TSTP Solution File: SWW212+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW212+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 : Timeout 300.09s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW212+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 6 07:10:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.49/1.77 ============================== Prover9 ===============================
% 1.49/1.77 Prover9 (32) version 2009-11A, November 2009.
% 1.49/1.77 Process 28912 was started by sandbox on n027.cluster.edu,
% 1.49/1.77 Mon Jun 6 07:10:55 2022
% 1.49/1.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28570_n027.cluster.edu".
% 1.49/1.77 ============================== end of head ===========================
% 1.49/1.77
% 1.49/1.77 ============================== INPUT =================================
% 1.49/1.77
% 1.49/1.77 % Reading from file /tmp/Prover9_28570_n027.cluster.edu
% 1.49/1.77
% 1.49/1.77 set(prolog_style_variables).
% 1.49/1.77 set(auto2).
% 1.49/1.77 % set(auto2) -> set(auto).
% 1.49/1.77 % set(auto) -> set(auto_inference).
% 1.49/1.77 % set(auto) -> set(auto_setup).
% 1.49/1.77 % set(auto_setup) -> set(predicate_elim).
% 1.49/1.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.49/1.77 % set(auto) -> set(auto_limits).
% 1.49/1.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.49/1.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.49/1.77 % set(auto) -> set(auto_denials).
% 1.49/1.77 % set(auto) -> set(auto_process).
% 1.49/1.77 % set(auto2) -> assign(new_constants, 1).
% 1.49/1.77 % set(auto2) -> assign(fold_denial_max, 3).
% 1.49/1.77 % set(auto2) -> assign(max_weight, "200.000").
% 1.49/1.77 % set(auto2) -> assign(max_hours, 1).
% 1.49/1.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.49/1.77 % set(auto2) -> assign(max_seconds, 0).
% 1.49/1.77 % set(auto2) -> assign(max_minutes, 5).
% 1.49/1.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.49/1.77 % set(auto2) -> set(sort_initial_sos).
% 1.49/1.77 % set(auto2) -> assign(sos_limit, -1).
% 1.49/1.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.49/1.77 % set(auto2) -> assign(max_megs, 400).
% 1.49/1.77 % set(auto2) -> assign(stats, some).
% 1.49/1.77 % set(auto2) -> clear(echo_input).
% 1.49/1.77 % set(auto2) -> set(quiet).
% 1.49/1.77 % set(auto2) -> clear(print_initial_clauses).
% 1.49/1.77 % set(auto2) -> clear(print_given).
% 1.49/1.77 assign(lrs_ticks,-1).
% 1.49/1.77 assign(sos_limit,10000).
% 1.49/1.77 assign(order,kbo).
% 1.49/1.77 set(lex_order_vars).
% 1.49/1.77 clear(print_given).
% 1.49/1.77
% 1.49/1.77 % formulas(sos). % not echoed (1274 formulas)
% 1.49/1.77
% 1.49/1.77 ============================== end of input ==========================
% 1.49/1.77
% 1.49/1.77 % From the command line: assign(max_seconds, 300).
% 1.49/1.77
% 1.49/1.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.49/1.77
% 1.49/1.77 % Formulas that are not ordinary clauses:
% 1.49/1.77 1 (all V_gb_2 all V_fa_2 ((all B_x hAPP(V_fa_2,B_x) = hAPP(V_gb_2,B_x)) -> V_fa_2 = V_gb_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 2 (all V_xa_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_xa_2)) <-> V_xa_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 3 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 4 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_norm__zero) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 5 (all V_xa_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 6 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 7 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 8 (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(v_s,B_n)),v_r)) # label(fact_assms) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 9 (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].
% 1.49/1.77 10 (all V_n_2 all V_fa_2 (c_SEQ_Osubseq(V_fa_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)))) # label(fact_seq__suble) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 11 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) # label(fact_norm__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 12 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 13 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 14 (all V_fa_2 (c_SEQ_Osubseq(V_fa_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)))))) # label(fact_subseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 15 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_b)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))) # label(fact_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 16 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)))) # label(fact_norm__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 17 (all V_xa_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 18 (all V_xa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_xa_2 <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 19 (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].
% 1.49/1.77 20 (all V_xa_2 all V_gb_2 all V_fa_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_fa_2,V_gb_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_gb_2,V_xa_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 21 (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].
% 1.49/1.77 22 (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].
% 1.49/1.77 23 (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].
% 1.49/1.77 24 (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].
% 1.49/1.77 25 (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].
% 1.49/1.77 26 (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].
% 1.49/1.77 27 (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].
% 1.49/1.77 28 (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].
% 1.49/1.77 29 (all V_xa_2 all V_ya_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 30 (all V_xa_2 all V_gb_2 all V_fa_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_fa_2,V_gb_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_gb_2,V_xa_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 31 (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].
% 1.49/1.77 32 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (V_xa_2 = V_ya_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 33 (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].
% 1.49/1.77 34 (all V_gb_2 all V_fa_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_fa_2,V_gb_2) <-> (all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_gb_2,B_x)))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 35 (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].
% 1.49/1.77 36 (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].
% 1.49/1.77 37 (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].
% 1.49/1.77 38 (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].
% 1.49/1.77 39 (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].
% 1.49/1.77 40 (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].
% 1.49/1.77 41 (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].
% 1.49/1.77 42 (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].
% 1.49/1.77 43 (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].
% 1.49/1.77 44 (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].
% 1.49/1.77 45 (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].
% 1.49/1.77 46 (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].
% 1.49/1.77 47 (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].
% 1.49/1.77 48 (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].
% 1.49/1.77 49 (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].
% 1.49/1.77 50 (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].
% 1.49/1.77 51 (all V_xa_2 all V_ya_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 52 (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].
% 1.49/1.77 53 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) | V_xa_2 = V_ya_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 54 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_xa_2 != V_ya_2 <-> c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) | c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 55 (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].
% 1.49/1.77 56 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) -> (V_a_2 = V_b_2 <-> V_c_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 57 (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].
% 1.49/1.77 58 (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].
% 1.49/1.77 59 (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].
% 1.49/1.77 60 (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].
% 1.49/1.77 61 (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].
% 1.49/1.77 62 (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].
% 1.49/1.77 63 (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].
% 1.49/1.77 64 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 65 (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].
% 1.49/1.77 66 (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].
% 1.49/1.77 67 (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].
% 1.49/1.77 68 (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].
% 1.49/1.77 69 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 70 (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].
% 1.49/1.77 71 (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].
% 1.49/1.77 72 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) | V_xa_2 = V_ya_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 73 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & -c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 74 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) & V_xa_2 != V_ya_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 75 (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].
% 1.49/1.77 76 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 77 (all V_ya_2 all V_xa_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 78 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 79 (all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (V_a_2 = V_b_2 <-> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 80 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 81 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 82 (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].
% 1.49/1.77 83 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) | V_xa_2 = V_ya_2)) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 84 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) & V_xa_2 != V_ya_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 85 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_xa_2),V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 86 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Odecseq(T_a,V_X_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))))))) # label(fact_decseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 87 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(V_X_2,B_n)),B_K))))))) # label(fact_Bseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 88 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Oincseq(T_a,V_X_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))))))) # label(fact_incseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 89 (all V_e_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e_2) -> (exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),B_n))),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),V_e_2))))) # label(fact__096_B_Be_O_A0_A_060_Ae_A_061_061_062_AEX_AN_O_AALL_An_062_061N_O_Acmod_A_Is_A_I_If_Ao_Ag_J_An_J_A_N_AComplex_Ax_Ay_J_A_060_Ae_096) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 90 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Omonoseq(T_a,V_X_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)))) | (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))))))) # label(fact_monoseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 91 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 92 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 93 (all V_c all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.77 94 (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].
% 1.49/1.77 95 (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].
% 1.49/1.78 96 (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].
% 1.49/1.78 97 (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].
% 1.49/1.78 98 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 99 (all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 100 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 101 (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].
% 1.49/1.78 102 (all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 103 (all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 104 (all V_gb_2 all V_fa_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_gb_2) & -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2,V_fa_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 105 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 106 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Odecseq(T_a,V_X_2) -> c_SEQ_Omonoseq(T_a,V_X_2)))) # label(fact_decseq__imp__monoseq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 107 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Oincseq(T_a,V_X_2) -> c_SEQ_Omonoseq(T_a,V_X_2)))) # label(fact_incseq__imp__monoseq) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 108 (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].
% 1.49/1.78 109 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_m)))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 110 (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].
% 1.49/1.78 111 (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].
% 1.49/1.78 112 (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].
% 1.49/1.78 113 (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].
% 1.49/1.78 114 (all V_n all V_k all V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n),V_k))) # label(fact_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 115 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 116 (all V_n all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 117 (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].
% 1.49/1.78 118 (all V_P_2 all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.49/1.78 119 (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].
% 1.49/1.78 120 (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].
% 1.49/1.78 121 (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].
% 1.49/1.78 122 (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].
% 1.49/1.78 123 (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].
% 1.49/1.78 124 (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].
% 1.49/1.78 125 (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].
% 1.49/1.78 126 (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].
% 1.49/1.78 127 (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].
% 1.49/1.78 128 (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].
% 1.49/1.78 129 (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].
% 1.56/1.78 130 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 131 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 132 (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].
% 1.56/1.78 133 (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].
% 1.56/1.78 134 (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].
% 1.56/1.78 135 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_m)) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 136 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 137 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l)))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 138 (all V_n all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i)) # label(fact_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 139 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 140 (all V_n all V_m all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 141 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))))) # label(fact_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 142 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 143 (all V_d all V_c all V_b all V_a hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a),V_b)),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_c),V_d)) = hAPP(hAPP(c_Complex_Ocomplex_OComplex,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_b),V_d))) # label(fact_complex__diff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 144 (all V_b_2 all V_a_2 (hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) <-> V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_Complex__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 145 (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].
% 1.56/1.78 146 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) -> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(V_X_2,B_n)),B_K))))))) # label(fact_BseqD) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 147 (all V_X_2 all V_K_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2) -> ((all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(V_X_2,B_n)),V_K_2)) -> c_SEQ_OBseq(T_a,V_X_2))))) # label(fact_BseqI) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 148 (all V_K_2 all V_X_2 all V_N_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> ((all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(V_X_2,B_n)),V_K_2))) -> c_SEQ_OBseq(T_a,V_X_2)))) # label(fact_BseqI2_H) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 149 (all B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) -> (exists B_n0 all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_n0,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n))))),v_y____)),B_r))))) # label(fact_y) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 150 (all V_p_2 all T_a (class_Groups_Ozero(T_a) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_psize__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 151 (all V_real2 all V_real1 c_Complex_Ocomplex_Ocomplex__size(hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_real1),V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_complex_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 152 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) # label(fact_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 153 (all V_r hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),V_r) = hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_r)) # label(fact_real__norm__def) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 154 (all V_y all V_x hAPP(c_Complex_OIm,hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_x),V_y)) = V_y) # label(fact_Im) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 155 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_x))) # label(fact_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 156 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 157 (all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_abs__zero) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 158 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 159 (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,hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))) # label(fact_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 160 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) # label(fact_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 161 (all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)) = hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a))) # label(fact_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 162 (all V_y all V_x hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) # label(fact_Im_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 163 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a))) # label(fact_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 164 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 165 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))) # label(fact_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 166 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a))) # label(fact_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 167 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)) <-> V_a_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 168 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 169 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))))) # label(fact_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 170 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))) # label(fact_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 171 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))) # label(fact_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 172 (all T_e all T_d all T_c all T_a all T_b all V_x_H_2 all V_g_H_2 all V_f_H_2 all V_xa_2 all V_gb_2 all V_fa_2 (hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) -> hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_xa_2) = hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2))) # label(fact_comp__cong) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 173 (all V_real2_H_2 all V_real1_H_2 all V_real2_2 all V_real1_2 (hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_real1_2),V_real2_2) = hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_real1_H_2),V_real2_H_2) <-> V_real1_2 = V_real1_H_2 & V_real2_2 = V_real2_H_2)) # label(fact_complex_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 174 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_b))),hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))) # label(fact_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 175 (all V_real2 all V_real1 c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_real1),V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_complex_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 176 (all B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) -> (exists B_n0 all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_n0,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,hAPP(v_s,hAPP(v_f____,B_n)))),v_x____)),B_r))))) # label(fact_x) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 177 (all V_real2_2 all V_real1_2 all V_f1_2 all T_a c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_real1_2),V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)) # label(fact_complex_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 178 (all V_real2_2 all V_real1_2 all V_f1_2 all T_a c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_real1_2),V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)) # label(fact_complex_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 179 (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_Complex_OIm,hAPP(v_s,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_th) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 180 (all V_b all V_x all V_a (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b) -> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) & (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_x),B_y)),B_d) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a,B_y) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,V_b)))))))) # label(fact_lemma__interval) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 181 (all V_K_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> ((all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(V_X_2,B_n)),V_K_2)) -> c_SEQ_OBseq(T_a,V_X_2)))) # label(fact_BseqI_H) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 182 (all V_d all V_b all V_c all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),V_d)))) # label(fact_Deriv_Oadd__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 183 (all V_xa_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_xa_2 <-> V_xa_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 184 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(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].
% 1.56/1.78 185 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) <-> V_b_2 = V_c_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 186 (all V_c_2 all V_a_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) <-> V_b_2 = V_c_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 187 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(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].
% 1.56/1.78 188 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(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].
% 1.56/1.78 189 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(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].
% 1.56/1.78 190 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_norm__one) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 191 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_y))))) # label(fact_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 192 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x),V_r) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_y),V_s) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s)))))) # label(fact_norm__add__less) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 193 (all V_x -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) # label(fact_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 194 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(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].
% 1.56/1.78 195 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(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].
% 1.56/1.78 196 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(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].
% 1.56/1.78 197 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(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].
% 1.56/1.78 198 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(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].
% 1.56/1.78 199 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 200 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 201 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 202 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 203 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 204 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(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].
% 1.56/1.78 205 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(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].
% 1.56/1.78 206 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 207 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 208 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 209 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 210 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 211 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(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].
% 1.56/1.78 212 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(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].
% 1.56/1.78 213 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 214 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a)) # label(fact_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 215 (all V_y all V_x (hAPP(c_Complex_ORe,V_x) = hAPP(c_Complex_ORe,V_y) -> (hAPP(c_Complex_OIm,V_x) = hAPP(c_Complex_OIm,V_y) -> V_x = V_y))) # label(fact_complex__equality) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 216 (all V_ya_2 all V_xa_2 (V_xa_2 = V_ya_2 <-> hAPP(c_Complex_ORe,V_xa_2) = hAPP(c_Complex_ORe,V_ya_2) & hAPP(c_Complex_OIm,V_xa_2) = hAPP(c_Complex_OIm,V_ya_2))) # label(fact_expand__complex__eq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 217 (all V_y all V_x hAPP(c_Complex_ORe,hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_x),V_y)) = V_x) # label(fact_Re) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 218 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y)))) # label(fact_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 219 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) # label(fact_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 220 (all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)))))) # label(fact_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 221 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_x)))) # label(fact_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 222 (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),hAPP(hAPP(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].
% 1.56/1.78 223 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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].
% 1.56/1.78 224 (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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 225 (all V_ya_2 all V_xa_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_xa_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_xa_2),V_ya_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 226 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 227 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 228 (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,hAPP(hAPP(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].
% 1.56/1.78 229 (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),hAPP(hAPP(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].
% 1.56/1.78 230 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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].
% 1.56/1.78 231 (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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 232 (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,hAPP(hAPP(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].
% 1.56/1.78 233 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.56/1.78 234 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 235 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_x))) # label(fact_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 236 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))) # label(fact_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 237 (all V_z hAPP(hAPP(c_Complex_Ocomplex_OComplex,hAPP(c_Complex_ORe,V_z)),hAPP(c_Complex_OIm,V_z)) = V_z) # label(fact_complex__surj) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 238 (all V_y all V_x hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))) # label(fact_Re_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 239 (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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 240 (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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 241 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 242 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 243 (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,hAPP(hAPP(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].
% 1.57/1.78 244 (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,hAPP(hAPP(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].
% 1.57/1.78 245 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_x))) # label(fact_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 246 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))) # label(fact_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 247 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)))))) # label(fact_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 248 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_b))))) # label(fact_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 249 (all V_y all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)))),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))))) # label(fact_metric__bound__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 250 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_b)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))) # label(fact_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 251 (exists B_f (c_SEQ_Osubseq(B_f) & c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,v_s),v_f____),B_f)))) # label(fact__096EX_Afa_O_Asubseq_Afa_A_G_Amonoseq_A_I_Fn_O_A_IIm_Ao_As_Ao_Af_J_A_Ifa_An_J_J_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 252 -(all B_g (c_SEQ_Osubseq(B_g) -> -c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))))) # label(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 253 (exists B_f (c_SEQ_Osubseq(B_f) & c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,v_s),B_f)))) # label(fact__096EX_Af_O_Asubseq_Af_A_G_Amonoseq_A_I_Fn_O_A_IRe_Ao_As_J_A_If_An_J_J_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 254 (all V_ra_2 all V_a_2 all V_xa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_xa_2),V_a_2)),V_ra_2) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_ra_2),V_xa_2) & c_Orderings_Oord__class_Oless(T_a,V_xa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))))) # label(fact_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 255 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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].
% 1.57/1.78 256 (all V_l_2 all V_fa_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_fa_2,V_l_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_fa_2),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_l_2),c_Limits_Osequentially))) # label(fact_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 257 (all V_c_2 all T_a (class_RealVector_Ometric__space(T_a) -> c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2)))) # label(fact_convergent__const) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 258 (all V_l_2 all V_k_2 all T_a (class_RealVector_Ometric__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBK(T_a,tc_Nat_Onat,V_k_2),V_l_2,c_Limits_Osequentially) <-> V_k_2 = V_l_2))) # label(fact_LIMSEQ__const__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 259 (all V_k_2 all T_a (class_RealVector_Otopological__space(T_a) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBK(T_a,tc_Nat_Onat,V_k_2),V_k_2,c_Limits_Osequentially))) # label(fact_LIMSEQ__const) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 260 (all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(T_a,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(T_a),V_X_2),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a_2),c_Limits_Osequentially)))) # label(fact_LIMSEQ__norm) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 261 (all V_k_2 all V_a_2 all V_fa_2 all T_a (class_RealVector_Otopological__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_fa_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_fa_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)),V_a_2,c_Limits_Osequentially)))) # label(fact_LIMSEQ__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 262 (all V_b_2 all V_a_2 all V_fa_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_fa_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_fa_2),V_b_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2),c_Limits_Osequentially)))) # label(fact_LIMSEQ__add__const) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 263 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_Y_2,V_b_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2),c_Limits_Osequentially))))) # label(fact_LIMSEQ__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 264 (all V_a_2 all V_k_2 all V_fa_2 all T_a (class_RealVector_Otopological__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_fa_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)),V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,V_fa_2,V_a_2,c_Limits_Osequentially)))) # label(fact_LIMSEQ__offset) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 265 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_Y_2,V_b_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(T_a),V_X_2),V_Y_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2),c_Limits_Osequentially))))) # label(fact_LIMSEQ__diff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 266 (all V_b_2 all V_a_2 all V_fa_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_fa_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(T_a),V_fa_2),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2),c_Limits_Osequentially)))) # label(fact_LIMSEQ__diff__const) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 267 (all V_n_2 all V_L_2 all V_X_2 (c_SEQ_Odecseq(tc_RealDef_Oreal,V_X_2) -> (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_X_2,V_L_2,c_Limits_Osequentially) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_L_2,hAPP(V_X_2,V_n_2))))) # label(fact_decseq__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 268 (all V_n_2 all V_L_2 all V_X_2 (c_SEQ_Oincseq(tc_RealDef_Oreal,V_X_2) -> (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_X_2,V_L_2,c_Limits_Osequentially) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,V_n_2),V_L_2)))) # label(fact_incseq__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 269 (all V_b_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Ometric__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_b_2,c_Limits_Osequentially) -> V_a_2 = V_b_2)))) # label(fact_LIMSEQ__unique) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 270 (all V_L_2 all V_X_2 all T_a (class_RealVector_Ometric__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_L_2,c_Limits_Osequentially) -> c_SEQ_Oconvergent(T_a,V_X_2)))) # label(fact_convergentI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 271 (all V_X_2 all T_a (class_RealVector_Ometric__space(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) <-> (exists B_L c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,B_L,c_Limits_Osequentially))))) # label(fact_convergent__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 272 (all V_a_2 all V_xa_2 all V_X_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_X_2,V_xa_2,c_Limits_Osequentially) -> ((exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a_2,hAPP(V_X_2,B_n)))) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a_2,V_xa_2)))) # label(fact_LIMSEQ__le__const) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 273 (all V_a_2 all V_xa_2 all V_X_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_X_2,V_xa_2,c_Limits_Osequentially) -> ((exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_n),V_a_2))) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_a_2)))) # label(fact_LIMSEQ__le__const2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 274 (all V_ya_2 all V_Y_2 all V_xa_2 all V_X_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_X_2,V_xa_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_Y_2,V_ya_2,c_Limits_Osequentially) -> ((exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_n),hAPP(V_Y_2,B_n)))) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2))))) # label(fact_LIMSEQ__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 275 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(T_a,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(T_a),V_X_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) <-> c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,c_Groups_Ozero__class_Ozero(T_a),c_Limits_Osequentially)))) # label(fact_LIMSEQ__norm__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 276 (all V_fa_2 all V_L_2 all V_gb_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_gb_2,V_L_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(T_a),V_fa_2),V_gb_2),c_Groups_Ozero__class_Ozero(T_a),c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,V_fa_2,V_L_2,c_Limits_Osequentially))))) # label(fact_LIMSEQ__diff__approach__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 277 (all V_gb_2 all V_L_2 all V_fa_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_fa_2,V_L_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(T_a),V_fa_2),V_gb_2),c_Groups_Ozero__class_Ozero(T_a),c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,V_gb_2,V_L_2,c_Limits_Osequentially))))) # label(fact_LIMSEQ__diff__approach__zero2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 278 (all V_fa_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_fa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) <-> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_fa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially))) # label(fact_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 279 (all V_n all V_m (hAPP(hAPP(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].
% 1.57/1.78 280 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 281 (all V_m hAPP(hAPP(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].
% 1.57/1.78 282 (all V_n hAPP(hAPP(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].
% 1.57/1.78 283 (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,hAPP(hAPP(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].
% 1.57/1.78 284 (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,hAPP(hAPP(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].
% 1.57/1.78 285 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(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].
% 1.57/1.78 286 (all V_n all V_m all V_l all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(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].
% 1.57/1.78 287 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 288 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 289 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 290 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 291 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 292 (all V_i all V_j -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(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].
% 1.57/1.78 293 (all V_j all V_i -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(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].
% 1.57/1.78 294 (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,hAPP(hAPP(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].
% 1.57/1.78 295 (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,hAPP(hAPP(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].
% 1.57/1.78 296 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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].
% 1.57/1.78 297 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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].
% 1.57/1.78 298 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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].
