,a,1928,b)].
% 7.27/7.49 1931 class_Rings_Osemiring__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1931,a,1925,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1931,a,1926,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1931,a,1927,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1931,a,1928,b)].
% 7.27/7.49 1932 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(1932,a,1925,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(1932,a,1926,b)].
% 7.27/7.49 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(1932,a,1927,b)].
% 7.41/7.59 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Power_Opower__class_Opower(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(1932,a,1928,b)].
% 7.41/7.59 1933 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 7.41/7.59 1934 -class_Rings_Oring__1(A) | c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_power2__minus) # label(axiom). [clausify(847)].
% 7.41/7.59 1935 -class_Rings_Oring__1(A) | c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,B),hAPP(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)))),C)) = c_Power_Opower__class_Opower(A,B,hAPP(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)))),C)) # label(fact_ring__1__class_Opower__minus__even) # label(axiom). [clausify(858)].
% 7.41/7.59 1936 -class_Rings_Oring__1(A) | c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)),hAPP(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)))),B)) = c_Groups_Oone__class_Oone(A) # label(fact_power__minus1__even) # label(axiom). [clausify(871)].
% 7.41/7.59 1937 -class_Rings_Oring__1(A) | c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)),C)),c_Power_Opower__class_Opower(A,B,C)) # label(fact_power__minus) # label(axiom). [clausify(916)].
% 7.41/7.59 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(1933,a,1934,a)].
% 7.41/7.59 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),hAPP(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)))),B)) = c_Power_Opower__class_Opower(tc_Int_Oint,A,hAPP(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)))),B)). [resolve(1933,a,1935,a)].
% 7.41/7.59 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(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)))),A)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1933,a,1936,a)].
% 7.41/7.59 Derived: c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). [resolve(1933,a,1937,a)].
% 7.41/7.59 1938 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption].
% 7.41/7.59 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(1938,a,1934,a)].
% 7.41/7.59 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),hAPP(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)))),B)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,hAPP(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)))),B)). [resolve(1938,a,1935,a)].
% 7.53/7.70 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(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)))),A)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1938,a,1936,a)].
% 7.53/7.70 Derived: c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B)). [resolve(1938,a,1937,a)].
% 7.53/7.70 1939 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom). [assumption].
% 7.53/7.70 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(1939,a,1934,a)].
% 7.53/7.70 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),hAPP(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)))),B)) = c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,hAPP(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)))),B)). [resolve(1939,a,1935,a)].
% 7.53/7.70 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(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)))),A)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1939,a,1936,a)].
% 7.53/7.70 Derived: c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),B)),c_Power_Opower__class_Opower(tc_Complex_Ocomplex,A,B)). [resolve(1939,a,1937,a)].
% 7.53/7.70 1940 class_Rings_Oordered__ring__abs(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 7.53/7.70 1941 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oabs__class_Oabs(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(941)].
% 7.53/7.70 1942 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(941)].
% 7.53/7.70 1943 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oabs__class_Oabs(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(941)].
% 7.53/7.70 1944 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)) = hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(941)].
% 7.53/7.70 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_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1940,a,1941,a)].
% 7.53/7.70 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_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1940,a,1942,a)].
% 7.53/7.70 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),B) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1940,a,1943,a)].
% 7.53/7.70 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_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1940,a,1944,a)].
% 7.53/7.70 1945 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 7.53/7.70 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_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1945,a,1941,a)].
% 7.53/7.70 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1945,a,1942,a)].
% 7.53/7.70 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),B) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1945,a,1943,a)].
% 7.53/7.70 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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1945,a,1944,a)].
% 8.19/8.37 1946 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 8.19/8.37 1947 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_abs__of__nonpos) # label(axiom). [clausify(942)].
% 8.19/8.37 1948 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__minus__le__zero) # label(axiom). [clausify(943)].
% 8.19/8.37 1949 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_abs__of__neg) # label(axiom). [clausify(944)].
% 8.19/8.37 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A). [resolve(1946,a,1947,a)].
% 8.19/8.37 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1946,a,1948,a)].
% 8.19/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A). [resolve(1946,a,1949,a)].
% 8.19/8.37 1950 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 8.19/8.37 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A). [resolve(1950,a,1947,a)].
% 8.19/8.37 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1950,a,1948,a)].
% 8.19/8.37 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A). [resolve(1950,a,1949,a)].
% 8.19/8.37 1951 class_Groups_Oabs__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oabs__if) # label(axiom). [assumption].
% 8.19/8.37 1952 -class_Groups_Oabs__if(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_abs__if) # label(axiom). [clausify(945)].
% 8.19/8.37 1953 -class_Groups_Oabs__if(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__if) # label(axiom). [clausify(945)].
% 8.19/8.37 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A. [resolve(1951,a,1953,a)].
% 8.19/8.37 1954 class_Groups_Oabs__if(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oabs__if) # label(axiom). [assumption].
% 8.19/8.37 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A. [resolve(1954,a,1953,a)].
% 8.19/8.37
% 8.19/8.37 ============================== end predicate elimination =============
% 8.19/8.37
% 8.19/8.37 Auto_denials: (non-Horn, no changes).