% 1.57/1.78 299 (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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.78 300 (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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 301 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 302 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 303 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 304 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 305 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 306 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 307 (all V_n all V_k all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 308 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 309 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) # label(fact_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 310 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m) # label(fact_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 311 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m) # label(fact_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 312 (all V_fa_2 all V_L_2 all V_X_2 all T_a (class_RealVector_Otopological__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_L_2,c_Limits_Osequentially) -> (c_SEQ_Osubseq(V_fa_2) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,V_fa_2),V_L_2,c_Limits_Osequentially))))) # label(fact_LIMSEQ__subseq__LIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 313 (all V_xa_2 all V_a_2 (c_SEQ_Omonoseq(tc_RealDef_Oreal,V_a_2) -> (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_a_2,V_xa_2,c_Limits_Osequentially) -> (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_a_2,B_n),V_xa_2)) & (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_a_2,B_m),hAPP(V_a_2,B_n)))) | (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,hAPP(V_a_2,B_n))) & (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_a_2,B_n),hAPP(V_a_2,B_m))))))) # label(fact_monoseq__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 314 (all V_X_2 (c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2) -> (c_SEQ_Omonoseq(tc_RealDef_Oreal,V_X_2) -> c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)))) # label(fact_Bseq__monoseq__convergent) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 315 (all V_Y_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) -> (c_SEQ_Oconvergent(T_a,V_Y_2) -> c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2)))))) # label(fact_convergent__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 316 (all V_k_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) -> c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))))) # label(fact_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 317 (all V_k_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) -> c_SEQ_OBseq(T_a,V_X_2)))) # label(fact_Bseq__offset) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 318 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 319 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 320 (all V_n all V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 321 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2))) # label(fact_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 322 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))) # label(fact_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 323 (all V_i_2 all V_k_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2),V_i_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)))) # label(fact_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 324 (all V_m all V_n all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k)))) # label(fact_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 325 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 326 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))) # label(fact_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 327 (all V_i_2 all V_j_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2)))) # label(fact_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 328 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m)) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 329 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 <-> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)))) # label(fact_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 330 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 331 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k))) # label(fact_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 332 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 333 (all V_y all V_x hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))) # label(fact_Re_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 334 (all V_y all V_x hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) # label(fact_Im_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 335 (all V_d all V_c all V_b all V_a hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a),V_b)),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_c),V_d)) = hAPP(hAPP(c_Complex_Ocomplex_OComplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d))) # label(fact_complex__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 336 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (all B_d (V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) -> hBOOL(hAPP(V_P_2,B_d)))))) # label(fact_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 337 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) <-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) & -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_d (V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) & -hBOOL(hAPP(V_P_2,B_d))))))) # label(fact_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 338 (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].
% 1.57/1.79 339 (all V_z all V_w c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_z)))) # label(fact_complex__mod__triangle__sub) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 340 (all V_a all V_b c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a))),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_b)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_a))) # label(fact_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 341 (all V_b_2 all V_a_2 (hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a_2),V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) <-> V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_Complex__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 342 (all V_fa_2 all V_X_2 all T_a (class_SEQ_Ocomplete__space(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) -> (c_SEQ_Osubseq(V_fa_2) -> c_SEQ_Oconvergent(T_a,c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,V_fa_2)))))) # label(fact_convergent__subseq__convergent) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 343 (all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = hAPP(hAPP(c_Complex_Ocomplex_OComplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))) # label(fact_complex__add__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 344 (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].
% 1.57/1.79 345 (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].
% 1.57/1.79 346 (all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(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].
% 1.57/1.79 347 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 348 (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].
% 1.57/1.79 349 (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].
% 1.57/1.79 350 (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].
% 1.57/1.79 351 (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].
% 1.57/1.79 352 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(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].
% 1.57/1.79 353 (exists B_L c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))),B_L,c_Limits_Osequentially)) # label(fact__096EX_AL_O_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_N_N_N_N_062_AL_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 354 -(all B_y -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))),B_y,c_Limits_Osequentially)) # label(fact__096_B_Bthesis_O_A_I_B_By_O_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_N_N_N_N_062_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 355 -(all B_x -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____)),B_x,c_Limits_Osequentially)) # label(fact__096_B_Bthesis_O_A_I_B_Bx_O_A_I_Fn_O_ARe_A_Is_A_If_An_J_J_J_A_N_N_N_N_062_Ax_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 356 (exists B_L c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____)),B_L,c_Limits_Osequentially)) # label(fact__096EX_AL_O_A_I_Fn_O_ARe_A_Is_A_If_An_J_J_J_A_N_N_N_N_062_AL_096) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 357 (all V_net_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Limits_Otendsto(T_a,tc_RealDef_Oreal,c_COMBB(T_b,tc_RealDef_Oreal,T_a,c_RealVector_Onorm__class_Onorm(T_b),V_fa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_net_2) -> c_Limits_Otendsto(T_a,T_b,V_fa_2,c_Groups_Ozero__class_Ozero(T_b),V_net_2)))) # label(fact_tendsto__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 358 (all V_net_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,c_Groups_Ozero__class_Ozero(T_b),V_net_2) -> c_Limits_Otendsto(T_a,tc_RealDef_Oreal,c_COMBB(T_b,tc_RealDef_Oreal,T_a,c_RealVector_Onorm__class_Onorm(T_b),V_fa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_net_2)))) # label(fact_tendsto__norm__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 359 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 360 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 361 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 362 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 363 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 364 (all V_net_2 all V_a_2 all V_gb_2 all T_a (c_Limits_Otendsto(T_a,tc_Complex_Ocomplex,V_gb_2,V_a_2,V_net_2) -> c_Limits_Otendsto(T_a,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,T_a,c_Complex_ORe,V_gb_2),hAPP(c_Complex_ORe,V_a_2),V_net_2))) # label(fact_Re_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 365 (all V_net_2 all V_a_2 all V_gb_2 all T_a (c_Limits_Otendsto(T_a,tc_Complex_Ocomplex,V_gb_2,V_a_2,V_net_2) -> c_Limits_Otendsto(T_a,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,T_a,c_Complex_OIm,V_gb_2),hAPP(c_Complex_OIm,V_a_2),V_net_2))) # label(fact_Im_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 366 (all V_b_2 all V_gb_2 all V_net_2 all V_a_2 all V_fa_2 all T_a (c_Limits_Otendsto(T_a,tc_RealDef_Oreal,V_fa_2,V_a_2,V_net_2) -> (c_Limits_Otendsto(T_a,tc_RealDef_Oreal,V_gb_2,V_b_2,V_net_2) -> c_Limits_Otendsto(T_a,tc_Complex_Ocomplex,c_COMBS(T_a,tc_RealDef_Oreal,tc_Complex_Ocomplex,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_Complex_Ocomplex),T_a,c_Complex_Ocomplex_OComplex,V_fa_2),V_gb_2),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a_2),V_b_2),V_net_2)))) # label(fact_tendsto__Complex) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 367 (all V_X_2 (c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2) -> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2)))) # label(fact_Re_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 368 (all V_X_2 (c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2) -> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2)))) # label(fact_Im_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 369 (all V_l_2 all V_fa_2 all V_net_H_2 all V_net_2 all T_a all T_b (class_RealVector_Otopological__space(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Limits_Onet(T_a),V_net_2,V_net_H_2) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_l_2,V_net_H_2) -> c_Limits_Otendsto(T_a,T_b,V_fa_2,V_l_2,V_net_2))))) # label(fact_tendsto__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 370 (all V_a_2 all V_X_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2),hAPP(c_Complex_ORe,V_a_2),c_Limits_Osequentially))) # label(fact_Re_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 371 (all V_a_2 all V_X_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2),hAPP(c_Complex_OIm,V_a_2),c_Limits_Osequentially))) # label(fact_Im_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 372 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_X_2,V_a_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,V_Y_2,V_b_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_Complex_Ocomplex,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_Complex_Ocomplex),tc_Nat_Onat,c_Complex_Ocomplex_OComplex,V_X_2),V_Y_2),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a_2),V_b_2),c_Limits_Osequentially)))) # label(fact_LIMSEQ__Complex) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 373 (all V_net_2 all V_k_2 all T_a all T_b (class_RealVector_Otopological__space(T_b) -> c_Limits_Otendsto(T_a,T_b,c_COMBK(T_b,T_a,V_k_2),V_k_2,V_net_2))) # label(fact_tendsto__const) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 374 (all V_b_2 all V_gb_2 all V_net_2 all V_a_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_a_2,V_net_2) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_b_2,V_net_2) -> c_Limits_Otendsto(T_a,T_b,c_COMBS(T_a,T_b,T_b,c_COMBB(T_b,tc_fun(T_b,T_b),T_a,c_Groups_Oplus__class_Oplus(T_b),V_fa_2),V_gb_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2),V_net_2))))) # label(fact_tendsto__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 375 (all V_b_2 all V_gb_2 all V_net_2 all V_a_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_a_2,V_net_2) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_b_2,V_net_2) -> c_Limits_Otendsto(T_a,T_b,c_COMBS(T_a,T_b,T_b,c_COMBB(T_b,tc_fun(T_b,T_b),T_a,c_Groups_Ominus__class_Ominus(T_b),V_fa_2),V_gb_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2),V_net_2))))) # label(fact_tendsto__diff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 376 (all V_net_2 all V_a_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_a_2,V_net_2) -> c_Limits_Otendsto(T_a,tc_RealDef_Oreal,c_COMBB(T_b,tc_RealDef_Oreal,T_a,c_RealVector_Onorm__class_Onorm(T_b),V_fa_2),hAPP(c_RealVector_Onorm__class_Onorm(T_b),V_a_2),V_net_2)))) # label(fact_tendsto__norm) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 377 (all V_net_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Limits_Otendsto(T_a,tc_RealDef_Oreal,c_COMBB(T_b,tc_RealDef_Oreal,T_a,c_RealVector_Onorm__class_Onorm(T_b),V_fa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_net_2) <-> c_Limits_Otendsto(T_a,T_b,V_fa_2,c_Groups_Ozero__class_Ozero(T_b),V_net_2)))) # label(fact_tendsto__norm__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 378 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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].
% 1.57/1.79 379 (all V_z (hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),V_z),c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_unimodular__reduce__norm) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 380 (all V_L_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_L_2,c_Limits_Osequentially) <-> (all B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) -> (exists B_no all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_no,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_X_2,B_n)),V_L_2)),B_r)))))))) # label(fact_LIMSEQ__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 381 (all V_ra_2 all V_L_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_L_2,c_Limits_Osequentially) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ra_2) -> (exists B_no all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_no,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_X_2,B_n)),V_L_2)),V_ra_2))))))) # label(fact_LIMSEQ__D) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 382 (all V_X_2 all V_M_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) & class_Orderings_Oord(T_a) -> ((all B_n (c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_X_2,V_M_2)),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) -> (all B_n (c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_b),hAPP(V_X_2,B_n)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(T_b),hAPP(V_X_2,V_M_2))))))))) # label(fact_lemmaCauchy) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 383 (all V_net_H_2 all V_net_2 all T_a (c_Orderings_Oord__class_Oless(tc_Limits_Onet(T_a),V_net_2,V_net_H_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Limits_Onet(T_a),V_net_2,V_net_H_2) & -c_Orderings_Oord__class_Oless__eq(tc_Limits_Onet(T_a),V_net_H_2,V_net_2))) # label(fact_less__net__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 384 (all V_ya_2 all V_xa_2 (hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_xa_2),V_ya_2) = c_Complex_Oii <-> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_ya_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_Complex__eq__i) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 385 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hAPP(hAPP(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].
% 1.57/1.79 386 (all V_X_2 all T_a (class_RealVector_Ometric__space(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) <-> c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,c_SEQ_Olim(T_a,V_X_2),c_Limits_Osequentially)))) # label(fact_convergent__LIMSEQ__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 387 (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 = hAPP(hAPP(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].
% 1.57/1.79 388 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_natceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 389 (all V_c_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_c_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_c_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially))) # label(fact_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 390 (all V_c_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_c_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_c_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially))) # label(fact_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 391 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)),V_n)))) # label(fact_norm__power__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 392 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)),V_n))) # label(fact_norm__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 393 (all V_m_2 all V_a_2 all V_X_2 all T_a (class_Power_Opower(T_a) & class_RealVector_Oreal__normed__algebra(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a,c_COMBB(T_a,tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat,c_Power_Opower__class_Opower(T_a),V_X_2),V_m_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2),c_Limits_Osequentially)))) # label(fact_LIMSEQ__pow) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 394 (all V_x c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x))) # label(fact_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 395 (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_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)))) # label(fact_natceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 396 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_natceiling__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 397 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 398 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2))))) # label(fact_monoseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 399 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2))))) # label(fact_convergent__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 400 (all V_L_2 all V_X_2 all T_a (class_RealVector_Ometric__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_L_2,c_Limits_Osequentially) -> c_SEQ_Olim(T_a,V_X_2) = V_L_2))) # label(fact_limI) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 401 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2))))) # label(fact_Bseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 402 (all V_xa_2 all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Groups_Ozero__class_Ozero(T_a),c_Limits_Osequentially)))) # label(fact_LIMSEQ__power__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 403 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially)))) # label(fact_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 404 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))))) # label(fact_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 405 (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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_one__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 406 (all V_ya_2 all V_xa_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2,V_ya_2))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 407 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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].
% 1.57/1.79 408 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 409 (all V_n_2 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_xa_2)),V_n_2)) <-> V_xa_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 410 (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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(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].
% 1.57/1.79 411 (all V_n_2 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_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].
% 1.57/1.79 412 (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) -> hAPP(hAPP(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].
% 1.57/1.79 413 (all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 414 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) # label(fact_power__abs) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 415 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 416 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))) # label(fact_power__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 417 (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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_zero__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 418 (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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 419 (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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 420 (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) -> (hAPP(hAPP(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].
% 1.57/1.79 421 (all V_n_2 all V_m_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) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) <-> V_m_2 = V_n_2)))) # label(fact_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 422 (all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 423 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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].
% 1.57/1.79 424 (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) -> hAPP(hAPP(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) -> hAPP(hAPP(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].
% 1.57/1.79 425 (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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n)))) # label(fact_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 426 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))))) # label(fact_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 427 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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].
% 1.57/1.79 428 (all V_ya_2 all V_xa_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 429 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))))) # label(fact_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 430 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 431 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(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].
% 1.57/1.79 432 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 433 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_natfloor__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 434 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 435 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_RComplete_Onatceiling(V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_natceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 436 (all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 437 (all V_n all V_x c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) # label(fact_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 438 (all V_n all V_x (V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n))) # label(fact_natfloor__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 439 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)) # label(fact_real__of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 440 (all V_n all V_m hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))) # label(fact_power__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 441 (all V_z hAPP(hAPP(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].
% 1.57/1.79 442 (all V_z hAPP(hAPP(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].
% 1.57/1.79 443 (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_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x))) # label(fact_real__natfloor__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 444 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)))) # label(fact_le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 445 (all V_x hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x)) # label(fact_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 446 (all V_n c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n) # label(fact_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 447 (all V_m_2 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2) <-> V_n_2 = V_m_2)) # label(fact_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 448 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 449 (all V_w_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) & V_z_2 != V_w_2)) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 450 (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].
% 1.57/1.79 451 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 452 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 453 (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,hAPP(hAPP(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].
% 1.57/1.79 454 (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),hAPP(hAPP(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].
% 1.57/1.79 455 (all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 456 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 457 (all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)) <-> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 458 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) | V_w_2 = V_z_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 459 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 460 (all V_z_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 461 (all V_z_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 462 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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].
% 1.57/1.79 463 (all V_n c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n) # label(fact_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 464 (all V_a_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2)))) # label(fact_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 465 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 466 (all V_x all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a))) # label(fact_natfloor__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 467 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))) # label(fact_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 468 (all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 469 (all V_n -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 470 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 471 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 472 (all V_n 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(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n)))) # label(fact_less__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 473 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 474 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a))) # label(fact_natfloor__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 475 (all V_n all V_z (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 476 (all V_x all V_n (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_RComplete_Onatfloor(V_x) = V_n))) # label(fact_natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 477 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))) # label(fact_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 478 (all V_x c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))) # label(fact_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 479 (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_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)))) # label(fact_natfloor__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 480 (all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 481 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 482 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a))) # label(fact_natceiling__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 483 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(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].
% 1.57/1.79 484 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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].
% 1.57/1.79 485 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(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].
% 1.57/1.79 486 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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].
% 1.57/1.79 487 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(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].
% 1.57/1.79 488 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(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].
% 1.57/1.79 489 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_natfloor__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 490 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 491 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))) # label(fact_nat__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 492 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_nat__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 493 (all V_a_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2))))) # label(fact_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 494 (all V_x all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) -> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a))) # label(fact_natceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 495 (all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2))) # label(fact_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 496 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a))) # label(fact_natceiling__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 497 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 498 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 499 (all V_a_2 all V_b_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_b_2 = hAPP(hAPP(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].
% 1.57/1.79 500 (all V_n_2 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_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_xa_2))) # label(fact_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 501 (all V_r (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) -> (exists B_n (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)))))) # label(fact_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 502 (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),hAPP(hAPP(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].
% 1.57/1.79 503 (all V_a_2 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_a_2),hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially))) # label(fact_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 504 (all V_n all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 505 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 506 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 507 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 508 (all V_a all V_b all T_a (class_RealVector_Oreal__normed__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_b))))) # label(fact_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 509 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(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].
% 1.57/1.79 510 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)))) # label(fact_divide_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 511 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 512 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)))) # label(fact_divide_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 513 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))) # label(fact_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.79 514 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_RealVector_Oreal__normed__field(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_b)))) # label(fact_norm__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 515 (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].
% 1.57/1.80 516 (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].
% 1.57/1.80 517 (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].
% 1.57/1.80 518 (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].
% 1.57/1.80 519 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 520 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 521 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 522 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 523 (all V_ya_2 all V_net_2 all V_a_2 all V_gb_2 all T_a all T_b (class_RealVector_Oreal__normed__field(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_a_2,V_net_2) -> c_Limits_Otendsto(T_a,T_b,c_COMBC(T_a,T_b,T_b,c_COMBB(T_b,tc_fun(T_b,T_b),T_a,c_Rings_Oinverse__class_Odivide(T_b),V_gb_2),V_ya_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ya_2),V_net_2)))) # label(fact_divide_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 524 (all V_ya_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) -> c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_ya_2))))) # label(fact_divide_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 525 (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) -> (hAPP(hAPP(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].
% 1.57/1.80 526 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(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].
% 1.57/1.80 527 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (V_a = c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(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) -> hAPP(hAPP(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].
% 1.57/1.80 528 (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) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))) # label(fact_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 529 (all V_n all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(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].
% 1.57/1.80 530 (all V_ya_2 all V_xa_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_xa_2),V_ya_2)) <-> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_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_ya_2)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_ya_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 531 (all V_b_2 all V_gb_2 all V_net_2 all V_a_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__field(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_a_2,V_net_2) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_b_2,V_net_2) -> (V_b_2 != c_Groups_Ozero__class_Ozero(T_b) -> c_Limits_Otendsto(T_a,T_b,c_COMBS(T_a,T_b,T_b,c_COMBB(T_b,tc_fun(T_b,T_b),T_a,c_Rings_Oinverse__class_Odivide(T_b),V_fa_2),V_gb_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),V_net_2)))))) # label(fact_tendsto__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 532 (all V_ya_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_ya_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_ya_2),c_Limits_Osequentially)))) # label(fact_divide_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 533 (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(hAPP(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].
% 1.57/1.80 534 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_Y_2,V_b_2,c_Limits_Osequentially) -> (V_b_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_Y_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2),c_Limits_Osequentially)))))) # label(fact_LIMSEQ__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 535 (all V_m all V_n all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__diff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 536 (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) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))) # label(fact_abs__div__pos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 537 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(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].
% 1.57/1.80 538 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(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].
% 1.57/1.80 539 (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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))))) # label(fact_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 540 (all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) # label(fact_abs__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 541 (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),hAPP(hAPP(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].
% 1.57/1.80 542 (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,hAPP(hAPP(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].
% 1.57/1.80 543 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))))) # label(fact_divide__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 544 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)))))) # label(fact_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 545 (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),hAPP(hAPP(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].
% 1.57/1.80 546 (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,hAPP(hAPP(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].
% 1.57/1.80 547 (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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))))) # label(fact_divide__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 548 (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,hAPP(hAPP(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].
% 1.57/1.80 549 (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,hAPP(hAPP(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].
% 1.57/1.80 550 (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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))))) # label(fact_divide__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 551 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))))) # label(fact_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 552 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))))) # label(fact_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 553 (all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))) # label(fact_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 554 (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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))))) # label(fact_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 555 (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,hAPP(hAPP(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].
% 1.57/1.80 556 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))))))) # label(fact_frac__less2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 557 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))))))) # label(fact_frac__less) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 558 (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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))))))) # label(fact_frac__le) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 559 (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,hAPP(hAPP(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].
% 1.57/1.80 560 (all V_xa_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Series_Osums(T_a,hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),V_xa_2)))))) # label(fact_geometric__sums) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 561 (all V_x all V_y ((c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) -> c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)) & (-c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) -> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 562 (all V_y 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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y)))) # label(fact_natfloor__div__nat) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 563 (all V_ya_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Series_Osums(T_a,V_X_2,V_a_2) -> c_Series_Osums(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_ya_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_ya_2))))) # label(fact_divide_Osums) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 564 (all V_c_2 all V_a_2 all V_fa_2 all T_a (class_RealVector_Oreal__normed__field(T_a) -> (c_Series_Osums(T_a,V_fa_2,V_a_2) -> c_Series_Osums(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_fa_2),V_c_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_c_2))))) # label(fact_sums__divide) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 565 (all V_a_2 all V_X_2 (c_Series_Osums(tc_Complex_Ocomplex,V_X_2,V_a_2) -> c_Series_Osums(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2),hAPP(c_Complex_OIm,V_a_2)))) # label(fact_Im_Osums) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 566 (all V_a_2 all V_X_2 (c_Series_Osums(tc_Complex_Ocomplex,V_X_2,V_a_2) -> c_Series_Osums(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2),hAPP(c_Complex_ORe,V_a_2)))) # label(fact_Re_Osums) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 567 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Series_Osums(T_a,V_X_2,V_a_2) -> (c_Series_Osums(T_a,V_Y_2,V_b_2) -> c_Series_Osums(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(T_a),V_X_2),V_Y_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)))))) # label(fact_sums__diff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 568 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Series_Osums(T_a,V_X_2,V_a_2) -> (c_Series_Osums(T_a,V_Y_2,V_b_2) -> c_Series_Osums(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)))))) # label(fact_sums__add) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 569 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Series_Osums(T_a,c_COMBK(T_a,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sums__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 570 (all V_x all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)))) # label(fact_real__of__nat__div4) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 571 (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_Nat__Transfer_Otsub(V_x,V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 572 (all V_x all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x))),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))))) # label(fact_real__of__nat__div2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 573 (all V_x all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x))),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__of__nat__div3) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 574 (all V_x all V_y (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) -> c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y))) # label(fact_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 575 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m)))) # label(fact_div__less__dividend) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 576 (all V_k all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))))) # label(fact_div__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 577 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 578 (all V_b c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zdiv__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 579 (all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_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),V_b) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 580 (all V_a_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),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_a_2)))) # label(fact_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 581 (all V_a_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 582 (all V_a (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_zdiv__self) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 583 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 584 (all V_b all V_a_H all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))))) # label(fact_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 585 (all V_b all V_a_H all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))))) # label(fact_zdiv__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 586 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 587 (all V_b all V_b_H all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_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),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,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))))) # label(fact_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 588 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 589 (all V_a_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 590 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 591 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 592 (all V_b all V_b_H all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,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,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)))))) # label(fact_zdiv__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 593 (all V_b_2 all V_a_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_a_2) & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)))) # label(fact_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 594 (all V_i_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2)))) # label(fact_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 595 (all V_a_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)))) # label(fact_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 596 (all V_k_2 all V_i_2 (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> V_k_2 = 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_i_2) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2))) # label(fact_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 597 (all V_k all V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x)))) # label(fact_int__div__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 598 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 599 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 600 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 601 (all V_k all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)))) # label(fact_div__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 602 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_div__le__dividend) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 603 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_div__self) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 604 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_div__less) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 605 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 606 (all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2) -> c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially))) # label(fact_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 607 (all V_n 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(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)))) # label(fact_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 608 (all V_n_2 all V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_P_2,V_n_2)) -> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) & (all B_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) -> -hBOOL(hAPP(V_P_2,B_i)))) & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 609 (all V_c_2 all V_a_2 all V_fa_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Series_Osums(T_a,V_fa_2,V_a_2) -> c_Series_Osums(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_fa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2))))) # label(fact_sums__mult) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 610 (all V_c_2 all V_a_2 all V_fa_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Series_Osums(T_a,V_fa_2,V_a_2) -> c_Series_Osums(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_fa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))))) # label(fact_sums__mult2) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 611 (all V_xa_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Series_Osums(T_a,V_X_2,V_a_2) -> c_Series_Osums(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_X_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_a_2))))) # label(fact_mult__right_Osums) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 612 (all V_ya_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Series_Osums(T_a,V_X_2,V_a_2) -> c_Series_Osums(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ya_2))))) # label(fact_mult__left_Osums) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 613 (all V_x all V_r all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_x)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_r)))))) # label(fact_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.57/1.80 614 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))))) # label(fact_inverse__add) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 615 (all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(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].
% 1.59/1.80 616 (all V_xa_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_xa_2) = c_Groups_Oone__class_Oone(T_a) <-> V_xa_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 617 (all V_y all V_x hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),V_y) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_y))) # label(fact_divide__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 618 (all V_S all V_R hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_R),V_S) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_R),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_S))) # label(fact_real__divide__def) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 619 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_a))) # label(fact_inverse__divide) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 620 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))) # label(fact_field__divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 621 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 622 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(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].
% 1.59/1.80 623 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))) # label(fact_divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 624 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))) # label(fact_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 625 (all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)) = hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))) # label(fact_abs__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 626 (all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(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].
% 1.59/1.80 627 (all V_Y_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) -> (c_SEQ_Oconvergent(T_a,V_Y_2) -> c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2)))))) # label(fact_mult_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 628 (all V_ya_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) -> c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_ya_2))))) # label(fact_mult__left_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 629 (all V_xa_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_SEQ_Oconvergent(T_a,V_X_2) -> c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_X_2))))) # label(fact_mult__right_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 630 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(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].
% 1.59/1.80 631 (all V_n all V_b all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 632 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 633 (all V_n all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_n))) # label(fact_power__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 634 (all V_b_2 all V_a_2 all V_c_2 (V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 635 (all V_b_2 all V_a_2 all V_c_2 (V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2) <-> V_a_2 = V_b_2))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 636 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) # label(fact_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 637 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) # label(fact_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 638 (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) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 639 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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].
% 1.59/1.80 640 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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].
% 1.59/1.80 641 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(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].
% 1.59/1.80 642 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(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].
% 1.59/1.80 643 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(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].
% 1.59/1.80 644 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(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].
% 1.59/1.80 645 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(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].
% 1.59/1.80 646 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(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].
% 1.59/1.80 647 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(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].
% 1.59/1.80 648 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(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].
% 1.59/1.80 649 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(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].
% 1.59/1.80 650 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(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].
% 1.59/1.80 651 (all V_b_2 all V_a_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (hAPP(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].
% 1.59/1.80 652 (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(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].
% 1.59/1.80 653 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (hAPP(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].
% 1.59/1.80 654 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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].
% 1.59/1.80 655 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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].
% 1.59/1.80 656 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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].
% 1.59/1.80 657 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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].
% 1.59/1.80 658 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a) = hAPP(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].
% 1.59/1.80 659 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (hAPP(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].
% 1.59/1.80 660 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)) = V_a))) # label(fact_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 661 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(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].
% 1.59/1.80 662 (all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (hAPP(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].
% 1.59/1.80 663 (all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> hAPP(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].
% 1.59/1.80 664 (all V_a all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a))))) # label(fact_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 665 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x),V_r) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_y),V_s) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)))))) # label(fact_norm__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 666 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_y)))) # label(fact_norm__mult) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 667 (all V_a all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) & class_Rings_Odivision__ring__inverse__zero(T_a) -> hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_a)))) # label(fact_norm__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 668 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))) # label(fact_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 669 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 670 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(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].
% 1.59/1.80 671 (all V_b all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a) = hAPP(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].
% 1.59/1.80 672 (all V_b_2 all V_a_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a_2) = hAPP(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].
% 1.59/1.80 673 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)) = V_a)) # label(fact_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 674 (all V_xa_2 all V_net_2 all V_a_2 all V_gb_2 all T_a all T_b (class_RealVector_Oreal__normed__algebra(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_a_2,V_net_2) -> c_Limits_Otendsto(T_a,T_b,c_COMBB(T_b,T_b,T_a,hAPP(c_Groups_Otimes__class_Otimes(T_b),V_xa_2),V_gb_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_xa_2),V_a_2),V_net_2)))) # label(fact_mult__right_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 675 (all V_ya_2 all V_net_2 all V_a_2 all V_gb_2 all T_a all T_b (class_RealVector_Oreal__normed__algebra(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_a_2,V_net_2) -> c_Limits_Otendsto(T_a,T_b,c_COMBC(T_a,T_b,T_b,c_COMBB(T_b,tc_fun(T_b,T_b),T_a,c_Groups_Otimes__class_Otimes(T_b),V_gb_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ya_2),V_net_2)))) # label(fact_mult__left_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 676 (all V_b_2 all V_gb_2 all V_net_2 all V_a_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__algebra(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_a_2,V_net_2) -> (c_Limits_Otendsto(T_a,T_b,V_gb_2,V_b_2,V_net_2) -> c_Limits_Otendsto(T_a,T_b,c_COMBS(T_a,T_b,T_b,c_COMBB(T_b,tc_fun(T_b,T_b),T_a,c_Groups_Otimes__class_Otimes(T_b),V_fa_2),V_gb_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2),V_net_2))))) # label(fact_mult_Otendsto) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 677 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x)),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_y))))) # label(fact_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 678 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 679 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 680 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 681 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 682 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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].
% 1.59/1.80 683 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 684 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 685 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 686 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 687 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 688 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(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].
% 1.59/1.80 689 (all V_z hAPP(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].
% 1.59/1.80 690 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Oone__class_Oone(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a) = V_b))) # label(fact_inverse__unique) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.80 691 (all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(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].
% 1.59/1.80 692 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(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].
% 1.59/1.80 693 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(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].
% 1.59/1.80 694 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(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].
% 1.59/1.80 695 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(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].
% 1.59/1.80 696 (all V_x (V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(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].
% 1.59/1.80 697 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(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].
% 1.59/1.80 698 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(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].
% 1.59/1.80 699 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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].
% 1.59/1.80 700 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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].
% 1.59/1.80 701 (all V_z_2 all V_xa_2 all V_ya_2 all V_w_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2)) <-> V_w_2 = V_xa_2 | V_ya_2 = V_z_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 702 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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].
% 1.59/1.81 703 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(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].
% 1.59/1.81 704 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_a_2 != V_b_2 & V_c_2 != V_d_2 <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 705 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(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].
% 1.59/1.81 706 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))))) # label(fact_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 707 (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) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))))) # label(fact_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 708 (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),hAPP(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].
% 1.59/1.81 709 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(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].
% 1.59/1.81 710 (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),hAPP(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].
% 1.59/1.81 711 (all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(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].
% 1.59/1.81 712 (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),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))))) # label(fact_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 713 (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),hAPP(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].
% 1.59/1.81 714 (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,hAPP(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].
% 1.59/1.81 715 (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,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 716 (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,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 717 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(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].
% 1.59/1.81 718 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(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].
% 1.59/1.81 719 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(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].
% 1.59/1.81 720 (all V_n all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_n)))) # label(fact_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 721 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)) = hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))))) # label(fact_nonzero__abs__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 722 (all V_a all T_a (class_Fields_Ofield(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a) = hAPP(hAPP(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].
% 1.59/1.81 723 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a) = hAPP(hAPP(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].
% 1.59/1.81 724 (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(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].
% 1.59/1.81 725 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 726 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 727 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 728 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 729 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 730 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 731 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 732 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 733 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 734 (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(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].
% 1.59/1.81 735 (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(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].
% 1.59/1.81 736 (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(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].
% 1.59/1.81 737 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 738 (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(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].
% 1.59/1.81 739 (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(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].
% 1.59/1.81 740 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 741 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(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].
% 1.59/1.81 742 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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].
% 1.59/1.81 743 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(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].
% 1.59/1.81 744 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 745 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 746 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 747 (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(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].
% 1.59/1.81 748 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_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].
% 1.59/1.81 749 (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(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].
% 1.59/1.81 750 (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(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].
% 1.59/1.81 751 (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(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].
% 1.59/1.81 752 (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(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].
% 1.59/1.81 753 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 754 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_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].
% 1.59/1.81 755 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 756 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 757 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,hAPP(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].
% 1.59/1.81 758 (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 -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 759 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 760 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oring(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) <-> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 761 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oring(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 762 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 763 (all V_b all V_a all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))))) # label(fact_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 764 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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].
% 1.59/1.81 765 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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].
% 1.59/1.81 766 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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].
% 1.59/1.81 767 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b -> V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 768 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 769 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 <-> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 770 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2)))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 771 (all V_w_2 all V_xa_2 all V_z_2 all V_ya_2 all T_a (class_Fields_Ofield(T_a) -> (V_ya_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_z_2 != c_Groups_Ozero__class_Ozero(T_a) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_xa_2),V_ya_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 772 (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) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)))) # label(fact_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 773 (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) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)))) # label(fact_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 774 (all V_a_2 all V_c_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 <-> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 775 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) <-> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2) & (V_c_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].
% 1.59/1.81 776 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 777 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 778 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a))) # label(fact_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 779 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a))) # label(fact_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 780 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c = c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a)) & (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 781 (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,hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b),V_d) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)))))) # label(fact_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 782 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__add) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 783 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(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].
% 1.59/1.81 784 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(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].
% 1.59/1.81 785 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))))) # label(fact_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 786 (all V_ya_2 all V_xa_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 787 (all V_ya_2 all V_xa_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 788 (all V_net_2 all V_a_2 all V_fa_2 all T_a all T_b (class_RealVector_Oreal__normed__div__algebra(T_b) -> (c_Limits_Otendsto(T_a,T_b,V_fa_2,V_a_2,V_net_2) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> c_Limits_Otendsto(T_a,T_b,c_COMBB(T_b,T_b,T_a,c_Rings_Oinverse__class_Oinverse(T_b),V_fa_2),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),V_net_2))))) # label(fact_tendsto__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 789 (all V_b_2 all V_a_2 all V_fa_2 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(V_fa_2,V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(V_fa_2,V_b_2)),hAPP(V_fa_2,V_a_2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_b_2),V_a_2))),V_a_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(V_fa_2,V_b_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(V_fa_2,V_b_2)),hAPP(V_fa_2,V_a_2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),V_b_2),V_a_2))),V_b_2))) # label(fact_lemma__MVT) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 790 (all V_xa_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_X_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_a_2),c_Limits_Osequentially)))) # label(fact_mult__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 791 (all V_ya_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ya_2),c_Limits_Osequentially)))) # label(fact_mult__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 792 (all V_b_2 all V_Y_2 all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_Y_2,V_b_2,c_Limits_Osequentially) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Limits_Osequentially))))) # label(fact_LIMSEQ__mult) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 793 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(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].
% 1.59/1.81 794 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(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].
% 1.59/1.81 795 (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,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 796 (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,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 797 (all V_xa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_xa_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_xa_2)))) # label(fact_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 798 (all V_xa_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),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_xa_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2) & c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 799 (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),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_one__less__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 800 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a) = hAPP(hAPP(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].
% 1.59/1.81 801 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(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].
% 1.59/1.81 802 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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].
% 1.59/1.81 803 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(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].
% 1.59/1.81 804 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(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].
% 1.59/1.81 805 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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].
% 1.59/1.81 806 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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].
% 1.59/1.81 807 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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].
% 1.59/1.81 808 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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].
% 1.59/1.81 809 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 810 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 811 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 812 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 813 (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(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].
% 1.59/1.81 814 (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(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].
% 1.59/1.81 815 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 816 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2),V_d_2)))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 817 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 818 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_a_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2),V_d_2)))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 819 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 820 (all V_a_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))))) # label(fact_divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 821 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 822 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))))) # label(fact_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 823 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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].
% 1.59/1.81 824 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x) -> c_Orderings_Oord__class_Oless(T_a,V_z,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))))) # label(fact_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 825 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))))) # label(fact_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 826 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2),V_a_2) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 827 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))))))) # label(fact_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 828 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))))))) # label(fact_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 829 (all V_x all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))))) # label(fact_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 830 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_add__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 831 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(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].
% 1.59/1.81 832 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(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].
% 1.59/1.81 833 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(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].
% 1.59/1.81 834 (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) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(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].
% 1.59/1.81 835 (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))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))) # label(fact_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 836 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))))) # label(fact_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 837 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 838 (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 839 (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) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_diff__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 840 (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) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)))) # label(fact_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 841 (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) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)))) # label(fact_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 842 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))))) # label(fact_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 843 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))))) # label(fact_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 844 (all V_h all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__field(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))),V_h) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c)),V_h)),V_d)))) # label(fact_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 845 (all V_ya_2 all V_xa_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_ya_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 846 (all V_ya_2 all V_xa_2 all V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 847 (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,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),hAPP(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].
% 1.59/1.81 848 (all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(T_a),V_X_2),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a_2),c_Limits_Osequentially))))) # label(fact_LIMSEQ__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 849 (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),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))))) # label(fact_one__le__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 850 (all V_xa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_xa_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_xa_2)))) # label(fact_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 851 (all V_xa_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),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_xa_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 852 (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) -> (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(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].
% 1.59/1.81 853 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))))))) # label(fact_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.81 854 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))))))) # label(fact_divide__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.81 855 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2))))) # label(fact_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.81 856 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))))) # label(fact_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.81 857 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))))) # label(fact_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.81 858 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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].
% 1.60/1.81 859 (all V_a_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2),V_a_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)))))) # label(fact_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.81 860 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 861 (all V_a_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2),V_a_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)))))) # label(fact_divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 862 (all V_c_2 all V_b_2 all V_a_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 863 (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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 864 (all V_y all V_x all V_c all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),hAPP(c_RealVector_Onorm__class_Onorm(T_a),V_y))) -> V_x = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 865 (all V_a_2 all V_X_2 all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_a_2,c_Limits_Osequentially) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_SEQ_OBseq(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(T_a),V_X_2)))))) # label(fact_Bseq__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 866 (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) -> (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(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].
% 1.60/1.82 867 (all V_x all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))) # label(fact_realpow__minus__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 868 (all V_m all V_n all T_a (class_Power_Opower(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) # label(fact_realpow__num__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 869 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_x1))))))) # label(fact_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 870 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u)) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_x)),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),V_x1)),V_u)))))) # label(fact_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 871 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)) # label(fact_div__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 872 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))) # label(fact_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 873 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(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].
% 1.60/1.82 874 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n))) # label(fact_power__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 875 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_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].
% 1.60/1.82 876 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_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].
% 1.60/1.82 877 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 878 (all V_m hAPP(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].
% 1.60/1.82 879 (all V_n hAPP(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].
% 1.60/1.82 880 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 881 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 882 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 883 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 884 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 885 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 886 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 887 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 888 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 889 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 890 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 891 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 892 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 893 (all V_n hAPP(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].
% 1.60/1.82 894 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_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].
% 1.60/1.82 895 (all V_n hAPP(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].
% 1.60/1.82 896 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_m_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].
% 1.60/1.82 897 (all V_z hAPP(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].
% 1.60/1.82 898 (all V_z hAPP(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].
% 1.60/1.82 899 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 900 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(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_m_2,V_n_2))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 901 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(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_m_2,V_n_2))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 902 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 903 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 904 (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(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].
% 1.60/1.82 905 (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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 906 (all V_n all V_m (V_m = hAPP(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].
% 1.60/1.82 907 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 908 (all V_n all V_m (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) -> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 909 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))) # label(fact_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 910 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(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_m_2,V_n_2)))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 911 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(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_m_2,V_n_2)))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 912 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 913 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m)) # label(fact_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 914 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m)) # label(fact_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 915 (all V_b all V_a all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c))) # label(fact_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 916 (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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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].
% 1.60/1.82 917 (all V_r_H all V_q_H all V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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].
% 1.60/1.82 918 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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].
% 1.60/1.82 919 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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].
% 1.60/1.82 920 (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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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].
% 1.60/1.82 921 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(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].
% 1.60/1.82 922 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) -> (V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_P_2,B_i)))))))) # label(fact_split__div) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 923 (all V_d all V_c all V_b all V_a hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_a),V_b)),hAPP(hAPP(c_Complex_Ocomplex_OComplex,V_c),V_d)) = hAPP(hAPP(c_Complex_Ocomplex_OComplex,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c)))) # label(fact_complex__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 924 (all V_y all V_x hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))) # label(fact_complex__Im__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 925 (all V_y all V_x hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))) # label(fact_complex__Re__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 926 (all V_l_2 all V_xa_2 all V_X_2 all T_a (class_RealVector_Otopological__space(T_a) -> (c_Limits_Otendsto(tc_Nat_Onat,T_a,V_X_2,V_xa_2,c_Limits_Osequentially) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_l_2) -> c_Limits_Otendsto(tc_Nat_Onat,T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_l_2)),V_xa_2,c_Limits_Osequentially))))) # label(fact_LIMSEQ__linear) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 927 (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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(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].
% 1.60/1.82 928 (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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(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].
% 1.60/1.82 929 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_P_2,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_k_2) -> (all B_i ((exists B_j (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j))) -> hBOOL(hAPP(V_P_2,B_i))))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (all B_i ((exists B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j))) -> hBOOL(hAPP(V_P_2,B_i))))))) # label(fact_split__zdiv) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 930 (all V_r_1 all V_y all V_b_1 all V_a_1 (V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) -> ((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y)))) # label(fact_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 931 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))))) # label(fact_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 932 (all V_y all V_x hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = hAPP(hAPP(c_Complex_Ocomplex_OComplex,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))))) # label(fact_complex__mult__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 933 (all V_x all V_z all V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))))) # label(fact_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 934 (all V_z all V_x all V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z))) # label(fact_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 935 (all V_y all V_x hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),V_x),V_y) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),V_y))) # label(fact_complex__divide__def) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 936 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 937 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 938 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))) # label(fact_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 939 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 940 (all V_p all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) # label(fact_power__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 941 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))))) # label(fact_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 942 (all V_ya_2 all V_xa_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 943 (all V_ya_2 all V_xa_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)),c_Groups_Ozero__class_Ozero(T_a)) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 944 (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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 945 (all V_ya_2 all V_xa_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))) <-> V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) | V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 946 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(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].
% 1.60/1.82 947 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))))) # label(fact_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 948 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2),V_n_2)))) # label(fact_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 949 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(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_m_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 950 (all V_k all V_j all V_u all V_i hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(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].
% 1.60/1.82 951 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 952 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 953 (all V_n all V_m all V_k ((V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)))) # label(fact_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 954 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(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_m_2,V_n_2)))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 955 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) <-> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))) # label(fact_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 956 (all V_n all V_m all V_u all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)))) # label(fact_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 957 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))))) # label(fact_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 958 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2))) # label(fact_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 959 (all V_n all V_m all V_u all V_i all V_j (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n))) # label(fact_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 960 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2),V_n_2)))) # label(fact_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 961 (all V_n all V_m all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))) # label(fact_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 962 (all V_n all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (exists B_z c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_reduce__poly__simple) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 963 (all V_xa_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2)) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 964 (all V_a all V_r hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_a),V_r)) # label(fact_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 965 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oidom) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 966 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 967 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 968 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 969 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 970 (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].
% 1.60/1.82 971 (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].
% 1.60/1.82 972 (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].
% 1.60/1.82 973 (all T_1 class_Orderings_Opreorder(tc_Limits_Onet(T_1))) # label(arity_Limits__Onet__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 974 (all T_1 class_Orderings_Oorder(tc_Limits_Onet(T_1))) # label(arity_Limits__Onet__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 975 (all T_1 class_Orderings_Oord(tc_Limits_Onet(T_1))) # label(arity_Limits__Onet__Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 976 (all T_1 (class_Rings_Oidom(T_1) -> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 977 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 978 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 979 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 980 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 981 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 982 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 983 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 984 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 985 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 986 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 987 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 988 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 989 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 990 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 991 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 992 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 993 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 994 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 995 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 996 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 997 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 998 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 999 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1000 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1001 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__ring__abs) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1002 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1003 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1004 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1005 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1006 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1007 (all T_1 (class_Fields_Ofield(T_1) -> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1008 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1009 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__group__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1010 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1011 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1012 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1013 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1014 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.82 1015 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1016 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1017 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1018 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Omult__zero) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1019 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1020 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1021 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1022 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1023 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Power_Opower(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Power_Opower) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1024 (all T_1 (class_Groups_Ozero(T_1) -> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1025 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Oring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1026 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Oone(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oone) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1027 (all V_Q all V_P all T_b all T_a hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1028 (all V_R_2 all V_Q_2 all V_P_2 all T_c all T_a all T_b hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1029 (all V_R_2 all V_Q_2 all V_P_2 all T_a all T_c all T_b hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2)) # label(help_c__COMBC__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1030 (all V_R_2 all V_Q_2 all V_P_2 all T_a all T_c all T_b hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2))) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption].
% 1.60/1.83 1031 -(exists B_f (c_SEQ_Osubseq(B_f) & (exists B_z all B_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) -> (exists B_N all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(B_f,B_n))),B_z)),B_e))))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.60/1.83
% 1.60/1.83 ============================== end of process non-clausal formulas ===
% 1.60/1.83
% 1.60/1.83 ============================== PROCESS INITIAL CLAUSES ===============
% 1.60/1.83
% 1.60/1.83 ============================== PREDICATE ELIMINATION =================
% 1.60/1.83 1032 -c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)) # label(fact_seq__suble) # label(axiom). [clausify(10)].
% 1.60/1.83 1033 c_SEQ_Osubseq(v_ga____) # label(fact_g_I1_J) # label(axiom). [assumption].
% 1.60/1.85 1034 c_SEQ_Osubseq(v_f____) # label(fact_f_I1_J) # label(axiom). [assumption].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(v_ga____,A)). [resolve(1032,a,1033,a)].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(v_f____,A)). [resolve(1032,a,1034,a)].
% 1.60/1.85 1035 c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)) # label(fact_hs) # label(axiom). [assumption].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),A)). [resolve(1035,a,1032,a)].
% 1.60/1.85 1036 -c_SEQ_Osubseq(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)) # label(fact_subseq__def) # label(axiom). [clausify(14)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,A),hAPP(v_ga____,B)). [resolve(1036,a,1033,a)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A),hAPP(v_f____,B)). [resolve(1036,a,1034,a)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),A),hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),B)). [resolve(1036,a,1035,a)].
% 1.60/1.85 1037 c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(A),f3(A)) # label(fact_subseq__def) # label(axiom). [clausify(14)].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(A),f3(A)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1037,a,1032,a)].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(A),f3(A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). [resolve(1037,a,1036,a)].
% 1.60/1.85 1038 c_SEQ_Osubseq(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f2(A)),hAPP(A,f3(A))) # label(fact_subseq__def) # label(axiom). [clausify(14)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f2(A)),hAPP(A,f3(A))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(A,B)). [resolve(1038,a,1032,a)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f2(A)),hAPP(A,f3(A))) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). [resolve(1038,a,1036,a)].