% 8.19/8.37
% 8.19/8.37 Term ordering decisions:
% 8.19/8.37 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Int_Oint=1. tc_Nat_Onat=1. tc_Complex_Ocomplex=1. tc_Code__Numeral_Ocode__numeral=1. c_Int_OPls=1. c_NthRoot_Osqrt=1. c_Transcendental_Oln=1. c_Transcendental_Oarctan=1. v_m____=1. v_e=1. tc_HOL_Obool=1. v_d____=1. v_da____=1. c1=1. c2=1. hAPP=1. c_Groups_Otimes__class_Otimes=1. c_Int_Onumber__class_Onumber__of=1. c_Groups_Ouminus__class_Ouminus=1. c_Rings_Oinverse__class_Oinverse=1. c_Groups_Oabs__class_Oabs=1. c_Groups_Osgn__class_Osgn=1. tc_fun=1. f1=1. f7=1. f8=1. c_Groups_Ozero__class_Ozero=1. c_Groups_Oone__class_Oone=1. c_Int_OBit1=1. c_Int_OBit0=1. c_Transcendental_Oexp=1. c_Int_Osucc=1. c_Int_Opred=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt=1. c_Groups_Oplus__class_Oplus=1. c_Power_Opower__class_Opower=1. c_Rings_Oinverse__class_Odivide=1. f3=1. f4=1. f5=1. f6=1. f9=1. f2=1. f10=1.
% 8.61/8.84
% 8.61/8.84 ============================== end of process initial clauses ========
% 8.61/8.84
% 8.61/8.84 ============================== CLAUSES FOR SEARCH ====================
% 8.61/8.84
% 8.61/8.84 ============================== end of clauses for search =============
% 8.61/8.84
% 8.61/8.84 ============================== SEARCH ================================
% 8.61/8.84
% 8.61/8.84 % Starting search at 6.72 seconds.
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=55.000, iters=3464
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=45.000, iters=3346
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=43.000, iters=3336
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=42.000, iters=3347
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=37.000, iters=3337
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=33.000, iters=3339
% 8.61/8.84
% 8.61/8.84 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 72 (0.00 of 7.07 sec).
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=32.000, iters=3371
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=30.000, iters=3362
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=29.000, iters=3403
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=27.000, iters=3339
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=26.000, iters=3345
% 8.61/8.84
% 8.61/8.84 Low Water (keep): wt=25.000, iters=3356
% 8.61/8.84
% 8.61/8.84 ============================== PROOF =================================
% 8.61/8.84 % SZS status Theorem
% 8.61/8.84 % SZS output start Refutation
% 8.61/8.84
% 8.61/8.84 % Proof 1 at 7.19 (+ 0.02) seconds.
% 8.61/8.84 % Length of proof is 11.
% 8.61/8.84 % Level of proof is 3.
% 8.61/8.84 % Maximum clause weight is 20.000.
% 8.61/8.84 % Given clauses 578.
% 8.61/8.84
% 8.61/8.84 2 (all V_w all V_z hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 8.61/8.84 34 (all V_b_2 all V_a_2 all V_ca_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_ca_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 8.61/8.84 993 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption].
% 8.61/8.84 1004 -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(34)].
% 8.61/8.84 1956 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) # label(fact_m_I1_J) # label(axiom). [assumption].
% 8.61/8.84 1957 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) # label(fact_H_I3_J) # label(axiom). [assumption].
% 8.61/8.84 1965 hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A) # label(fact_real__mult__commute) # label(axiom). [clausify(2)].
% 8.61/8.84 2773 -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) # label(conj_0) # label(negated_conjecture). [assumption].
% 8.61/8.84 2774 -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_m____),v_da____),v_e). [copy(2773),rewrite([1965(6)])].
% 8.61/8.84 2964 -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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),C). [resolve(993,a,1004,a)].
% 8.61/8.84 8445 $F. [resolve(2964,b,1957,a),rewrite([1965(11)]),unit_del(a,1956),unit_del(b,2774)].
% 8.61/8.84
% 8.61/8.84 % SZS output end Refutation
% 8.61/8.84 ============================== end of proof ==========================
% 8.61/8.84
% 8.61/8.84 ============================== STATISTICS ============================
% 8.61/8.84
% 8.61/8.84 Given=578. Generated=15212. Kept=5774. proofs=1.
% 8.61/8.84 Usable=537. Sos=4360. Demods=607. Limbo=2, Disabled=3968. Hints=0.
% 8.61/8.84 Megabytes=12.55.
% 8.61/8.84 User_CPU=7.19, System_CPU=0.02, Wall_clock=8.
% 8.61/8.84
% 8.61/8.84 ============================== end of statistics =====================
% 8.61/8.84
% 8.61/8.84 ============================== end of search =========================
% 8.61/8.84
% 8.61/8.84 THEOREM PROVED
% 8.61/8.84 % SZS status Theorem
% 8.61/8.84
% 8.61/8.84 Exiting with 1 proof.
% 8.61/8.84
% 8.61/8.84 Process 15281 exit (max_proofs) Mon Jun 6 08:37:58 2022
% 8.61/8.84 Prover9 interrupted
%------------------------------------------------------------------------------