% 1.60/1.85 1039 c_SEQ_Osubseq(c1) # label(fact__096EX_Afa_O_Asubseq_Afa_A_G_Amonoseq_A_I_Fn_O_A_IIm_Ao_As_Ao_Af_J_A_Ifa_An_J_J_096) # label(axiom). [clausify(251)].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(c1,A)). [resolve(1039,a,1032,a)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c1,A),hAPP(c1,B)). [resolve(1039,a,1036,a)].
% 1.60/1.85 1040 c_SEQ_Osubseq(c2) # label(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) # label(axiom). [clausify(252)].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(c2,A)). [resolve(1040,a,1032,a)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c2,A),hAPP(c2,B)). [resolve(1040,a,1036,a)].
% 1.60/1.85 1041 c_SEQ_Osubseq(c3) # label(fact__096EX_Af_O_Asubseq_Af_A_G_Amonoseq_A_I_Fn_O_A_IRe_Ao_As_J_A_If_An_J_J_096) # label(axiom). [clausify(253)].
% 1.60/1.85 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,hAPP(c3,A)). [resolve(1041,a,1032,a)].
% 1.60/1.85 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c3,A),hAPP(c3,B)). [resolve(1041,a,1036,a)].
% 1.60/1.85 1042 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_SEQ_Osubseq(D) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,D),C,c_Limits_Osequentially) # label(fact_LIMSEQ__subseq__LIMSEQ) # label(axiom). [clausify(312)].
% 1.60/1.85 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_ga____),C,c_Limits_Osequentially). [resolve(1042,c,1033,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_f____),C,c_Limits_Osequentially). [resolve(1042,c,1034,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),C,c_Limits_Osequentially). [resolve(1042,c,1035,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,D),C,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(D),f3(D)). [resolve(1042,c,1037,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,D),C,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(D,f2(D)),hAPP(D,f3(D))). [resolve(1042,c,1038,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c1),C,c_Limits_Osequentially). [resolve(1042,c,1039,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c2),C,c_Limits_Osequentially). [resolve(1042,c,1040,a)].
% 1.70/1.97 Derived: -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c3),C,c_Limits_Osequentially). [resolve(1042,c,1041,a)].
% 1.70/1.97 1043 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | -c_SEQ_Osubseq(C) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)) # label(fact_convergent__subseq__convergent) # label(axiom). [clausify(342)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_ga____)). [resolve(1043,c,1033,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_f____)). [resolve(1043,c,1034,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))). [resolve(1043,c,1035,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(C),f3(C)). [resolve(1043,c,1037,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,f2(C)),hAPP(C,f3(C))). [resolve(1043,c,1038,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c1)). [resolve(1043,c,1039,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c2)). [resolve(1043,c,1040,a)].
% 1.70/1.97 Derived: -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c3)). [resolve(1043,c,1041,a)].
% 1.70/1.97 1044 -c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(A,B)) # label(conj_0) # label(negated_conjecture). [clausify(1031)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(v_ga____,A)). [resolve(1044,a,1033,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(v_f____,A)). [resolve(1044,a,1034,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),A)). [resolve(1044,a,1035,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(A,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(A),f3(A)). [resolve(1044,a,1037,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f2(A)),hAPP(A,f3(A))). [resolve(1044,a,1038,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(c1,A)). [resolve(1044,a,1039,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(c2,A)). [resolve(1044,a,1040,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f45(c3,A)). [resolve(1044,a,1041,a)].
% 1.70/1.97 1045 -c_SEQ_Osubseq(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,f46(A,C,B)) # label(conj_0) # label(negated_conjecture). [clausify(1031)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(v_ga____,B,A)). [resolve(1045,a,1033,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(v_f____,B,A)). [resolve(1045,a,1034,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),B,A)). [resolve(1045,a,1035,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(B,C,A)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(B),f3(B)). [resolve(1045,a,1037,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(B,C,A)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(B,f2(B)),hAPP(B,f3(B))). [resolve(1045,a,1038,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(c1,B,A)). [resolve(1045,a,1039,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(c2,B,A)). [resolve(1045,a,1040,a)].
% 1.70/1.97 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f46(c3,B,A)). [resolve(1045,a,1041,a)].
% 1.70/1.97 1046 -c_SEQ_Osubseq(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(A,f46(A,B,C)))),B)),f45(A,B)) # label(conj_0) # label(negated_conjecture). [clausify(1031)].
% 1.70/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(v_ga____,f46(v_ga____,A,B)))),A)),f45(v_ga____,A)). [resolve(1046,a,1033,a)].
% 1.70/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(v_f____,f46(v_f____,A,B)))),A)),f45(v_f____,A)). [resolve(1046,a,1034,a)].
% 1.70/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),f46(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),A,B)))),A)),f45(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),A)). [resolve(1046,a,1035,a)].
% 1.70/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(A,f46(A,B,C)))),B)),f45(A,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(A),f3(A)). [resolve(1046,a,1037,a)].
% 1.70/1.97 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(A,f46(A,B,C)))),B)),f45(A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f2(A)),hAPP(A,f3(A))). [resolve(1046,a,1038,a)].
% 1.87/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c1,f46(c1,A,B)))),A)),f45(c1,A)). [resolve(1046,a,1039,a)].
% 1.87/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c2,f46(c2,A,B)))),A)),f45(c2,A)). [resolve(1046,a,1040,a)].
% 1.87/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c3,f46(c3,A,B)))),A)),f45(c3,A)). [resolve(1046,a,1041,a)].
% 1.87/2.09 1047 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.87/2.09 1048 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__norm__iff) # label(axiom). [clausify(2)].
% 1.87/2.09 1049 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__norm__iff) # label(axiom). [clausify(2)].
% 1.87/2.09 1050 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_norm__not__less__zero) # label(axiom). [clausify(3)].
% 1.87/2.09 1051 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_norm__zero) # label(axiom). [clausify(4)].
% 1.87/2.09 1052 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealVector_Onorm__class_Onorm(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_norm__eq__zero) # label(axiom). [clausify(5)].
% 1.87/2.09 1053 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_norm__eq__zero) # label(axiom). [clausify(5)].
% 1.87/2.09 1054 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)) = hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B)) # label(fact_norm__minus__commute) # label(axiom). [clausify(11)].
% 1.87/2.09 1055 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C)),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C))) # label(fact_norm__triangle__ineq2) # label(axiom). [clausify(15)].
% 1.87/2.09 1056 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)) # label(fact_norm__ge__zero) # label(axiom). [clausify(16)].
% 1.87/2.09 1057 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_norm__le__zero__iff) # label(axiom). [clausify(17)].
% 1.87/2.09 1058 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_norm__le__zero__iff) # label(axiom). [clausify(17)].
% 1.87/2.09 1059 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f7(B,A)) # label(fact_Bseq__def) # label(axiom). [clausify(87)].
% 1.87/2.09 1060 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(B,C)),f7(B,A)) # label(fact_Bseq__def) # label(axiom). [clausify(87)].
% 1.87/2.09 1061 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(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,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(B,f8(B,A,C))),C) # label(fact_Bseq__def) # label(axiom). [clausify(87)].
% 1.87/2.09 1062 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f16(B,A)) # label(fact_BseqD) # label(axiom). [clausify(146)].
% 1.87/2.09 1063 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(B,C)),f16(B,A)) # label(fact_BseqD) # label(axiom). [clausify(146)].
% 1.87/2.09 1064 -class_RealVector_Oreal__normed__vector(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,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(C,f17(C,B,A))),B) | c_SEQ_OBseq(A,C) # label(fact_BseqI) # label(axiom). [clausify(147)].
% 1.87/2.09 1065 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,f18(C,D,B,A)) | c_SEQ_OBseq(A,D) # label(fact_BseqI2_H) # label(axiom). [clausify(148)].
% 1.87/2.09 1066 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(B,f18(C,B,D,A))),C) | c_SEQ_OBseq(A,B) # label(fact_BseqI2_H) # label(axiom). [clausify(148)].
% 1.87/2.09 1067 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)) = hAPP(c_RealVector_Onorm__class_Onorm(A),B) # label(fact_abs__norm__cancel) # label(axiom). [clausify(161)].
% 1.87/2.09 1068 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C))),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C))) # label(fact_norm__triangle__ineq3) # label(axiom). [clausify(174)].
% 1.87/2.09 1069 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(B,f22(C,B,A))),C) | c_SEQ_OBseq(A,B) # label(fact_BseqI_H) # label(axiom). [clausify(181)].
% 1.87/2.09 1070 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C))) # label(fact_norm__triangle__ineq) # label(axiom). [clausify(191)].
% 1.87/2.09 1071 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),E)) # label(fact_norm__add__less) # label(axiom). [clausify(192)].
% 1.87/2.09 1072 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D))),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E)))) # label(fact_norm__diff__triangle__ineq) # label(axiom). [clausify(220)].
% 1.87/2.09 1073 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C))) # label(fact_norm__triangle__ineq4) # label(axiom). [clausify(248)].
% 1.87/2.09 1074 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C)),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_norm__diff__ineq) # label(axiom). [clausify(250)].
% 1.87/2.09 1075 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(A),B),hAPP(c_RealVector_Onorm__class_Onorm(A),C),c_Limits_Osequentially) # label(fact_LIMSEQ__norm) # label(axiom). [clausify(260)].
% 1.87/2.09 1076 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D),c_Limits_Osequentially) # label(fact_LIMSEQ__add__const) # label(axiom). [clausify(262)].
% 1.87/2.09 1077 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,D,E,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E),c_Limits_Osequentially) # label(fact_LIMSEQ__add) # label(axiom). [clausify(263)].
% 1.87/2.09 1078 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,D,E,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(A),B),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E),c_Limits_Osequentially) # label(fact_LIMSEQ__diff) # label(axiom). [clausify(265)].
% 1.87/2.09 1079 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(A),B),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D),c_Limits_Osequentially) # label(fact_LIMSEQ__diff__const) # label(axiom). [clausify(266)].
% 1.87/2.09 1080 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,B,c_Groups_Ozero__class_Ozero(A),c_Limits_Osequentially) # label(fact_LIMSEQ__norm__zero) # label(axiom). [clausify(275)].
% 1.87/2.09 1081 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,c_Groups_Ozero__class_Ozero(A),c_Limits_Osequentially) # label(fact_LIMSEQ__norm__zero) # label(axiom). [clausify(275)].
% 1.87/2.09 1082 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(A),D),B),c_Groups_Ozero__class_Ozero(A),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,D,C,c_Limits_Osequentially) # label(fact_LIMSEQ__diff__approach__zero) # label(axiom). [clausify(276)].
% 1.87/2.09 1083 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(A),B),D),c_Groups_Ozero__class_Ozero(A),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,D,C,c_Limits_Osequentially) # label(fact_LIMSEQ__diff__approach__zero2) # label(axiom). [clausify(277)].
% 1.87/2.09 1084 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_Oconvergent(A,B) | -c_SEQ_Oconvergent(A,C) | c_SEQ_Oconvergent(A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(A),B),C)) # label(fact_convergent__add) # label(axiom). [clausify(315)].
% 1.87/2.09 1085 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_SEQ_OBseq(A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C))) # label(fact_Bseq__ignore__initial__segment) # label(axiom). [clausify(316)].
% 1.87/2.09 1086 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C))) | c_SEQ_OBseq(A,B) # label(fact_Bseq__offset) # label(axiom). [clausify(317)].
% 1.87/2.09 1087 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(B,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A),C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | c_Limits_Otendsto(B,A,C,c_Groups_Ozero__class_Ozero(A),D) # label(fact_tendsto__norm__zero__cancel) # label(axiom). [clausify(357)].
% 1.87/2.09 1088 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(B,A,C,c_Groups_Ozero__class_Ozero(A),D) | c_Limits_Otendsto(B,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A),C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) # label(fact_tendsto__norm__zero) # label(axiom). [clausify(358)].
% 1.87/2.09 1089 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(B,A,C,D,E) | -c_Limits_Otendsto(B,A,F,V6,E) | c_Limits_Otendsto(B,A,c_COMBS(B,A,A,c_COMBB(A,tc_fun(A,A),B,c_Groups_Oplus__class_Oplus(A),C),F),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),V6),E) # label(fact_tendsto__add) # label(axiom). [clausify(374)].
% 1.87/2.09 1090 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(B,A,C,D,E) | -c_Limits_Otendsto(B,A,F,V6,E) | c_Limits_Otendsto(B,A,c_COMBS(B,A,A,c_COMBB(A,tc_fun(A,A),B,c_Groups_Ominus__class_Ominus(A),C),F),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),V6),E) # label(fact_tendsto__diff) # label(axiom). [clausify(375)].
% 1.87/2.09 1091 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(B,A,C,D,E) | c_Limits_Otendsto(B,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A),C),hAPP(c_RealVector_Onorm__class_Onorm(A),D),E) # label(fact_tendsto__norm) # label(axiom). [clausify(376)].
% 1.87/2.09 1092 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(B,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A),C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | c_Limits_Otendsto(B,A,C,c_Groups_Ozero__class_Ozero(A),D) # label(fact_tendsto__norm__zero__iff) # label(axiom). [clausify(377)].
% 1.87/2.09 1093 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(B,tc_RealDef_Oreal,c_COMBB(A,tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A),C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Limits_Otendsto(B,A,C,c_Groups_Ozero__class_Ozero(A),D) # label(fact_tendsto__norm__zero__iff) # label(axiom). [clausify(377)].
% 1.87/2.09 1094 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f30(C,B,A,D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(B,E)),C)),D) # label(fact_LIMSEQ__iff) # label(axiom). [clausify(380)].
% 1.87/2.09 1095 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f31(C,B,A)) # label(fact_LIMSEQ__iff) # label(axiom). [clausify(380)].
% 1.87/2.09 1096 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,D,f32(C,B,A,D)) # label(fact_LIMSEQ__iff) # label(axiom). [clausify(380)].
% 1.87/2.09 1097 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(B,f32(C,B,A,D))),C)),f31(C,B,A)) # label(fact_LIMSEQ__iff) # label(axiom). [clausify(380)].
% 1.87/2.09 1098 -class_RealVector_Oreal__normed__vector(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(D,C,B,A),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(B,E)),C)),D) # label(fact_LIMSEQ__D) # label(axiom). [clausify(381)].
% 1.87/2.09 1099 -class_RealVector_Oreal__normed__vector(A) | -class_Orderings_Oord(B) | c_Orderings_Oord__class_Oless__eq(B,C,f34(D,C,B,A)) | -c_Orderings_Oord__class_Oless__eq(B,C,E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(D,E)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(D,C)))) # label(fact_lemmaCauchy) # label(axiom). [clausify(382)].
% 1.87/2.09 1100 -class_RealVector_Oreal__normed__vector(A) | -class_Orderings_Oord(B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(C,D)),hAPP(C,f34(C,D,B,A)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(B,D,E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(C,E)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(C,D)))) # label(fact_lemmaCauchy) # label(axiom). [clausify(382)].
% 1.87/2.09 1101 -class_RealVector_Oreal__normed__vector(A) | -c_Series_Osums(A,B,C) | -c_Series_Osums(A,D,E) | c_Series_Osums(A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(A),B),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E)) # label(fact_sums__diff) # label(axiom). [clausify(567)].
% 1.87/2.09 1102 -class_RealVector_Oreal__normed__vector(A) | -c_Series_Osums(A,B,C) | -c_Series_Osums(A,D,E) | c_Series_Osums(A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_sums__add) # label(axiom). [clausify(568)].
% 1.87/2.09 1103 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(A,c_COMBK(A,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(A)) # label(fact_sums__zero) # label(axiom). [clausify(569)].
% 1.87/2.09 1104 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),hAPP(c_RealVector_Onorm__class_Onorm(A),D))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_norm__ratiotest__lemma) # label(axiom). [clausify(864)].
% 1.87/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1047,a,1048,a)].
% 1.87/2.09 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1047,a,1049,a)].
% 1.87/2.09 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1047,a,1050,a)].
% 1.87/2.09 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1047,a,1051,a)].
% 1.87/2.09 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1047,a,1052,a)].
% 1.87/2.09 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1047,a,1053,a)].
% 1.87/2.09 Derived: hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),A)). [resolve(1047,a,1054,a)].
% 1.87/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B))). [resolve(1047,a,1055,a)].
% 1.87/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)). [resolve(1047,a,1056,a)].
% 1.87/2.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1047,a,1057,a)].
% 1.87/2.09 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1047,a,1058,a)].
% 1.87/2.09 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f7(A,tc_RealDef_Oreal)). [resolve(1047,a,1059,a)].
% 1.87/2.09 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(A,B)),f7(A,tc_RealDef_Oreal)). [resolve(1047,a,1060,a)].
% 1.87/2.09 Derived: c_SEQ_OBseq(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,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(A,f8(A,tc_RealDef_Oreal,B))),B). [resolve(1047,a,1061,a)].
% 1.87/2.09 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f16(A,tc_RealDef_Oreal)). [resolve(1047,a,1062,a)].
% 1.87/2.09 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(A,B)),f16(A,tc_RealDef_Oreal)). [resolve(1047,a,1063,a)].
% 1.87/2.09 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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(B,f17(B,A,tc_RealDef_Oreal))),A) | c_SEQ_OBseq(tc_RealDef_Oreal,B). [resolve(1047,a,1064,a)].
% 1.87/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f18(B,C,A,tc_RealDef_Oreal)) | c_SEQ_OBseq(tc_RealDef_Oreal,C). [resolve(1047,a,1065,a)].
% 1.87/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(A,f18(B,A,C,tc_RealDef_Oreal))),B) | c_SEQ_OBseq(tc_RealDef_Oreal,A). [resolve(1047,a,1066,a)].
% 1.87/2.10 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A). [resolve(1047,a,1067,a)].
% 1.87/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B))),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B))). [resolve(1047,a,1068,a)].
% 1.87/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(A,f22(B,A,tc_RealDef_Oreal))),B) | c_SEQ_OBseq(tc_RealDef_Oreal,A). [resolve(1047,a,1069,a)].
% 1.87/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B))). [resolve(1047,a,1070,a)].
% 1.87/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1047,a,1071,a)].
% 1.87/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C))),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),D)))). [resolve(1047,a,1072,a)].
% 1.87/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B))). [resolve(1047,a,1073,a)].
% 1.87/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))). [resolve(1047,a,1074,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B),c_Limits_Osequentially). [resolve(1047,a,1075,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBC(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),c_Limits_Osequentially). [resolve(1047,a,1076,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,C,D,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D),c_Limits_Osequentially). [resolve(1047,a,1077,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,C,D,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),D),c_Limits_Osequentially). [resolve(1047,a,1078,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBC(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),C),c_Limits_Osequentially). [resolve(1047,a,1079,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially). [resolve(1047,a,1080,a)].
% 1.87/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially). [resolve(1047,a,1081,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,C,B,c_Limits_Osequentially). [resolve(1047,a,1082,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,C,B,c_Limits_Osequentially). [resolve(1047,a,1083,a)].
% 1.87/2.10 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | -c_SEQ_Oconvergent(tc_RealDef_Oreal,B) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)). [resolve(1047,a,1084,a)].
% 1.87/2.10 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))). [resolve(1047,a,1085,a)].
% 1.87/2.10 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))) | c_SEQ_OBseq(tc_RealDef_Oreal,A). [resolve(1047,a,1086,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Limits_Otendsto(A,tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1047,a,1087,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1047,a,1088,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | -c_Limits_Otendsto(A,tc_RealDef_Oreal,E,F,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBS(A,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),E),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),F),D). [resolve(1047,a,1089,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | -c_Limits_Otendsto(A,tc_RealDef_Oreal,E,F,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBS(A,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),A,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),F),D). [resolve(1047,a,1090,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),C),D). [resolve(1047,a,1091,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f30(B,A,tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(A,D)),B)),C). [resolve(1047,a,1094,a)].
% 1.87/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f31(B,A,tc_RealDef_Oreal)). [resolve(1047,a,1095,a)].
% 1.87/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,f32(B,A,tc_RealDef_Oreal,C)). [resolve(1047,a,1096,a)].
% 1.87/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(A,f32(B,A,tc_RealDef_Oreal,C))),B)),f31(B,A,tc_RealDef_Oreal)). [resolve(1047,a,1097,a)].
% 1.87/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(C,B,A,tc_RealDef_Oreal),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(A,D)),B)),C). [resolve(1047,a,1098,a)].
% 1.87/2.10 Derived: -class_Orderings_Oord(A) | c_Orderings_Oord__class_Oless__eq(A,B,f34(C,B,A,tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(C,D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(C,B)))). [resolve(1047,a,1099,a)].
% 1.87/2.10 Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(B,C)),hAPP(B,f34(B,C,A,tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(B,D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(B,C)))). [resolve(1047,a,1100,a)].
% 1.89/2.10 Derived: -c_Series_Osums(tc_RealDef_Oreal,A,B) | -c_Series_Osums(tc_RealDef_Oreal,C,D) | c_Series_Osums(tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),D)). [resolve(1047,a,1101,a)].
% 1.89/2.10 Derived: -c_Series_Osums(tc_RealDef_Oreal,A,B) | -c_Series_Osums(tc_RealDef_Oreal,C,D) | c_Series_Osums(tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1047,a,1102,a)].
% 1.89/2.10 Derived: c_Series_Osums(tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1047,a,1103,a)].
% 1.89/2.10 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,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),C))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1047,a,1104,a)].
% 1.89/2.10 1105 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.89/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1105,a,1048,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1105,a,1049,a)].
% 1.89/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1105,a,1050,a)].
% 1.89/2.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1105,a,1051,a)].
% 1.89/2.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1105,a,1052,a)].
% 1.89/2.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1105,a,1053,a)].
% 1.89/2.10 Derived: hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A)). [resolve(1105,a,1054,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B))). [resolve(1105,a,1055,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)). [resolve(1105,a,1056,a)].
% 1.89/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1105,a,1057,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1105,a,1058,a)].
% 1.89/2.10 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f7(A,tc_Complex_Ocomplex)). [resolve(1105,a,1059,a)].
% 1.89/2.10 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(A,B)),f7(A,tc_Complex_Ocomplex)). [resolve(1105,a,1060,a)].
% 1.89/2.10 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,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,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(A,f8(A,tc_Complex_Ocomplex,B))),B). [resolve(1105,a,1061,a)].
% 1.89/2.10 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f16(A,tc_Complex_Ocomplex)). [resolve(1105,a,1062,a)].
% 1.89/2.10 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(A,B)),f16(A,tc_Complex_Ocomplex)). [resolve(1105,a,1063,a)].
% 1.89/2.10 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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(B,f17(B,A,tc_Complex_Ocomplex))),A) | c_SEQ_OBseq(tc_Complex_Ocomplex,B). [resolve(1105,a,1064,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f18(B,C,A,tc_Complex_Ocomplex)) | c_SEQ_OBseq(tc_Complex_Ocomplex,C). [resolve(1105,a,1065,a)].
% 1.89/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(A,f18(B,A,C,tc_Complex_Ocomplex))),B) | c_SEQ_OBseq(tc_Complex_Ocomplex,A). [resolve(1105,a,1066,a)].
% 1.89/2.10 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A). [resolve(1105,a,1067,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B))),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B))). [resolve(1105,a,1068,a)].
% 1.89/2.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(A,f22(B,A,tc_Complex_Ocomplex))),B) | c_SEQ_OBseq(tc_Complex_Ocomplex,A). [resolve(1105,a,1069,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B))). [resolve(1105,a,1070,a)].
% 1.89/2.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1105,a,1071,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C))),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)))). [resolve(1105,a,1072,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B))). [resolve(1105,a,1073,a)].
% 1.89/2.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))). [resolve(1105,a,1074,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B),c_Limits_Osequentially). [resolve(1105,a,1075,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),c_Limits_Osequentially). [resolve(1105,a,1076,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,C,D,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D),c_Limits_Osequentially). [resolve(1105,a,1077,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,C,D,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D),c_Limits_Osequentially). [resolve(1105,a,1078,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C),c_Limits_Osequentially). [resolve(1105,a,1079,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Limits_Osequentially). [resolve(1105,a,1080,a)].
% 1.89/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Limits_Osequentially). [resolve(1105,a,1081,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),C),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,C,B,c_Limits_Osequentially). [resolve(1105,a,1082,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,C,B,c_Limits_Osequentially). [resolve(1105,a,1083,a)].
% 1.89/2.10 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | -c_SEQ_Oconvergent(tc_Complex_Ocomplex,B) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)). [resolve(1105,a,1084,a)].
% 1.89/2.10 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_SEQ_OBseq(tc_Complex_Ocomplex,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))). [resolve(1105,a,1085,a)].
% 1.89/2.10 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))) | c_SEQ_OBseq(tc_Complex_Ocomplex,A). [resolve(1105,a,1086,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),C). [resolve(1105,a,1087,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),C) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1105,a,1088,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | -c_Limits_Otendsto(A,tc_Complex_Ocomplex,E,F,D) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBS(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),E),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),F),D). [resolve(1105,a,1089,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | -c_Limits_Otendsto(A,tc_Complex_Ocomplex,E,F,D) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBS(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),C),F),D). [resolve(1105,a,1090,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,A,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),C),D). [resolve(1105,a,1091,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f30(B,A,tc_Complex_Ocomplex,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(A,D)),B)),C). [resolve(1105,a,1094,a)].
% 1.89/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f31(B,A,tc_Complex_Ocomplex)). [resolve(1105,a,1095,a)].
% 1.89/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,f32(B,A,tc_Complex_Ocomplex,C)). [resolve(1105,a,1096,a)].
% 1.89/2.10 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(A,f32(B,A,tc_Complex_Ocomplex,C))),B)),f31(B,A,tc_Complex_Ocomplex)). [resolve(1105,a,1097,a)].
% 1.89/2.10 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f33(C,B,A,tc_Complex_Ocomplex),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(A,D)),B)),C). [resolve(1105,a,1098,a)].
% 1.89/2.10 Derived: -class_Orderings_Oord(A) | c_Orderings_Oord__class_Oless__eq(A,B,f34(C,B,A,tc_Complex_Ocomplex)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(C,D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(C,B)))). [resolve(1105,a,1099,a)].
% 1.89/2.10 Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(B,C)),hAPP(B,f34(B,C,A,tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(B,D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(B,C)))). [resolve(1105,a,1100,a)].
% 1.89/2.10 Derived: -c_Series_Osums(tc_Complex_Ocomplex,A,B) | -c_Series_Osums(tc_Complex_Ocomplex,C,D) | c_Series_Osums(tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)). [resolve(1105,a,1101,a)].
% 1.89/2.10 Derived: -c_Series_Osums(tc_Complex_Ocomplex,A,B) | -c_Series_Osums(tc_Complex_Ocomplex,C,D) | c_Series_Osums(tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D)). [resolve(1105,a,1102,a)].
% 1.90/2.21 Derived: c_Series_Osums(tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1105,a,1103,a)].
% 1.90/2.21 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,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),C))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1105,a,1104,a)].
% 1.90/2.21 1106 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.90/2.21 1107 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(6)].
% 1.90/2.21 1108 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(6)].
% 1.90/2.21 1109 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(7)].
% 1.90/2.21 1110 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(7)].
% 1.90/2.21 1111 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(12)].
% 1.90/2.21 1112 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(12)].
% 1.90/2.21 1113 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(13)].
% 1.90/2.21 1114 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(13)].
% 1.90/2.21 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1106,a,1107,a)].
% 1.90/2.21 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1106,a,1108,a)].
% 1.90/2.21 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1106,a,1109,a)].
% 1.90/2.21 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1106,a,1110,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1106,a,1111,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1106,a,1112,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1106,a,1113,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1106,a,1114,a)].
% 1.90/2.22 1115 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.90/2.22 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1115,a,1107,a)].
% 1.90/2.22 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1115,a,1108,a)].
% 1.90/2.22 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1115,a,1109,a)].
% 1.90/2.22 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1115,a,1110,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1115,a,1111,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1115,a,1112,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1115,a,1113,a)].
% 1.90/2.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1115,a,1114,a)].
% 1.90/2.22 1116 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) # label(axiom). [clausify(993)].
% 1.90/2.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1116,b,1107,a)].
% 1.90/2.22 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1116,b,1108,a)].
% 2.10/2.31 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1116,b,1109,a)].
% 2.10/2.31 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1116,b,1110,a)].
% 2.10/2.31 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1116,b,1111,a)].
% 2.10/2.31 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1116,b,1112,a)].
% 2.10/2.31 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C). [resolve(1116,b,1113,a)].
% 2.10/2.31 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C). [resolve(1116,b,1114,a)].
% 2.10/2.31 1117 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.10/2.31 1118 -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(19)].
% 2.10/2.31 1119 -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(33)].
% 2.10/2.31 1120 -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(35)].
% 2.10/2.31 1121 -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(50)].
% 2.10/2.31 1122 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | B = C # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(51)].
% 2.10/2.31 1123 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) | B != C # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(51)].
% 2.10/2.31 1124 -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(52)].
% 2.10/2.31 1125 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | C = B # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(53)].
% 2.10/2.31 1126 -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(53)].
% 2.10/2.31 1127 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(53)].
% 2.10/2.32 1128 -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__neq__iff) # label(axiom). [clausify(54)].
% 2.10/2.32 1129 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(54)].
% 2.10/2.32 1130 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom). [clausify(54)].
% 2.10/2.32 1131 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,B,C) | C = B # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(64)].
% 2.10/2.32 1132 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(64)].
% 2.10/2.32 1133 -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(66)].
% 2.10/2.32 1134 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | C = B # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(69)].
% 2.10/2.32 1135 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,C) | C != B # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(69)].
% 2.10/2.32 1136 -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(70)].
% 2.10/2.32 1137 -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(71)].
% 2.10/2.32 1138 -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(75)].
% 2.10/2.32 1139 -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(76)].
% 2.10/2.32 1140 -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(76)].
% 2.10/2.32 1141 -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(77)].
% 2.10/2.32 1142 -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(77)].
% 2.10/2.32 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A). [resolve(1117,a,1118,a)].
% 2.10/2.32 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | B = A | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1117,a,1120,a)].
% 2.10/2.32 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | A != B. [resolve(1117,a,1123,a)].
% 2.10/2.32 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1117,a,1126,a)].
% 2.10/2.32 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | B != A. [resolve(1117,a,1127,a)].
% 2.10/2.32 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). [resolve(1117,a,1130,a)].
% 2.10/2.32 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | B = A. [resolve(1117,a,1131,a)].
% 2.10/2.32 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1117,a,1133,a)].
% 2.10/2.32 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | B != A. [resolve(1117,a,1135,a)].
% 2.10/2.32 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). [resolve(1117,a,1136,a)].
% 2.10/2.32 1143 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1143,a,1118,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B = A | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1143,a,1120,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A) | A != B. [resolve(1143,a,1123,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1143,a,1126,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B != A. [resolve(1143,a,1127,a)].
% 2.10/2.33 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(1143,a,1130,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B = A. [resolve(1143,a,1131,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1143,a,1133,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | B != A. [resolve(1143,a,1135,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1143,a,1136,a)].
% 2.10/2.33 1144 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A). [resolve(1144,a,1118,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | B = A | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1144,a,1120,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | A != B. [resolve(1144,a,1123,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1144,a,1126,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | B != A. [resolve(1144,a,1127,a)].
% 2.10/2.33 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). [resolve(1144,a,1130,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | B = A. [resolve(1144,a,1131,a)].
% 2.10/2.33 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1144,a,1133,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | B != A. [resolve(1144,a,1135,a)].
% 2.10/2.33 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A). [resolve(1144,a,1136,a)].
% 2.10/2.33 1145 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1013)].
% 2.10/2.33 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1145,b,1118,a)].
% 2.10/2.33 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C = B | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1145,b,1120,a)].
% 2.10/2.33 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B) | B != C. [resolve(1145,b,1123,a)].
% 2.10/2.33 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1145,b,1126,a)].
% 2.10/2.33 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C != B. [resolve(1145,b,1127,a)].
% 2.10/2.33 Derived: -class_Rings_Olinordered__idom(A) | B != C | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1145,b,1130,a)].
% 2.19/2.43 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C = B. [resolve(1145,b,1131,a)].
% 2.19/2.43 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1145,b,1133,a)].
% 2.19/2.43 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | C != B. [resolve(1145,b,1135,a)].
% 2.19/2.43 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1145,b,1136,a)].
% 2.19/2.43 1146 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 2.19/2.43 1147 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | B = C # label(fact_right__minus__eq) # label(axiom). [clausify(78)].
% 2.19/2.43 1148 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | B != C # label(fact_right__minus__eq) # label(axiom). [clausify(78)].
% 2.19/2.43 1149 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),B) # label(fact_diff__self) # label(axiom). [clausify(80)].
% 2.19/2.43 1150 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(81)].
% 2.19/2.43 1151 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(213)].
% 2.19/2.43 1152 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),C) = B # label(fact_add__diff__cancel) # label(axiom). [clausify(214)].
% 2.19/2.43 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) | A = B. [resolve(1146,a,1147,a)].
% 2.19/2.43 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) | A != B. [resolve(1146,a,1148,a)].
% 2.19/2.43 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),A). [resolve(1146,a,1149,a)].
% 2.19/2.43 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1146,a,1150,a)].
% 2.19/2.43 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A. [resolve(1146,a,1151,a)].
% 2.19/2.43 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),B) = A. [resolve(1146,a,1152,a)].
% 2.19/2.43 1153 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom). [assumption].
% 2.19/2.43 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | A = B. [resolve(1153,a,1147,a)].
% 2.19/2.43 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | A != B. [resolve(1153,a,1148,a)].
% 2.19/2.43 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),A). [resolve(1153,a,1149,a)].
% 2.19/2.43 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1153,a,1150,a)].
% 2.19/2.43 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),B) = A. [resolve(1153,a,1151,a)].
% 2.19/2.43 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),B) = A. [resolve(1153,a,1152,a)].
% 2.19/2.43 1154 class_Groups_Ogroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ogroup__add) # label(axiom). [assumption].
% 2.31/2.53 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) | A = B. [resolve(1154,a,1147,a)].
% 2.31/2.53 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) | A != B. [resolve(1154,a,1148,a)].
% 2.31/2.53 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A). [resolve(1154,a,1149,a)].
% 2.31/2.53 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1154,a,1150,a)].
% 2.31/2.53 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(1154,a,1151,a)].
% 2.31/2.53 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(1154,a,1152,a)].
% 2.31/2.53 1155 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom). [clausify(1017)].
% 2.31/2.53 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) | B = C. [resolve(1155,b,1147,a)].
% 2.31/2.53 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) | B != C. [resolve(1155,b,1148,a)].
% 2.31/2.53 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),B). [resolve(1155,b,1149,a)].
% 2.31/2.53 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1155,b,1150,a)].
% 2.31/2.53 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),C) = B. [resolve(1155,b,1151,a)].
% 2.31/2.53 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),C) = B. [resolve(1155,b,1152,a)].
% 2.31/2.53 1156 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.31/2.53 1157 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) = hAPP(c_Groups_Oabs__class_Oabs(A),B) # label(fact_abs__idempotent) # label(axiom). [clausify(152)].
% 2.31/2.53 1158 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Oabs__class_Oabs(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__eq__0) # label(axiom). [clausify(156)].
% 2.31/2.53 1159 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Oabs__class_Oabs(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__eq__0) # label(axiom). [clausify(156)].
% 2.31/2.53 1160 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Oabs__class_Oabs(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__zero) # label(axiom). [clausify(157)].
% 2.31/2.53 1161 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),B),C) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_abs__le__D1) # label(axiom). [clausify(158)].
% 2.31/2.53 1162 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(c_Groups_Oabs__class_Oabs(A),B)) # label(fact_abs__ge__self) # label(axiom). [clausify(159)].
% 2.31/2.53 1163 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B)) # label(fact_abs__minus__commute) # label(axiom). [clausify(160)].
% 2.31/2.53 1164 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | hAPP(c_Groups_Oabs__class_Oabs(A),B) = B # label(fact_abs__of__nonneg) # label(axiom). [clausify(163)].
% 2.31/2.53 1165 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__le__zero__iff) # label(axiom). [clausify(164)].
% 2.31/2.53 1166 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__le__zero__iff) # label(axiom). [clausify(164)].
% 2.31/2.53 1167 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) # label(fact_abs__ge__zero) # label(axiom). [clausify(165)].
% 2.31/2.53 1168 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | hAPP(c_Groups_Oabs__class_Oabs(A),B) = B # label(fact_abs__of__pos) # label(axiom). [clausify(166)].
% 2.31/2.53 1169 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(167)].
% 2.31/2.53 1170 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(167)].
% 2.31/2.53 1171 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Oabs__class_Oabs(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__not__less__zero) # label(axiom). [clausify(168)].
% 2.31/2.53 1172 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B))) # label(fact_abs__triangle__ineq2__sym) # label(axiom). [clausify(169)].
% 2.31/2.53 1173 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C))) # label(fact_abs__triangle__ineq2) # label(axiom). [clausify(170)].
% 2.31/2.53 1174 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C))) # label(fact_abs__triangle__ineq3) # label(axiom). [clausify(171)].
% 2.31/2.53 1175 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__add__abs) # label(axiom). [clausify(219)].
% 2.31/2.53 1176 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))) # label(fact_abs__triangle__ineq) # label(axiom). [clausify(236)].
% 2.31/2.53 1177 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))) # label(fact_abs__triangle__ineq4) # label(axiom). [clausify(246)].
% 2.31/2.53 1178 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D))),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E)))) # label(fact_abs__diff__triangle__ineq) # label(axiom). [clausify(247)].
% 2.31/2.53 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(1156,a,1157,a)].
% 2.31/2.53 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1156,a,1158,a)].
% 2.31/2.53 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1156,a,1159,a)].
% 2.31/2.53 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1156,a,1160,a)].
% 2.31/2.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B). [resolve(1156,a,1161,a)].
% 2.31/2.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)). [resolve(1156,a,1162,a)].
% 2.31/2.53 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A)). [resolve(1156,a,1163,a)].
% 2.31/2.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) = A. [resolve(1156,a,1164,a)].
% 2.31/2.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1156,a,1165,a)].
% 2.31/2.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1156,a,1166,a)].
% 2.31/2.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)). [resolve(1156,a,1167,a)].
% 2.31/2.53 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) = A. [resolve(1156,a,1168,a)].
% 2.31/2.53 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1156,a,1169,a)].
% 2.31/2.53 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1156,a,1170,a)].
% 2.31/2.53 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1156,a,1171,a)].
% 2.31/2.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A))). [resolve(1156,a,1172,a)].
% 2.31/2.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B))). [resolve(1156,a,1173,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B))). [resolve(1156,a,1174,a)].
% 2.31/2.54 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(1156,a,1175,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))). [resolve(1156,a,1176,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))). [resolve(1156,a,1177,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C))),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),D)))). [resolve(1156,a,1178,a)].
% 2.31/2.54 1179 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.31/2.54 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A). [resolve(1179,a,1157,a)].
% 2.31/2.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1179,a,1158,a)].
% 2.31/2.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1179,a,1159,a)].
% 2.31/2.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1179,a,1160,a)].
% 2.31/2.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B). [resolve(1179,a,1161,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)). [resolve(1179,a,1162,a)].
% 2.31/2.54 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)) = hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),A)). [resolve(1179,a,1163,a)].
% 2.31/2.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A) = A. [resolve(1179,a,1164,a)].
% 2.31/2.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1179,a,1165,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1179,a,1166,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)). [resolve(1179,a,1167,a)].
% 2.31/2.54 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A) = A. [resolve(1179,a,1168,a)].
% 2.31/2.54 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1179,a,1169,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1179,a,1170,a)].
% 2.31/2.54 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1179,a,1171,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),A))). [resolve(1179,a,1172,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B))). [resolve(1179,a,1173,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B))),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B))). [resolve(1179,a,1174,a)].
% 2.31/2.54 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(1179,a,1175,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B))). [resolve(1179,a,1176,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B))). [resolve(1179,a,1177,a)].
% 2.31/2.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C))),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),D)))). [resolve(1179,a,1178,a)].
% 2.31/2.54 1180 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) # label(axiom). [clausify(983)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B). [resolve(1180,b,1157,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1180,b,1158,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1180,b,1159,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1180,b,1160,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C). [resolve(1180,b,1161,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)). [resolve(1180,b,1162,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),B)). [resolve(1180,b,1163,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B) = B. [resolve(1180,b,1164,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1180,b,1165,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1180,b,1166,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)). [resolve(1180,b,1167,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B) = B. [resolve(1180,b,1168,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1180,b,1169,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1180,b,1170,a)].
% 2.31/2.54 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1180,b,1171,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),B))). [resolve(1180,b,1172,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C))). [resolve(1180,b,1173,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C))),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C))). [resolve(1180,b,1174,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)). [resolve(1180,b,1175,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C))). [resolve(1180,b,1176,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C))). [resolve(1180,b,1177,a)].
% 2.40/2.65 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),D))),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),E)))). [resolve(1180,b,1178,a)].
% 2.40/2.65 1181 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.40/2.65 1182 -class_Groups_Oab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(184)].
% 2.40/2.65 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(1181,a,1182,a)].
% 2.49/2.76 1183 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1183,a,1182,a)].
% 2.49/2.76 1184 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(1184,a,1182,a)].
% 2.49/2.76 1185 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(1185,a,1182,a)].
% 2.49/2.76 1186 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__add) # label(axiom). [clausify(999)].
% 2.49/2.76 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D)). [resolve(1186,b,1182,a)].
% 2.49/2.76 1187 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 1188 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(185)].
% 2.49/2.76 1189 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(185)].
% 2.49/2.76 1190 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__cancel) # label(axiom). [clausify(186)].
% 2.49/2.76 1191 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B != D # label(fact_add__right__cancel) # label(axiom). [clausify(186)].
% 2.49/2.76 1192 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__imp__eq) # label(axiom). [clausify(187)].
% 2.49/2.76 1193 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__imp__eq) # label(axiom). [clausify(189)].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(1187,a,1188,a)].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C) | B != C. [resolve(1187,a,1189,a)].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(1187,a,1190,a)].
% 2.49/2.76 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B) | A != C. [resolve(1187,a,1191,a)].
% 2.62/2.86 1194 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B = C. [resolve(1194,a,1188,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B != C. [resolve(1194,a,1189,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A = C. [resolve(1194,a,1190,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A != C. [resolve(1194,a,1191,a)].
% 2.62/2.86 1195 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(1195,a,1188,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B != C. [resolve(1195,a,1189,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A = C. [resolve(1195,a,1190,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A != C. [resolve(1195,a,1191,a)].
% 2.62/2.86 1196 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(1196,a,1188,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B != C. [resolve(1196,a,1189,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(1196,a,1190,a)].
% 2.62/2.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A != C. [resolve(1196,a,1191,a)].
% 2.62/2.86 1197 -class_Groups_Ocancel__comm__monoid__add(A) | class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) # label(axiom). [clausify(994)].
% 2.62/2.86 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D) | C = D. [resolve(1197,b,1188,a)].
% 2.62/2.86 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D) | C != D. [resolve(1197,b,1189,a)].
% 2.62/2.86 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C) | B = D. [resolve(1197,b,1190,a)].
% 2.62/2.86 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C) | B != D. [resolve(1197,b,1191,a)].
% 2.62/2.86 1198 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.62/2.86 1199 -class_Groups_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__imp__eq) # label(axiom). [clausify(188)].
% 2.62/2.86 1200 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.87/3.08 1201 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.87/3.08 1202 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.87/3.08 1203 -class_Groups_Ocancel__comm__monoid__add(A) | class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) # label(axiom). [clausify(986)].
% 2.87/3.08 1204 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 2.87/3.08 1205 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(A),c_Groups_Oone__class_Oone(A)) # label(fact_norm__one) # label(axiom). [clausify(190)].
% 2.87/3.08 1206 -class_RealVector_Oreal__normed__algebra__1(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),C)) # label(fact_norm__power__ineq) # label(axiom). [clausify(391)].
% 2.87/3.08 1207 -class_RealVector_Oreal__normed__algebra__1(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Limits_Otendsto(tc_Nat_Onat,A,hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(A),c_Limits_Osequentially) # label(fact_LIMSEQ__power__zero) # label(axiom). [clausify(402)].
% 2.87/3.08 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1204,a,1205,a)].
% 2.87/3.08 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),B)). [resolve(1204,a,1206,a)].
% 2.87/3.08 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Limits_Osequentially). [resolve(1204,a,1207,a)].
% 2.87/3.08 1208 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 2.87/3.08 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1208,a,1205,a)].
% 2.87/3.08 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),B)). [resolve(1208,a,1206,a)].
% 2.87/3.08 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Limits_Osequentially). [resolve(1208,a,1207,a)].
% 2.87/3.08 1209 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.87/3.08 1210 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_add__0__left) # label(axiom). [clausify(194)].
% 2.87/3.08 1211 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(197)].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(1209,a,1210,a)].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1209,a,1211,a)].
% 2.92/3.19 1212 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A. [resolve(1212,a,1210,a)].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1212,a,1211,a)].
% 2.92/3.19 1213 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A. [resolve(1213,a,1210,a)].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1213,a,1211,a)].
% 2.92/3.19 1214 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(1214,a,1210,a)].
% 2.92/3.19 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1214,a,1211,a)].
% 2.92/3.19 1215 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom). [clausify(1015)].
% 2.92/3.19 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = B. [resolve(1215,b,1210,a)].
% 2.92/3.19 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1215,b,1211,a)].
% 2.92/3.19 1216 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 2.92/3.19 1217 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom). [clausify(196)].
% 2.92/3.19 1218 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom). [clausify(196)].
% 2.92/3.19 1219 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(222)].
% 2.92/3.19 1220 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(222)].
% 2.92/3.19 1221 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(223)].
% 2.92/3.19 1222 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(223)].
% 2.92/3.19 1223 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(229)].
% 2.92/3.19 1224 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(229)].
% 2.92/3.19 1225 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(230)].
% 2.92/3.19 1226 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(230)].
% 2.92/3.19 1227 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom). [clausify(385)].
% 2.92/3.19 1228 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom). [clausify(385)].
% 2.92/3.19 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1216,a,1217,a)].
% 2.92/3.19 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1216,a,1218,a)].
% 2.92/3.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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(1216,a,1219,a)].
% 2.92/3.19 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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(1216,a,1220,a)].
% 2.92/3.19 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(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(1216,a,1221,a)].
% 2.92/3.19 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(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(1216,a,1222,a)].
% 2.92/3.19 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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(1216,a,1223,a)].
% 2.92/3.19 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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(1216,a,1224,a)].
% 2.92/3.19 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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(1216,a,1225,a)].
% 2.92/3.20 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(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(1216,a,1226,a)].
% 2.92/3.20 1229 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 2.92/3.20 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1229,a,1217,a)].
% 2.92/3.20 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1229,a,1218,a)].
% 2.92/3.20 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1229,a,1219,a)].
% 2.92/3.20 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1229,a,1220,a)].
% 2.92/3.20 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1229,a,1221,a)].
% 2.92/3.20 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1229,a,1222,a)].
% 2.92/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1229,a,1223,a)].
% 2.92/3.20 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1229,a,1224,a)].
% 2.92/3.20 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1229,a,1225,a)].
% 2.92/3.20 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1229,a,1226,a)].
% 2.92/3.20 1230 -class_Rings_Olinordered__idom(A) | class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) # label(axiom). [clausify(985)].
% 2.92/3.20 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1230,b,1217,a)].
% 2.92/3.20 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1230,b,1218,a)].
% 2.92/3.20 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1230,b,1219,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1230,b,1220,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1230,b,1221,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1230,b,1222,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1230,b,1223,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1230,b,1224,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1230,b,1225,a)].
% 3.09/3.30 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1230,b,1226,a)].
% 3.09/3.30 1231 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].
% 3.09/3.30 1232 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(199)].
% 3.09/3.30 1233 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(199)].
% 3.09/3.30 1234 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(200)].
% 3.09/3.30 1235 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(200)].
% 3.09/3.30 1236 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(204)].
% 3.09/3.30 1237 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(205)].
% 3.09/3.30 1238 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(206)].
% 3.09/3.30 1239 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(206)].
% 3.09/3.30 1240 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(207)].
% 3.09/3.30 1241 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(207)].
% 3.09/3.30 1242 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(211)].
% 3.09/3.30 1243 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),hAPP(hAPP(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(212)].
% 3.09/3.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1231,a,1232,a)].
% 3.09/3.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C). [resolve(1231,a,1233,a)].
% 3.09/3.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1231,a,1234,a)].
% 3.09/3.30 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1231,a,1235,a)].
% 3.09/3.30 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1231,a,1238,a)].
% 3.09/3.30 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C). [resolve(1231,a,1239,a)].
% 3.09/3.30 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1231,a,1240,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1231,a,1241,a)].
% 3.09/3.31 1244 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].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1244,a,1232,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1244,a,1233,a)].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1244,a,1234,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1244,a,1235,a)].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1244,a,1238,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1244,a,1239,a)].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1244,a,1240,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1244,a,1241,a)].
% 3.09/3.31 1245 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].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1245,a,1232,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C). [resolve(1245,a,1233,a)].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1245,a,1234,a)].
% 3.09/3.31 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1245,a,1235,a)].
% 3.09/3.31 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1245,a,1238,a)].
% 3.18/3.41 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C). [resolve(1245,a,1239,a)].
% 3.18/3.41 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1245,a,1240,a)].
% 3.18/3.41 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1245,a,1241,a)].
% 3.18/3.41 1246 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [clausify(978)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1246,b,1232,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1246,b,1233,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1246,b,1234,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1246,b,1235,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1246,b,1238,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1246,b,1239,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1246,b,1240,a)].
% 3.18/3.41 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1246,b,1241,a)].
% 3.18/3.41 1247 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.18/3.41 1248 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_add__right__mono) # label(axiom). [clausify(201)].
% 3.31/3.52 1249 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)) # label(fact_add__left__mono) # label(axiom). [clausify(202)].
% 3.31/3.52 1250 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_add__mono) # label(axiom). [clausify(203)].
% 3.31/3.52 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(1247,a,1250,a)].
% 3.31/3.52 1251 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). [resolve(1251,a,1250,a)].
% 3.31/3.53 1252 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1252,a,1250,a)].
% 3.31/3.53 1253 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) # label(axiom). [clausify(982)].
% 3.31/3.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E)). [resolve(1253,b,1250,a)].
% 3.31/3.53 1254 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.53 1255 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_add__strict__right__mono) # label(axiom). [clausify(208)].
% 3.31/3.53 1256 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)) # label(fact_add__strict__left__mono) # label(axiom). [clausify(209)].
% 3.31/3.53 1257 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_add__strict__mono) # label(axiom). [clausify(210)].
% 3.31/3.53 1258 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_add__less__le__mono) # label(axiom). [clausify(233)].
% 3.31/3.53 1259 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_add__le__less__mono) # label(axiom). [clausify(234)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(1254,a,1257,a)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(1254,a,1258,a)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(1254,a,1259,a)].
% 3.31/3.53 1260 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). [resolve(1260,a,1257,a)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). [resolve(1260,a,1258,a)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). [resolve(1260,a,1259,a)].
% 3.31/3.53 1261 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1261,a,1257,a)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1261,a,1258,a)].
% 3.31/3.53 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(1261,a,1259,a)].
% 3.31/3.53 1262 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [clausify(977)].
% 3.31/3.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E)). [resolve(1262,b,1257,a)].
% 3.31/3.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E)). [resolve(1262,b,1258,a)].
% 3.37/3.64 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E)). [resolve(1262,b,1259,a)].
% 3.37/3.64 1263 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.37/3.64 1264 -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) # label(fact_add__nonneg__nonneg) # label(axiom). [clausify(224)].
% 3.37/3.64 1265 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(225)].
% 3.37/3.64 1266 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(225)].
% 3.37/3.64 1267 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(225)].
% 3.37/3.64 1268 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)) # label(fact_add__increasing) # label(axiom). [clausify(226)].
% 3.37/3.64 1269 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)) # label(fact_add__increasing2) # label(axiom). [clausify(227)].
% 3.37/3.64 1270 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__nonpos) # label(axiom). [clausify(228)].
% 3.37/3.64 1271 -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) # label(fact_add__pos__pos) # label(axiom). [clausify(231)].
% 3.37/3.64 1272 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__neg) # label(axiom). [clausify(232)].
% 3.37/3.64 1273 -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) # label(fact_add__pos__nonneg) # label(axiom). [clausify(239)].
% 3.37/3.64 1274 -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) # label(fact_add__nonneg__pos) # label(axiom). [clausify(240)].
% 3.37/3.64 1275 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)) # label(fact_add__strict__increasing) # label(axiom). [clausify(241)].
% 3.37/3.64 1276 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)) # label(fact_add__strict__increasing2) # label(axiom). [clausify(242)].
% 3.37/3.64 1277 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__nonpos) # label(axiom). [clausify(243)].
% 3.37/3.64 1278 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__neg) # label(axiom). [clausify(244)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)). [resolve(1263,a,1264,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1263,a,1265,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1263,a,1266,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1263,a,1267,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(1263,a,1268,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A)). [resolve(1263,a,1269,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1263,a,1270,a)].
% 3.37/3.64 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(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)). [resolve(1263,a,1271,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1263,a,1272,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)). [resolve(1263,a,1273,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(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(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)). [resolve(1263,a,1274,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(1263,a,1275,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(1263,a,1276,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1263,a,1277,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1263,a,1278,a)].
% 3.37/3.64 1279 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)). [resolve(1279,a,1264,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1279,a,1265,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1279,a,1266,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1279,a,1267,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)). [resolve(1279,a,1268,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A)). [resolve(1279,a,1269,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1279,a,1270,a)].
% 3.37/3.64 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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)). [resolve(1279,a,1271,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1279,a,1272,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)). [resolve(1279,a,1273,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)). [resolve(1279,a,1274,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)). [resolve(1279,a,1275,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)). [resolve(1279,a,1276,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1279,a,1277,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1279,a,1278,a)].
% 3.37/3.64 1280 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)). [resolve(1280,a,1264,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1280,a,1265,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1280,a,1266,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1280,a,1267,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(1280,a,1268,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),A)). [resolve(1280,a,1269,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1280,a,1270,a)].
% 3.37/3.64 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(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)). [resolve(1280,a,1271,a)].
% 3.37/3.64 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1280,a,1272,a)].
% 3.37/3.64 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)). [resolve(1280,a,1273,a)].
% 3.37/3.65 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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)). [resolve(1280,a,1274,a)].
% 3.37/3.65 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(1280,a,1275,a)].
% 3.37/3.65 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(1280,a,1276,a)].
% 3.37/3.65 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1280,a,1277,a)].
% 3.37/3.65 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1280,a,1278,a)].
% 3.37/3.65 1281 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) # label(axiom). [clausify(984)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)). [resolve(1281,b,1264,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1281,b,1265,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1281,b,1266,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1281,b,1267,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)). [resolve(1281,b,1268,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),B)). [resolve(1281,b,1269,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1281,b,1270,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)). [resolve(1281,b,1271,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1281,b,1272,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)). [resolve(1281,b,1273,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)). [resolve(1281,b,1274,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)). [resolve(1281,b,1275,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)). [resolve(1281,b,1276,a)].
% 3.37/3.65 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1281,b,1277,a)].
% 3.53/3.76 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1281,b,1278,a)].
% 3.53/3.76 1282 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.53/3.76 1283 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(255)].
% 3.53/3.76 1284 -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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)) # label(fact_pos__add__strict) # label(axiom). [clausify(347)].
% 3.53/3.76 1285 -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(348)].
% 3.53/3.76 1286 -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(349)].
% 3.53/3.76 1287 -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(350)].
% 3.53/3.76 1288 -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(351)].
% 3.53/3.76 1289 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))) # label(fact_less__add__one) # label(axiom). [clausify(352)].
% 3.53/3.76 1290 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__strict__mono) # label(axiom). [clausify(404)].
% 3.53/3.76 1291 -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),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_one__less__power) # label(axiom). [clausify(405)].
% 3.53/3.76 1292 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(406)].
% 3.53/3.76 1293 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(406)].
% 3.53/3.76 1294 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(407)].
% 3.53/3.76 1295 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)) # label(fact_power__decreasing) # label(axiom). [clausify(408)].
% 3.53/3.76 1296 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__mono) # label(axiom). [clausify(416)].
% 3.53/3.76 1297 -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),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_zero__le__power) # label(axiom). [clausify(417)].
% 3.53/3.76 1298 -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),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_zero__less__power) # label(axiom). [clausify(418)].
% 3.53/3.76 1299 -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),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_one__le__power) # label(axiom). [clausify(419)].
% 3.53/3.76 1300 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C = D # label(fact_power__inject__exp) # label(axiom). [clausify(421)].
% 3.53/3.76 1301 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C != D # label(fact_power__inject__exp) # label(axiom). [clausify(421)].
% 3.53/3.76 1302 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(423)].
% 3.53/3.76 1303 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) # label(fact_power__strict__increasing) # label(axiom). [clausify(426)].
% 3.53/3.76 1304 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(427)].
% 3.53/3.76 1305 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(428)].
% 3.53/3.76 1306 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(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(428)].
% 3.53/3.76 1307 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) # label(fact_power__increasing) # label(axiom). [clausify(429)].
% 3.53/3.76 1308 -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,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)) # label(fact_power__strict__decreasing) # label(axiom). [clausify(430)].
% 3.53/3.76 1309 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),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),D) | -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(431)].
% 3.53/3.76 1310 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_less__1__mult) # label(axiom). [clausify(759)].
% 3.53/3.76 1311 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_power__gt1__lemma) # label(axiom). [clausify(837)].
% 3.53/3.76 1312 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_power__less__power__Suc) # label(axiom). [clausify(838)].
% 3.53/3.76 1313 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__Suc__less) # label(axiom). [clausify(863)].
% 3.53/3.76 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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(1282,a,1283,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(1282,a,1284,a)].
% 3.53/3.76 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(1282,a,1285,a)].
% 3.53/3.76 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(1282,a,1286,a)].
% 3.53/3.76 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(1282,a,1287,a)].
% 3.53/3.76 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(1282,a,1288,a)].
% 3.53/3.76 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1282,a,1289,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(1282,a,1290,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1282,a,1291,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1282,a,1292,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1282,a,1293,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)). [resolve(1282,a,1295,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(1282,a,1296,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1282,a,1297,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1282,a,1298,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1282,a,1299,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B = C. [resolve(1282,a,1300,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B != C. [resolve(1282,a,1301,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(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(1282,a,1302,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)). [resolve(1282,a,1303,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1282,a,1304,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)). [resolve(1282,a,1307,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)). [resolve(1282,a,1308,a)].
% 3.53/3.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(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),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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1282,a,1309,a)].
% 3.53/3.76 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)). [resolve(1282,a,1310,a)].
% 3.53/3.76 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1282,a,1311,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(1282,a,1312,a)].
% 3.53/3.76 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1282,a,1313,a)].
% 3.53/3.76 1314 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.53/3.76 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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(1314,a,1283,a)].
% 3.53/3.76 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,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)). [resolve(1314,a,1284,a)].
% 3.53/3.76 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(1314,a,1285,a)].
% 3.53/3.76 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(1314,a,1286,a)].
% 3.53/3.76 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(1314,a,1287,a)].
% 3.53/3.76 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(1314,a,1288,a)].
% 3.53/3.76 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1314,a,1289,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)). [resolve(1314,a,1290,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1314,a,1291,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1314,a,1292,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1314,a,1293,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)). [resolve(1314,a,1295,a)].
% 3.53/3.76 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),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)). [resolve(1314,a,1296,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1314,a,1297,a)].
% 3.53/3.76 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1314,a,1298,a)].
% 3.53/3.76 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1314,a,1299,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B = C. [resolve(1314,a,1300,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B != C. [resolve(1314,a,1301,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(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(1314,a,1302,a)].
% 3.53/3.76 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)). [resolve(1314,a,1303,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1314,a,1304,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)). [resolve(1314,a,1307,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)). [resolve(1314,a,1308,a)].
% 3.53/3.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(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),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1314,a,1309,a)].
% 3.53/3.76 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_Oone__class_Oone(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)). [resolve(1314,a,1310,a)].
% 3.53/3.76 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_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1314,a,1311,a)].
% 3.53/3.76 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(1314,a,1312,a)].
% 3.53/3.76 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1314,a,1313,a)].
% 3.53/3.77 1315 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.53/3.77 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1315,a,1283,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(1315,a,1284,a)].
% 3.53/3.77 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(1315,a,1285,a)].
% 3.53/3.77 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(1315,a,1286,a)].
% 3.53/3.77 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(1315,a,1287,a)].
% 3.53/3.77 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(1315,a,1288,a)].
% 3.53/3.77 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1315,a,1289,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)). [resolve(1315,a,1290,a)].
% 3.53/3.77 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1315,a,1291,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1315,a,1292,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1315,a,1293,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)). [resolve(1315,a,1295,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)). [resolve(1315,a,1296,a)].
% 3.53/3.77 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1315,a,1297,a)].
% 3.53/3.77 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1315,a,1298,a)].
% 3.53/3.77 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1315,a,1299,a)].
% 3.53/3.77 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | B = C. [resolve(1315,a,1300,a)].
% 3.53/3.77 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | B != C. [resolve(1315,a,1301,a)].
% 3.53/3.77 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(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(1315,a,1302,a)].
% 3.53/3.77 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)). [resolve(1315,a,1303,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1315,a,1304,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)). [resolve(1315,a,1307,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)). [resolve(1315,a,1308,a)].
% 3.53/3.77 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(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),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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C. [resolve(1315,a,1309,a)].
% 3.53/3.77 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1315,a,1310,a)].
% 3.53/3.77 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1315,a,1311,a)].
% 3.53/3.77 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))). [resolve(1315,a,1312,a)].
% 3.53/3.77 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1315,a,1313,a)].
% 3.53/3.77 1316 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(996)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1316,b,1283,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)). [resolve(1316,b,1284,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1316,b,1285,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1316,b,1286,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1316,b,1287,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1316,b,1288,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1316,b,1289,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)). [resolve(1316,b,1290,a)].
% 3.53/3.77 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(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_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1316,b,1291,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D). [resolve(1316,b,1292,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D). [resolve(1316,b,1293,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B)). [resolve(1316,b,1295,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)). [resolve(1316,b,1296,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1316,b,1297,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1316,b,1298,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1316,b,1299,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | C = D. [resolve(1316,b,1300,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | C != D. [resolve(1316,b,1301,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1316,b,1302,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)). [resolve(1316,b,1303,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). [resolve(1316,b,1304,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)). [resolve(1316,b,1307,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B)). [resolve(1316,b,1308,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | B = D. [resolve(1316,b,1309,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)). [resolve(1316,b,1310,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1316,b,1311,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))). [resolve(1316,b,1312,a)].
% 3.53/3.78 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1316,b,1313,a)].
% 3.67/3.91 1317 class_RealVector_Ometric__space(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Ometric__space) # label(axiom). [assumption].
% 3.67/3.91 1318 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(A,c_COMBK(A,tc_Nat_Onat,B)) # label(fact_convergent__const) # label(axiom). [clausify(257)].
% 3.67/3.91 1319 -class_RealVector_Ometric__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBK(A,tc_Nat_Onat,B),C,c_Limits_Osequentially) | C = B # label(fact_LIMSEQ__const__iff) # label(axiom). [clausify(258)].
% 3.67/3.91 1320 -class_RealVector_Ometric__space(A) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBK(A,tc_Nat_Onat,B),C,c_Limits_Osequentially) | C != B # label(fact_LIMSEQ__const__iff) # label(axiom). [clausify(258)].
% 3.67/3.91 1321 -class_RealVector_Ometric__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,D,c_Limits_Osequentially) | C = D # label(fact_LIMSEQ__unique) # label(axiom). [clausify(269)].
% 3.67/3.91 1322 -class_RealVector_Ometric__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_SEQ_Oconvergent(A,B) # label(fact_convergentI) # label(axiom). [clausify(270)].
% 3.67/3.91 1323 -class_RealVector_Ometric__space(A) | -c_SEQ_Oconvergent(A,B) | c_Limits_Otendsto(tc_Nat_Onat,A,B,f23(B,A),c_Limits_Osequentially) # label(fact_convergent__def) # label(axiom). [clausify(271)].
% 3.67/3.91 1324 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(A,B) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) # label(fact_convergent__def) # label(axiom). [clausify(271)].
% 3.67/3.91 1325 -class_RealVector_Ometric__space(A) | -c_SEQ_Oconvergent(A,B) | c_Limits_Otendsto(tc_Nat_Onat,A,B,c_SEQ_Olim(A,B),c_Limits_Osequentially) # label(fact_convergent__LIMSEQ__iff) # label(axiom). [clausify(386)].
% 3.67/3.91 1326 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(A,B) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,c_SEQ_Olim(A,B),c_Limits_Osequentially) # label(fact_convergent__LIMSEQ__iff) # label(axiom). [clausify(386)].
% 3.67/3.91 1327 -class_RealVector_Ometric__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_SEQ_Olim(A,B) = C # label(fact_limI) # label(axiom). [clausify(400)].
% 3.67/3.91 Derived: c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,tc_Nat_Onat,A)). [resolve(1317,a,1318,a)].
% 3.67/3.91 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,tc_Nat_Onat,A),B,c_Limits_Osequentially) | B = A. [resolve(1317,a,1319,a)].
% 3.67/3.91 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,tc_Nat_Onat,A),B,c_Limits_Osequentially) | B != A. [resolve(1317,a,1320,a)].
% 3.67/3.91 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,C,c_Limits_Osequentially) | B = C. [resolve(1317,a,1321,a)].
% 3.67/3.91 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_SEQ_Oconvergent(tc_RealDef_Oreal,A). [resolve(1317,a,1322,a)].
% 3.67/3.91 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,f23(A,tc_RealDef_Oreal),c_Limits_Osequentially). [resolve(1317,a,1323,a)].
% 3.67/3.91 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,c_SEQ_Olim(tc_RealDef_Oreal,A),c_Limits_Osequentially). [resolve(1317,a,1325,a)].
% 3.67/3.91 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_SEQ_Olim(tc_RealDef_Oreal,A) = B. [resolve(1317,a,1327,a)].
% 3.67/3.91 1328 class_RealVector_Ometric__space(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Ometric__space) # label(axiom). [assumption].
% 3.67/3.91 Derived: c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,tc_Nat_Onat,A)). [resolve(1328,a,1318,a)].
% 3.67/3.91 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,tc_Nat_Onat,A),B,c_Limits_Osequentially) | B = A. [resolve(1328,a,1319,a)].
% 3.83/4.03 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,tc_Nat_Onat,A),B,c_Limits_Osequentially) | B != A. [resolve(1328,a,1320,a)].
% 3.83/4.03 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,C,c_Limits_Osequentially) | B = C. [resolve(1328,a,1321,a)].
% 3.83/4.03 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,A). [resolve(1328,a,1322,a)].
% 3.83/4.03 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,f23(A,tc_Complex_Ocomplex),c_Limits_Osequentially). [resolve(1328,a,1323,a)].
% 3.83/4.03 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,c_SEQ_Olim(tc_Complex_Ocomplex,A),c_Limits_Osequentially). [resolve(1328,a,1325,a)].
% 3.83/4.03 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_SEQ_Olim(tc_Complex_Ocomplex,A) = B. [resolve(1328,a,1327,a)].
% 3.83/4.03 1329 class_RealVector_Otopological__space(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Otopological__space) # label(axiom). [assumption].
% 3.83/4.03 1330 -class_RealVector_Otopological__space(A) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBK(A,tc_Nat_Onat,B),B,c_Limits_Osequentially) # label(fact_LIMSEQ__const) # label(axiom). [clausify(259)].
% 3.83/4.03 1331 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D)),C,c_Limits_Osequentially) # label(fact_LIMSEQ__ignore__initial__segment) # label(axiom). [clausify(261)].
% 3.83/4.03 1332 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C)),D,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,B,D,c_Limits_Osequentially) # label(fact_LIMSEQ__offset) # label(axiom). [clausify(264)].
% 3.83/4.03 1333 -class_RealVector_Otopological__space(A) | -c_Orderings_Oord__class_Oless__eq(tc_Limits_Onet(B),C,D) | -c_Limits_Otendsto(B,A,E,F,D) | c_Limits_Otendsto(B,A,E,F,C) # label(fact_tendsto__mono) # label(axiom). [clausify(369)].
% 3.83/4.03 1334 -class_RealVector_Otopological__space(A) | c_Limits_Otendsto(B,A,c_COMBK(A,B,C),C,D) # label(fact_tendsto__const) # label(axiom). [clausify(373)].
% 3.83/4.03 1335 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D)),C,c_Limits_Osequentially) # label(fact_LIMSEQ__linear) # label(axiom). [clausify(926)].
% 3.83/4.03 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,tc_Nat_Onat,A),A,c_Limits_Osequentially). [resolve(1329,a,1330,a)].
% 3.83/4.03 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C)),B,c_Limits_Osequentially). [resolve(1329,a,1331,a)].
% 3.83/4.03 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B)),C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,C,c_Limits_Osequentially). [resolve(1329,a,1332,a)].
% 3.83/4.03 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Limits_Onet(A),B,C) | -c_Limits_Otendsto(A,tc_RealDef_Oreal,D,E,C) | c_Limits_Otendsto(A,tc_RealDef_Oreal,D,E,B). [resolve(1329,a,1333,a)].
% 3.83/4.03 Derived: c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,A,B),B,C). [resolve(1329,a,1334,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C)),B,c_Limits_Osequentially). [resolve(1329,a,1335,a)].
% 3.83/4.04 1336 class_RealVector_Otopological__space(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Otopological__space) # label(axiom). [assumption].
% 3.83/4.04 Derived: c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,tc_Nat_Onat,A),A,c_Limits_Osequentially). [resolve(1336,a,1330,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C)),B,c_Limits_Osequentially). [resolve(1336,a,1331,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B)),C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,C,c_Limits_Osequentially). [resolve(1336,a,1332,a)].
% 3.83/4.04 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Limits_Onet(A),B,C) | -c_Limits_Otendsto(A,tc_Complex_Ocomplex,D,E,C) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,D,E,B). [resolve(1336,a,1333,a)].
% 3.83/4.04 Derived: c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,A,B),B,C). [resolve(1336,a,1334,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C)),B,c_Limits_Osequentially). [resolve(1336,a,1335,a)].
% 3.83/4.04 1337 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_ga____),C,c_Limits_Osequentially). [resolve(1042,c,1033,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,v_ga____),B,c_Limits_Osequentially). [resolve(1337,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,v_ga____),B,c_Limits_Osequentially). [resolve(1337,a,1336,a)].
% 3.83/4.04 1338 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_f____),C,c_Limits_Osequentially). [resolve(1042,c,1034,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,v_f____),B,c_Limits_Osequentially). [resolve(1338,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,v_f____),B,c_Limits_Osequentially). [resolve(1338,a,1336,a)].
% 3.83/4.04 1339 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),C,c_Limits_Osequentially). [resolve(1042,c,1035,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),B,c_Limits_Osequentially). [resolve(1339,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),B,c_Limits_Osequentially). [resolve(1339,a,1336,a)].
% 3.83/4.04 1340 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,D),C,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(D),f3(D)). [resolve(1042,c,1037,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,C),B,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(C),f3(C)). [resolve(1340,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,C),B,c_Limits_Osequentially) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(C),f3(C)). [resolve(1340,a,1336,a)].
% 3.83/4.04 1341 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,D),C,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(D,f2(D)),hAPP(D,f3(D))). [resolve(1042,c,1038,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,C),B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,f2(C)),hAPP(C,f3(C))). [resolve(1341,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,C),B,c_Limits_Osequentially) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,f2(C)),hAPP(C,f3(C))). [resolve(1341,a,1336,a)].
% 3.83/4.04 1342 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c1),C,c_Limits_Osequentially). [resolve(1042,c,1039,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c1),B,c_Limits_Osequentially). [resolve(1342,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c1),B,c_Limits_Osequentially). [resolve(1342,a,1336,a)].
% 3.83/4.04 1343 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c2),C,c_Limits_Osequentially). [resolve(1042,c,1040,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c2),B,c_Limits_Osequentially). [resolve(1343,a,1329,a)].
% 3.83/4.04 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c2),B,c_Limits_Osequentially). [resolve(1343,a,1336,a)].
% 3.83/4.04 1344 -class_RealVector_Otopological__space(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c3),C,c_Limits_Osequentially). [resolve(1042,c,1041,a)].
% 3.90/4.16 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c3),B,c_Limits_Osequentially). [resolve(1344,a,1329,a)].
% 3.90/4.16 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c3),B,c_Limits_Osequentially). [resolve(1344,a,1336,a)].
% 3.90/4.16 1345 class_Rings_Ozero__neq__one(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.90/4.16 1346 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_one__neq__zero) # label(axiom). [clausify(344)].
% 3.90/4.16 1347 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_zero__neq__one) # label(axiom). [clausify(345)].
% 3.90/4.16 1348 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_power__eq__0__iff) # label(axiom). [clausify(420)].
% 3.90/4.16 1349 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C # label(fact_power__eq__0__iff) # label(axiom). [clausify(420)].
% 3.90/4.16 1350 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | 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(420)].
% 3.90/4.16 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1345,a,1346,a)].
% 3.90/4.16 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1345,a,1348,d)].
% 3.90/4.16 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1345,a,1349,d)].
% 3.90/4.16 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1345,a,1350,d)].
% 3.90/4.16 1351 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.90/4.16 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1351,a,1346,a)].
% 3.90/4.16 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1351,a,1348,d)].
% 3.90/4.16 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1351,a,1349,d)].
% 3.90/4.16 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1351,a,1350,d)].
% 3.96/4.17 1352 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.96/4.17 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1352,a,1346,a)].
% 3.96/4.17 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1352,a,1348,d)].
% 3.96/4.17 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1352,a,1349,d)].
% 3.96/4.17 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Omult__zero(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1352,a,1350,d)].
% 3.96/4.17 1353 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.96/4.17 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1353,a,1346,a)].
% 3.96/4.17 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1353,a,1348,d)].
% 3.96/4.17 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1353,a,1349,d)].
% 3.96/4.17 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Omult__zero(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1353,a,1350,d)].
% 3.96/4.17 1354 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom). [clausify(1010)].
% 3.96/4.17 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1354,b,1346,a)].
% 3.96/4.17 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1354,b,1348,d)].
% 3.96/4.17 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C. [resolve(1354,b,1349,d)].
% 4.08/4.29 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C. [resolve(1354,b,1350,d)].
% 4.08/4.29 1355 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 4.08/4.29 1356 -class_RealVector_Oreal__normed__div__algebra(A) | hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),C) # label(fact_norm__power) # label(axiom). [clausify(392)].
% 4.08/4.29 1357 -class_RealVector_Oreal__normed__div__algebra(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(c_RealVector_Onorm__class_Onorm(A),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_RealVector_Onorm__class_Onorm(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) # label(fact_Bseq__inverse__lemma) # label(axiom). [clausify(613)].
% 4.08/4.29 1358 -class_RealVector_Oreal__normed__div__algebra(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)) = hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_nonzero__norm__inverse) # label(axiom). [clausify(664)].
% 4.08/4.29 1359 -class_RealVector_Oreal__normed__div__algebra(A) | hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C)) # label(fact_norm__mult) # label(axiom). [clausify(666)].
% 4.08/4.29 1360 -class_RealVector_Oreal__normed__div__algebra(A) | -class_Rings_Odivision__ring__inverse__zero(A) | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)) = hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_norm__inverse) # label(axiom). [clausify(667)].
% 4.08/4.29 1361 -class_RealVector_Oreal__normed__div__algebra(A) | -c_Limits_Otendsto(B,A,C,D,E) | c_Groups_Ozero__class_Ozero(A) = D | c_Limits_Otendsto(B,A,c_COMBB(A,A,B,c_Rings_Oinverse__class_Oinverse(A),C),hAPP(c_Rings_Oinverse__class_Oinverse(A),D),E) # label(fact_tendsto__inverse) # label(axiom). [clausify(788)].
% 4.08/4.29 1362 -class_RealVector_Oreal__normed__div__algebra(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Groups_Ozero__class_Ozero(A) = C | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBB(A,A,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(A),B),hAPP(c_Rings_Oinverse__class_Oinverse(A),C),c_Limits_Osequentially) # label(fact_LIMSEQ__inverse) # label(axiom). [clausify(848)].
% 4.08/4.29 1363 -class_RealVector_Oreal__normed__div__algebra(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Groups_Ozero__class_Ozero(A) = C | c_SEQ_OBseq(A,c_COMBB(A,A,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_Bseq__inverse) # label(axiom). [clausify(865)].
% 4.08/4.29 Derived: hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),B). [resolve(1355,a,1356,a)].
% 4.08/4.29 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(c_RealVector_Onorm__class_Onorm(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,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1355,a,1357,a)].
% 4.08/4.30 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1355,a,1358,a)].
% 4.08/4.30 Derived: hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B)). [resolve(1355,a,1359,a)].
% 4.08/4.30 Derived: -class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1355,a,1360,a)].
% 4.08/4.30 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = C | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),C),D). [resolve(1355,a,1361,a)].
% 4.08/4.30 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_SEQ_OBseq(tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1355,a,1363,a)].
% 4.08/4.30 1364 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 4.08/4.30 Derived: hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),B). [resolve(1364,a,1356,a)].
% 4.08/4.30 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),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,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1364,a,1357,a)].
% 4.08/4.30 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)). [resolve(1364,a,1358,a)].
% 4.08/4.30 Derived: hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B)). [resolve(1364,a,1359,a)].
% 4.08/4.30 Derived: -class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)). [resolve(1364,a,1360,a)].
% 4.08/4.30 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C | c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),C),D). [resolve(1364,a,1361,a)].
% 4.20/4.43 Derived: -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_SEQ_OBseq(tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Nat_Onat,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)). [resolve(1364,a,1363,a)].
% 4.20/4.43 1365 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 4.20/4.43 1366 -class_Power_Opower(A) | -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,A,c_COMBB(A,tc_fun(tc_Nat_Onat,A),tc_Nat_Onat,c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),c_Limits_Osequentially) # label(fact_LIMSEQ__pow) # label(axiom). [clausify(393)].
% 4.20/4.43 1367 -class_RealVector_Oreal__normed__algebra(A) | -c_Series_Osums(A,B,C) | c_Series_Osums(A,c_COMBB(A,A,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_sums__mult) # label(axiom). [clausify(609)].
% 4.20/4.43 1368 -class_RealVector_Oreal__normed__algebra(A) | -c_Series_Osums(A,B,C) | c_Series_Osums(A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_sums__mult2) # label(axiom). [clausify(610)].
% 4.20/4.43 1369 -class_RealVector_Oreal__normed__algebra(A) | -c_Series_Osums(A,B,C) | c_Series_Osums(A,c_COMBB(A,A,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_mult__right_Osums) # label(axiom). [clausify(611)].
% 4.20/4.43 1370 -class_RealVector_Oreal__normed__algebra(A) | -c_Series_Osums(A,B,C) | c_Series_Osums(A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__left_Osums) # label(axiom). [clausify(612)].
% 4.20/4.43 1371 -class_RealVector_Oreal__normed__algebra(A) | -c_SEQ_Oconvergent(A,B) | -c_SEQ_Oconvergent(A,C) | c_SEQ_Oconvergent(A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult_Oconvergent) # label(axiom). [clausify(627)].
% 4.20/4.43 1372 -class_RealVector_Oreal__normed__algebra(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__left_Oconvergent) # label(axiom). [clausify(628)].
% 4.20/4.43 1373 -class_RealVector_Oreal__normed__algebra(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_COMBB(A,A,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_mult__right_Oconvergent) # label(axiom). [clausify(629)].
% 4.20/4.43 1374 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__right_Ozero) # label(axiom). [clausify(654)].
% 4.20/4.43 1375 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult_Ozero__right) # label(axiom). [clausify(655)].
% 4.20/4.43 1376 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__left_Ozero) # label(axiom). [clausify(656)].
% 4.20/4.43 1377 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult_Ozero__left) # label(axiom). [clausify(657)].
% 4.20/4.43 1378 -class_RealVector_Oreal__normed__algebra(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E)) # label(fact_norm__mult__less) # label(axiom). [clausify(665)].
% 4.20/4.43 1379 -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(B,A,C,D,E) | c_Limits_Otendsto(B,A,c_COMBB(A,A,B,hAPP(c_Groups_Otimes__class_Otimes(A),F),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D),E) # label(fact_mult__right_Otendsto) # label(axiom). [clausify(674)].
% 4.20/4.43 1380 -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(B,A,C,D,E) | c_Limits_Otendsto(B,A,c_COMBC(B,A,A,c_COMBB(A,tc_fun(A,A),B,c_Groups_Otimes__class_Otimes(A),C),F),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),F),E) # label(fact_mult__left_Otendsto) # label(axiom). [clausify(675)].
% 4.20/4.43 1381 -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(B,A,C,D,E) | -c_Limits_Otendsto(B,A,F,V6,E) | c_Limits_Otendsto(B,A,c_COMBS(B,A,A,c_COMBB(A,tc_fun(A,A),B,c_Groups_Otimes__class_Otimes(A),C),F),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),V6),E) # label(fact_mult_Otendsto) # label(axiom). [clausify(676)].
% 4.20/4.43 1382 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C))) # label(fact_norm__mult__ineq) # label(axiom). [clausify(677)].
% 4.20/4.43 1383 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__left_Odiff) # label(axiom). [clausify(678)].
% 4.20/4.43 1384 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult_Odiff__left) # label(axiom). [clausify(679)].
% 4.20/4.43 1385 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult__right_Odiff) # label(axiom). [clausify(680)].
% 4.20/4.43 1386 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult_Odiff__right) # label(axiom). [clausify(681)].
% 4.20/4.43 1387 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__left_Oadd) # label(axiom). [clausify(684)].
% 4.20/4.43 1388 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult_Oadd__left) # label(axiom). [clausify(685)].
% 4.20/4.43 1389 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult__right_Oadd) # label(axiom). [clausify(686)].
% 4.20/4.43 1390 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult_Oadd__right) # label(axiom). [clausify(687)].
% 4.20/4.43 1391 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult_Oprod__diff__prod) # label(axiom). [clausify(763)].
% 4.20/4.43 1392 -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBB(A,A,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),c_Limits_Osequentially) # label(fact_mult__right_OLIMSEQ) # label(axiom). [clausify(790)].
% 4.20/4.43 1393 -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBC(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),c_Limits_Osequentially) # label(fact_mult__left_OLIMSEQ) # label(axiom). [clausify(791)].
% 4.20/4.43 1394 -class_RealVector_Oreal__normed__algebra(A) | -c_Limits_Otendsto(tc_Nat_Onat,A,B,C,c_Limits_Osequentially) | -c_Limits_Otendsto(tc_Nat_Onat,A,D,E,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,A,c_COMBS(tc_Nat_Onat,A,A,c_COMBB(A,tc_fun(A,A),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E),c_Limits_Osequentially) # label(fact_LIMSEQ__mult) # label(axiom). [clausify(792)].
% 4.20/4.43 Derived: -class_Power_Opower(tc_RealDef_Oreal) | -c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_RealDef_Oreal,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_Nat_Onat,tc_RealDef_Oreal),tc_Nat_Onat,c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C),c_Limits_Osequentially). [resolve(1365,a,1366,b)].
% 4.20/4.43 Derived: -c_Series_Osums(tc_RealDef_Oreal,A,B) | c_Series_Osums(tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)). [resolve(1365,a,1367,a)].
% 4.20/4.43 Derived: -c_Series_Osums(tc_RealDef_Oreal,A,B) | c_Series_Osums(tc_RealDef_Oreal,c_COMBC(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(1365,a,1368,a)].
% 4.20/4.43 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | -c_SEQ_Oconvergent(tc_RealDef_Oreal,B) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBS(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1365,a,1371,a)].
% 4.20/4.43 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBC(tc_Nat_Onat,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1365,a,1372,a)].
% 4.20/4.43 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)). [resolve(1365,a,1373,a)].
% 4.20/4.43 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1365,a,1374,a)].
% 4.20/4.43 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1365,a,1376,a)].
% 4.20/4.43 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1365,a,1378,a)].
% 4.20/4.43 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_RealDef_Oreal,A,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C),D). [resolve(1365,a,1379,a)].
% 4.20/4.43 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBC(A,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E),D). [resolve(1365,a,1380,a)].
% 4.20/4.43 Derived: -c_Limits_Otendsto(A,tc_RealDef_Oreal,B,C,D) | -c_Limits_Otendsto(A,tc_RealDef_Oreal,E,F,D) | c_Limits_Otendsto(A,tc_RealDef_Oreal,c_COMBS(A,tc_RealDef_Oreal,tc_RealDef_Oreal,c_COMBB(tc_RealDef_Oreal,tc_fun(tc_RealDef_Oreal,tc_RealDef_Oreal),A,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),F),D). [resolve(1365,a,1381,a)].
% 4.20/4.43 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B))). [resolve(1365,a,1382,a)].
% 4.20/4.43 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(1365,a,1383,a)].
% 4.20/4.43 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1365,a,1385,a)].
% 4.20/4.43 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(1365,a,1387,a)].
% 4.20/4.43 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1365,a,1389,a)].
% 4.20/4.43 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),C),D))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1365,a,1391,a)].
% 4.20/4.43 1395 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 4.20/4.43 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,A,B,c_Limits_Osequentially) | c_Limits_Otendsto(tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Nat_Onat,tc_Complex_Ocomplex),tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C),c_Limits_Osequentially). [resolve(1395,a,1366,b)].
% 4.20/4.43 Derived: -c_Series_Osums(tc_Complex_Ocomplex,A,B) | c_Series_Osums(tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)). [resolve(1395,a,1367,a)].
% 4.20/4.43 Derived: -c_Series_Osums(tc_Complex_Ocomplex,A,B) | c_Series_Osums(tc_Complex_Ocomplex,c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(1395,a,1368,a)].
% 4.20/4.43 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | -c_SEQ_Oconvergent(tc_Complex_Ocomplex,B) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_COMBS(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(1395,a,1371,a)].
% 4.20/4.44 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_COMBC(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(1395,a,1372,a)].
% 4.20/4.44 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)). [resolve(1395,a,1373,a)].
% 4.20/4.44 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1395,a,1374,a)].
% 4.20/4.44 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1395,a,1376,a)].
% 4.20/4.44 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1395,a,1378,a)].
% 4.20/4.44 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,A,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),E),C),D). [resolve(1395,a,1379,a)].
% 4.20/4.44 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),E),D). [resolve(1395,a,1380,a)].
% 4.27/4.56 Derived: -c_Limits_Otendsto(A,tc_Complex_Ocomplex,B,C,D) | -c_Limits_Otendsto(A,tc_Complex_Ocomplex,E,F,D) | c_Limits_Otendsto(A,tc_Complex_Ocomplex,c_COMBS(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),F),D). [resolve(1395,a,1381,a)].
% 4.27/4.56 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B))). [resolve(1395,a,1382,a)].
% 4.27/4.56 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(1395,a,1383,a)].
% 4.27/4.56 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(1395,a,1385,a)].
% 4.27/4.56 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(1395,a,1387,a)].
% 4.27/4.56 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(1395,a,1389,a)].
% 4.27/4.56 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(1395,a,1391,a)].
% 4.27/4.56 1396 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.27/4.56 1397 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) # label(fact_field__power__not__zero) # label(axiom). [clausify(412)].
% 4.27/4.56 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B). [resolve(1396,a,1397,a)].
% 4.27/4.56 1398 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.43/4.69 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B). [resolve(1398,a,1397,a)].
% 4.43/4.69 1399 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.43/4.69 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B). [resolve(1399,a,1397,a)].
% 4.43/4.69 1400 -class_Rings_Oidom(A) | class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) # label(axiom). [clausify(987)].
% 4.43/4.69 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C). [resolve(1400,b,1397,a)].
% 4.43/4.69 1401 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 4.43/4.69 1402 -class_Groups_Omonoid__mult(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_power__one) # label(axiom). [clausify(413)].
% 4.43/4.69 1403 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_power__one__right) # label(axiom). [clausify(415)].
% 4.43/4.69 1404 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__commutes) # label(axiom). [clausify(632)].
% 4.43/4.69 1405 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(692)].
% 4.43/4.69 1406 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(694)].
% 4.43/4.69 1407 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) # label(fact_power__add) # label(axiom). [clausify(782)].
% 4.43/4.69 1408 -class_Groups_Omonoid__mult(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B) # label(fact_realpow__minus__mult) # label(axiom). [clausify(867)].
% 4.43/4.69 1409 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) # label(fact_power__mult) # label(axiom). [clausify(874)].
% 4.43/4.69 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A). [resolve(1401,a,1402,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1401,a,1403,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1401,a,1404,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(1401,a,1405,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1401,a,1406,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1401,a,1407,a)].
% 4.43/4.69 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A). [resolve(1401,a,1408,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1401,a,1409,a)].
% 4.43/4.69 1410 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 4.43/4.69 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A). [resolve(1410,a,1402,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1410,a,1403,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(1410,a,1404,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(1410,a,1405,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1410,a,1406,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1410,a,1407,a)].
% 4.43/4.69 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A). [resolve(1410,a,1408,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1410,a,1409,a)].
% 4.43/4.69 1411 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption].
% 4.43/4.69 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). [resolve(1411,a,1402,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1411,a,1403,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(1411,a,1404,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A) = A. [resolve(1411,a,1405,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1411,a,1406,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1411,a,1407,a)].
% 4.43/4.69 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),A). [resolve(1411,a,1408,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1411,a,1409,a)].
% 4.43/4.69 1412 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom). [assumption].
% 4.43/4.69 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(1412,a,1402,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1412,a,1403,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(1412,a,1404,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(1412,a,1405,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1412,a,1406,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1412,a,1407,a)].
% 4.43/4.69 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),A). [resolve(1412,a,1408,a)].
% 4.43/4.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1412,a,1409,a)].
% 4.43/4.69 1413 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1014)].
% 4.43/4.69 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B). [resolve(1413,b,1402,a)].
% 4.43/4.69 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B. [resolve(1413,b,1403,a)].
% 4.43/4.69 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1413,b,1404,a)].
% 4.43/4.69 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B) = B. [resolve(1413,b,1405,a)].
% 4.59/4.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1413,b,1406,a)].
% 4.59/4.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)). [resolve(1413,b,1407,a)].
% 4.59/4.82 Derived: -class_Rings_Ocomm__semiring__1(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),B). [resolve(1413,b,1408,a)].
% 4.59/4.82 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)). [resolve(1413,b,1409,a)].
% 4.59/4.82 1414 class_Rings_Osemiring__0(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__0) # label(axiom). [assumption].
% 4.59/4.82 1415 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom). [clausify(424)].
% 4.59/4.82 1416 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom). [clausify(424)].
% 4.59/4.82 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(1414,a,1415,b)].
% 4.59/4.82 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(1414,a,1416,b)].
% 4.59/4.82 1417 class_Rings_Osemiring__0(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__0) # label(axiom). [assumption].
% 4.59/4.82 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(1417,a,1415,b)].
% 4.59/4.82 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(1417,a,1416,b)].
% 4.59/4.82 1418 class_Rings_Osemiring__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__0) # label(axiom). [assumption].
% 4.59/4.82 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1418,a,1415,b)].
% 4.59/4.82 Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1418,a,1416,b)].
% 4.72/4.96 1419 class_Rings_Osemiring__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring__0) # label(axiom). [assumption].
% 4.72/4.96 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1419,a,1415,b)].
% 4.72/4.96 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1419,a,1416,b)].
% 4.72/4.96 1420 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom). [clausify(1016)].
% 4.72/4.96 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B). [resolve(1420,b,1415,b)].
% 4.72/4.96 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B). [resolve(1420,b,1416,b)].
% 4.72/4.96 1421 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].
% 4.72/4.96 1422 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom). [clausify(499)].
% 4.72/4.96 1423 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom). [clausify(499)].
% 4.72/4.96 1424 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom). [clausify(701)].
% 4.72/4.96 1425 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B != D # label(fact_crossproduct__eq) # label(axiom). [clausify(701)].
% 4.72/4.96 1426 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | C != E # label(fact_crossproduct__eq) # label(axiom). [clausify(701)].
% 4.72/4.96 1427 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(704)].
% 4.72/4.96 1428 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(704)].
% 4.72/4.96 1429 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(704)].
% 4.72/4.96 1430 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Ozero__class_Ozero(A) = B | C != D | E = F | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(758)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1421,a,1422,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1421,a,1423,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | A = C | B = D. [resolve(1421,a,1424,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | A != C. [resolve(1421,a,1425,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | B != D. [resolve(1421,a,1426,a)].
% 4.72/4.96 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)). [resolve(1421,a,1430,a)].
% 4.72/4.96 1431 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].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1431,a,1422,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1431,a,1423,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | A = C | B = D. [resolve(1431,a,1424,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | A != C. [resolve(1431,a,1425,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | B != D. [resolve(1431,a,1426,a)].
% 4.72/4.96 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)). [resolve(1431,a,1430,a)].
% 4.72/4.96 1432 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].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1432,a,1422,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1432,a,1423,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | A = C | B = D. [resolve(1432,a,1424,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | A != C. [resolve(1432,a,1425,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | B != D. [resolve(1432,a,1426,a)].
% 4.72/4.96 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)). [resolve(1432,a,1430,a)].
% 4.72/4.96 1433 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].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1433,a,1422,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1433,a,1423,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | A = C | B = D. [resolve(1433,a,1424,a)].
% 4.72/4.96 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | A != C. [resolve(1433,a,1425,a)].
% 4.82/5.09 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | B != D. [resolve(1433,a,1426,a)].
% 4.82/5.09 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)). [resolve(1433,a,1430,a)].
% 4.82/5.09 1434 -class_Rings_Oidom(A) | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [clausify(976)].
% 4.82/5.09 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1434,b,1422,a)].
% 4.82/5.09 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1434,b,1423,a)].
% 4.82/5.09 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | B = D | C = E. [resolve(1434,b,1424,a)].
% 4.82/5.09 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | B != D. [resolve(1434,b,1425,a)].
% 4.82/5.09 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | C != E. [resolve(1434,b,1426,a)].
% 4.82/5.09 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | C != D | E = F | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),F)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)). [resolve(1434,b,1430,a)].
% 4.82/5.09 1435 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 4.82/5.09 1436 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D)),C) # label(fact_power__divide) # label(axiom). [clausify(504)].
% 4.82/5.09 1437 -class_Fields_Ofield__inverse__zero(A) | -class_RealVector_Oreal__normed__field(A) | hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(A),B)),hAPP(c_RealVector_Onorm__class_Onorm(A),C)) # label(fact_norm__divide) # label(axiom). [clausify(514)].
% 4.82/5.09 1438 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),c_Groups_Oone__class_Oone(A)),B)),C) # label(fact_power__one__over) # label(axiom). [clausify(529)].
% 4.82/5.09 1439 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Oone__class_Oone(A) != hAPP(c_Rings_Oinverse__class_Oinverse(A),B) | c_Groups_Oone__class_Oone(A) = B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(616)].
% 4.82/5.09 1440 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Rings_Oinverse__class_Oinverse(A),B) | c_Groups_Oone__class_Oone(A) != B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(616)].
% 4.82/5.09 1441 -class_Fields_Ofield__inverse__zero(A) | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) # label(fact_inverse__divide) # label(axiom). [clausify(619)].
% 4.82/5.09 1442 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_times__divide__times__eq) # label(axiom). [clausify(621)].
% 4.82/5.09 1443 -class_Fields_Ofield__inverse__zero(A) | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) # label(fact_inverse__mult__distrib) # label(axiom). [clausify(624)].
% 4.82/5.09 1444 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Rings_Oinverse__class_Oinverse(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_field__inverse__zero) # label(axiom). [clausify(626)].
% 4.82/5.09 1445 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D) # label(fact_mult__divide__mult__cancel__left) # label(axiom). [clausify(772)].
% 4.82/5.09 1446 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D) # label(fact_mult__divide__mult__cancel__right) # label(axiom). [clausify(773)].
% 4.82/5.09 1447 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) != D | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) = B # label(fact_divide__eq__eq) # label(axiom). [clausify(774)].
% 4.82/5.09 1448 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(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(774)].
% 4.82/5.09 1449 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(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(774)].
% 4.82/5.09 1450 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) = D | hAPP(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(774)].
% 4.82/5.09 1451 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) = D | hAPP(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(774)].
% 4.82/5.09 1452 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) != D | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) = B # label(fact_eq__divide__eq) # label(axiom). [clausify(775)].
% 4.82/5.09 1453 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(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(775)].
% 4.82/5.09 1454 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(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(775)].
% 4.82/5.09 1455 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) = D | hAPP(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(775)].
% 4.82/5.09 1456 -class_Fields_Ofield__inverse__zero(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) = D | hAPP(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(775)].
% 4.82/5.09 1457 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)),D) # label(fact_add__frac__num) # label(axiom). [clausify(832)].
% 4.82/5.09 1458 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)) # label(fact_add__num__frac) # label(axiom). [clausify(834)].
% 4.82/5.09 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C)),B). [resolve(1435,a,1436,a)].
% 4.82/5.09 Derived: -class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) | hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),B)). [resolve(1435,a,1437,a)].
% 4.82/5.09 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)),B). [resolve(1435,a,1438,a)].
% 4.82/5.09 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = A. [resolve(1435,a,1439,a)].
% 4.82/5.09 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != A. [resolve(1435,a,1440,a)].
% 4.82/5.09 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A). [resolve(1435,a,1441,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1435,a,1442,a)].
% 4.82/5.10 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)). [resolve(1435,a,1443,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1435,a,1444,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C). [resolve(1435,a,1445,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C). [resolve(1435,a,1446,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B) != C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B) = A. [resolve(1435,a,1447,a)].
% 4.82/5.10 Derived: hAPP(hAPP(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(1435,a,1448,a)].
% 4.82/5.10 Derived: hAPP(hAPP(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(1435,a,1449,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1435,a,1450,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C. [resolve(1435,a,1451,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A)),C). [resolve(1435,a,1457,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A)). [resolve(1435,a,1458,a)].
% 4.82/5.10 1459 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),B). [resolve(1459,a,1436,a)].
% 4.82/5.10 Derived: -class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) | hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A)),hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),B)). [resolve(1459,a,1437,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A)),B). [resolve(1459,a,1438,a)].
% 4.82/5.10 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A. [resolve(1459,a,1439,a)].
% 4.82/5.10 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1459,a,1440,a)].
% 4.82/5.10 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A). [resolve(1459,a,1441,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(1459,a,1442,a)].
% 4.82/5.10 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(1459,a,1443,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1459,a,1444,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C). [resolve(1459,a,1445,a)].
% 4.82/5.10 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C). [resolve(1459,a,1446,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B) = A. [resolve(1459,a,1447,a)].
% 4.82/5.10 Derived: hAPP(hAPP(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(1459,a,1448,a)].
% 4.82/5.10 Derived: hAPP(hAPP(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(1459,a,1449,a)].
% 4.82/5.10 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1459,a,1450,a)].
% 5.01/5.24 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C. [resolve(1459,a,1451,a)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A)),C). [resolve(1459,a,1457,a)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A)). [resolve(1459,a,1458,a)].
% 5.01/5.24 1460 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom). [assumption].
% 5.01/5.24 1461 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_divide__zero__left) # label(axiom). [clausify(506)].
% 5.01/5.24 1462 -class_Rings_Odivision__ring(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_divide__1) # label(axiom). [clausify(509)].
% 5.01/5.24 1463 -class_Rings_Odivision__ring(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_add__divide__distrib) # label(axiom). [clausify(511)].
% 5.01/5.24 1464 -class_Rings_Odivision__ring(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_diff__divide__distrib) # label(axiom). [clausify(513)].
% 5.01/5.24 1465 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) | C = B # label(fact_right__inverse__eq) # label(axiom). [clausify(525)].
% 5.01/5.24 1466 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) | C != B # label(fact_right__inverse__eq) # label(axiom). [clausify(525)].
% 5.01/5.24 1467 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),B) # label(fact_divide__self) # label(axiom). [clausify(526)].
% 5.01/5.24 1468 -class_Rings_Odivision__ring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) # label(fact_times__divide__eq__right) # label(axiom). [clausify(622)].
% 5.01/5.24 1469 -class_Rings_Odivision__ring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) # label(fact_divide__inverse) # label(axiom). [clausify(623)].
% 5.01/5.24 1470 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_nonzero__inverse__mult__distrib) # label(axiom). [clausify(638)].
% 5.01/5.24 1471 -class_Rings_Odivision__ring(A) | hAPP(c_Rings_Oinverse__class_Oinverse(A),B) != hAPP(c_Rings_Oinverse__class_Oinverse(A),C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | B = C # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(658)].
% 5.01/5.24 1472 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Rings_Oinverse__class_Oinverse(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__zero__imp__zero) # label(axiom). [clausify(659)].
% 5.01/5.24 1473 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) = B # label(fact_nonzero__inverse__inverse__eq) # label(axiom). [clausify(660)].
% 5.01/5.24 1474 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Rings_Oinverse__class_Oinverse(A),B) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom). [clausify(661)].
% 5.01/5.24 1475 -class_Rings_Odivision__ring(A) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | hAPP(c_Rings_Oinverse__class_Oinverse(A),B) = C # label(fact_inverse__unique) # label(axiom). [clausify(690)].
% 5.01/5.24 1476 -class_Rings_Odivision__ring(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Rings_Oinverse__class_Oinverse(A),c_Groups_Oone__class_Oone(A)) # label(fact_inverse__1) # label(axiom). [clausify(691)].
% 5.01/5.24 1477 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_right__inverse) # label(axiom). [clausify(697)].
% 5.01/5.24 1478 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),B) # label(fact_left__inverse) # label(axiom). [clausify(698)].
% 5.01/5.24 1479 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) # label(fact_division__ring__inverse__add) # label(axiom). [clausify(706)].
% 5.01/5.24 1480 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B))),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) # label(fact_division__ring__inverse__diff) # label(axiom). [clausify(707)].
% 5.01/5.24 1481 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),C) # label(fact_nonzero__power__inverse) # label(axiom). [clausify(720)].
% 5.01/5.24 1482 -class_Rings_Odivision__ring(A) | hAPP(c_Rings_Oinverse__class_Oinverse(A),B) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_inverse__eq__divide) # label(axiom). [clausify(723)].
% 5.01/5.24 1483 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B) != D | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B) = C # label(fact_eq__divide__imp) # label(axiom). [clausify(767)].
% 5.01/5.24 1484 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B) != D | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B) = C # label(fact_divide__eq__imp) # label(axiom). [clausify(768)].
% 5.01/5.24 1485 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(769)].
% 5.01/5.24 1486 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(769)].
% 5.01/5.24 1487 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(770)].
% 5.01/5.24 1488 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(770)].
% 5.01/5.24 1489 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(c_Rings_Oinverse__class_Oinverse(A),B) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_nonzero__inverse__eq__divide) # label(axiom). [clausify(800)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A). [resolve(1460,a,1461,a)].
% 5.01/5.24 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1460,a,1462,a)].
% 5.01/5.24 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1460,a,1463,a)].
% 5.01/5.24 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1460,a,1464,a)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A) | B = A. [resolve(1460,a,1465,a)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A) | B != A. [resolve(1460,a,1466,a)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),A). [resolve(1460,a,1467,a)].
% 5.01/5.24 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C). [resolve(1460,a,1468,a)].
% 5.01/5.24 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B). [resolve(1460,a,1469,a)].
% 5.01/5.24 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1460,a,1470,a)].
% 5.01/5.24 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) != hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | A = B. [resolve(1460,a,1471,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1460,a,1472,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) = A. [resolve(1460,a,1473,a)].
% 5.01/5.25 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) = B. [resolve(1460,a,1475,a)].
% 5.01/5.25 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1460,a,1476,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1460,a,1477,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),A). [resolve(1460,a,1478,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)). [resolve(1460,a,1479,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),A))),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)). [resolve(1460,a,1480,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),B). [resolve(1460,a,1481,a)].
% 5.01/5.25 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). [resolve(1460,a,1482,a)].
% 5.01/5.25 1490 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom). [assumption].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A). [resolve(1490,a,1461,a)].
% 5.01/5.25 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1490,a,1462,a)].
% 5.01/5.25 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(1490,a,1463,a)].
% 5.01/5.25 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(1490,a,1464,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A) | B = A. [resolve(1490,a,1465,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A) | B != A. [resolve(1490,a,1466,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A). [resolve(1490,a,1467,a)].
% 5.01/5.25 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C). [resolve(1490,a,1468,a)].
% 5.01/5.25 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B). [resolve(1490,a,1469,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)). [resolve(1490,a,1470,a)].
% 5.01/5.25 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | A = B. [resolve(1490,a,1471,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1490,a,1472,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A. [resolve(1490,a,1473,a)].
% 5.01/5.25 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = B. [resolve(1490,a,1475,a)].
% 5.01/5.25 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1490,a,1476,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)). [resolve(1490,a,1477,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),A). [resolve(1490,a,1478,a)].
% 5.01/5.25 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(1490,a,1479,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A))),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(1490,a,1480,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),B). [resolve(1490,a,1481,a)].
% 5.12/5.38 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(1490,a,1482,a)].
% 5.12/5.38 1491 class_Fields_Ofield(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield) # label(axiom). [assumption].
% 5.12/5.38 1492 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)),D) # label(fact_nonzero__power__divide) # label(axiom). [clausify(528)].
% 5.12/5.38 1493 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),D),C)) # label(fact_power__diff) # label(axiom). [clausify(535)].
% 5.12/5.38 1494 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(c_Rings_Oinverse__class_Oinverse(A),B))),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) # label(fact_inverse__add) # label(axiom). [clausify(614)].
% 5.12/5.38 1495 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)),B) # label(fact_field__inverse) # label(axiom). [clausify(615)].
% 5.12/5.38 1496 -class_Fields_Ofield(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Rings_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C) # label(fact_field__divide__inverse) # label(axiom). [clausify(620)].
% 5.12/5.38 1497 -class_Fields_Ofield(A) | hAPP(c_Rings_Oinverse__class_Oinverse(A),B) = hAPP(hAPP(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(722)].
% 5.12/5.38 1498 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),E),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C) # label(fact_frac__eq__eq) # label(axiom). [clausify(771)].
% 5.12/5.38 1499 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),E),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C) # label(fact_frac__eq__eq) # label(axiom). [clausify(771)].
% 5.12/5.38 1500 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),E),C)) # label(fact_add__frac__eq) # label(axiom). [clausify(830)].
% 5.12/5.38 1501 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)),D) # label(fact_divide__add__eq__iff) # label(axiom). [clausify(831)].
% 5.12/5.38 1502 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) # label(fact_add__divide__eq__iff) # label(axiom). [clausify(833)].
% 5.12/5.38 1503 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),E),C)) # label(fact_diff__frac__eq) # label(axiom). [clausify(839)].
% 5.12/5.38 1504 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)),D) # label(fact_divide__diff__eq__iff) # label(axiom). [clausify(840)].
% 5.12/5.38 1505 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) # label(fact_diff__divide__eq__iff) # label(axiom). [clausify(841)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)). [resolve(1491,a,1493,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A))),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)). [resolve(1491,a,1494,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),B) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),D),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B). [resolve(1491,a,1498,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),B) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),D),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B). [resolve(1491,a,1499,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),D),B)). [resolve(1491,a,1500,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A)),C). [resolve(1491,a,1501,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)). [resolve(1491,a,1502,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),D),B)). [resolve(1491,a,1503,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))),A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A)),C). [resolve(1491,a,1504,a)].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C)),A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)). [resolve(1491,a,1505,a)].
% 5.12/5.38 1506 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom). [assumption].
% 5.12/5.38 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)). [resolve(1506,a,1493,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A))),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(1506,a,1494,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B). [resolve(1506,a,1498,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B). [resolve(1506,a,1499,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),A)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),B)). [resolve(1506,a,1500,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A)),C). [resolve(1506,a,1501,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),A)). [resolve(1506,a,1502,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),A)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),B)). [resolve(1506,a,1503,a)].
% 5.12/5.39 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A)),C). [resolve(1506,a,1504,a)].
% 5.32/5.52 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C)),A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),A)). [resolve(1506,a,1505,a)].
% 5.32/5.52 1507 -class_Fields_Ofield(A) | class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [clausify(1007)].
% 5.32/5.52 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1507,a,1491,a)].
% 5.32/5.52 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1507,a,1506,a)].
% 5.32/5.52 1508 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 5.32/5.52 1509 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(c_Groups_Oabs__class_Oabs(A),C)),B) # label(fact_abs__div__pos) # label(axiom). [clausify(536)].
% 5.32/5.52 1510 -class_Fields_Olinordered__field__inverse__zero(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__divide) # label(axiom). [clausify(540)].
% 5.32/5.52 1511 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(541)].
% 5.32/5.52 1512 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(541)].
% 5.32/5.52 1513 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(541)].
% 5.32/5.52 1514 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(541)].
% 5.32/5.52 1515 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(541)].
% 5.32/5.52 1516 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(541)].
% 5.32/5.52 1517 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(542)].
% 5.32/5.52 1518 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(542)].
% 5.32/5.52 1519 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(542)].
% 5.32/5.52 1520 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(542)].
% 5.32/5.52 1521 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(542)].
% 5.32/5.52 1522 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(542)].
% 5.32/5.52 1523 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_divide__right__mono) # label(axiom). [clausify(543)].
% 5.32/5.52 1524 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D)) # label(fact_divide__right__mono__neg) # label(axiom). [clausify(544)].
% 5.32/5.52 1525 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(545)].
% 5.32/5.52 1526 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(545)].
% 5.32/5.52 1527 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(545)].
% 5.32/5.52 1528 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(545)].
% 5.32/5.52 1529 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(545)].
% 5.32/5.52 1530 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(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(545)].
% 5.32/5.52 1531 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(546)].
% 5.32/5.52 1532 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(546)].
% 5.32/5.52 1533 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(546)].
% 5.32/5.52 1534 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(546)].
% 5.32/5.52 1535 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(546)].
% 5.32/5.52 1536 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(546)].
% 5.32/5.52 1537 -class_Fields_Olinordered__field__inverse__zero(A) | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_abs__inverse) # label(axiom). [clausify(625)].
% 5.32/5.52 1538 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(708)].
% 5.32/5.52 1539 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(708)].
% 5.32/5.52 1540 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(709)].
% 5.32/5.52 1541 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(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(709)].
% 5.32/5.52 1542 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(710)].
% 5.32/5.52 1543 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(710)].
% 5.32/5.52 1544 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(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(711)].
% 5.32/5.52 1545 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(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(711)].
% 5.32/5.52 1546 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(797)].
% 5.32/5.52 1547 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(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(797)].
% 5.32/5.52 1548 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(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(797)].
% 5.32/5.52 1549 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(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(798)].
% 5.32/5.52 1550 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(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(798)].
% 5.32/5.52 1551 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(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(798)].
% 5.32/5.52 1552 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_less__divide__eq) # label(axiom). [clausify(819)].
% 5.32/5.52 1553 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_less__divide__eq) # label(axiom). [clausify(819)].
% 5.32/5.52 1554 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(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(819)].
% 5.32/5.52 1555 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(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(819)].
% 5.32/5.52 1556 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(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(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(819)].
% 5.32/5.52 1557 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(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(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(819)].
% 5.32/5.52 1558 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless(A,hAPP(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(819)].
% 5.32/5.52 1559 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless(A,hAPP(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(819)].
% 5.32/5.52 1560 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(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(819)].
% 5.32/5.52 1561 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(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(819)].
% 5.32/5.52 1562 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_divide__less__eq) # label(axiom). [clausify(820)].
% 5.32/5.52 1563 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) # label(fact_divide__less__eq) # label(axiom). [clausify(820)].
% 5.32/5.52 1564 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(820)].
% 5.32/5.52 1565 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(820)].
% 5.32/5.52 1566 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(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(820)].
% 5.32/5.52 1567 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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(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(820)].
% 5.32/5.52 1568 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(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(820)].
% 5.32/5.52 1569 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(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(820)].
% 5.32/5.52 1570 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(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(820)].
% 5.32/5.52 1571 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(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(820)].
% 5.32/5.52 1572 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,hAPP(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(850)].
% 5.32/5.52 1573 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(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(850)].
% 5.32/5.52 1574 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,hAPP(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(850)].
% 5.32/5.52 1575 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),hAPP(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(851)].
% 5.32/5.52 1576 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),hAPP(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(851)].
% 5.32/5.52 1577 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),hAPP(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(851)].
% 5.32/5.52 1578 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C)) # label(fact_divide__left__mono__neg) # label(axiom). [clausify(853)].
% 5.32/5.52 1579 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_divide__le__eq) # label(axiom). [clausify(861)].
% 5.32/5.52 1580 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) # label(fact_divide__le__eq) # label(axiom). [clausify(861)].
% 5.32/5.52 1581 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(861)].
% 5.32/5.52 1582 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(861)].
% 5.32/5.52 1583 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(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(861)].
% 5.32/5.52 1584 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(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(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(861)].
% 5.32/5.52 1585 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(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(861)].
% 5.32/5.52 1586 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(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(861)].
% 5.32/5.52 1587 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(861)].
% 5.32/5.52 1588 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(861)].
% 5.32/5.52 1589 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_le__divide__eq) # label(axiom). [clausify(862)].
% 5.32/5.52 1590 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_le__divide__eq) # label(axiom). [clausify(862)].
% 5.32/5.52 1591 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(862)].
% 5.32/5.52 1592 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(862)].
% 5.32/5.52 1593 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(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(862)].
% 5.32/5.52 1594 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(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(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(862)].
% 5.32/5.52 1595 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(862)].
% 5.32/5.52 1596 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(862)].
% 5.32/5.52 1597 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(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(862)].
% 5.32/5.52 1598 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(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(862)].
% 5.32/5.52 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)),A). [resolve(1508,a,1509,a)].
% 5.32/5.52 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(1508,a,1510,a)].
% 5.32/5.52 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1512,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1513,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1515,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1516,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1518,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1519,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1521,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1522,a)].
% 5.32/5.53 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1508,a,1523,a)].
% 5.32/5.53 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C)). [resolve(1508,a,1524,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1525,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1526,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1527,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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(1508,a,1528,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). [resolve(1508,a,1529,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1530,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1531,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1532,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1533,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1534,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1535,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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,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). [resolve(1508,a,1536,a)].
% 5.32/5.53 Derived: hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1508,a,1537,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1508,a,1538,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1508,a,1539,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1540,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1541,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1508,a,1542,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1508,a,1543,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(1508,a,1544,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(1508,a,1545,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1546,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1547,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1548,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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(1508,a,1549,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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(1508,a,1550,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1508,a,1551,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B). [resolve(1508,a,1552,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1508,a,1553,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(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(1508,a,1554,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(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(1508,a,1555,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1556,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(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(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(1508,a,1557,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1508,a,1558,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(1508,a,1559,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)). [resolve(1508,a,1562,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A). [resolve(1508,a,1563,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1564,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1565,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1566,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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(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(1508,a,1567,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(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). [resolve(1508,a,1568,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(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(1508,a,1569,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(1508,a,1572,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(1508,a,1573,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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(1508,a,1574,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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(1508,a,1575,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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(1508,a,1576,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1508,a,1577,a)].
% 5.32/5.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),B)). [resolve(1508,a,1578,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)). [resolve(1508,a,1579,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A). [resolve(1508,a,1580,a)].
% 5.32/5.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1581,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(1508,a,1582,a)].
% 5.32/5.53 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1583,a)].
% 5.32/5.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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(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(1508,a,1584,a)].
% 5.32/5.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(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). [resolve(1508,a,1585,a)].
% 5.32/5.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(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(1508,a,1586,a)].
% 5.32/5.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1587,a)].
% 5.32/5.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1588,a)].
% 5.32/5.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B). [resolve(1508,a,1589,a)].
% 5.32/5.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(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,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1508,a,1590,a)].
% 5.32/5.54 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(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(1508,a,1591,a)].
% 5.32/5.54 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(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(1508,a,1592,a)].
% 5.44/5.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1593,a)].
% 5.44/5.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(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(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(1508,a,1594,a)].
% 5.44/5.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C). [resolve(1508,a,1595,a)].
% 5.44/5.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1508,a,1596,a)].
% 5.44/5.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1508,a,1597,a)].
% 5.44/5.67 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(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(1508,a,1598,a)].
% 5.44/5.67 1599 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption].
% 5.44/5.67 1600 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(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(537)].
% 5.44/5.67 1601 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,B,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(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(538)].
% 5.44/5.67 1602 -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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) # label(fact_divide__nonpos__neg) # label(axiom). [clausify(539)].
% 5.44/5.67 1603 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) # label(fact_divide__pos__pos) # label(axiom). [clausify(547)].
% 5.44/5.67 1604 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__pos__neg) # label(axiom). [clausify(548)].
% 5.44/5.67 1605 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__neg__pos) # label(axiom). [clausify(549)].
% 5.44/5.67 1606 -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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) # label(fact_divide__neg__neg) # label(axiom). [clausify(550)].
% 5.44/5.67 1607 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_divide__strict__right__mono) # label(axiom). [clausify(551)].
% 5.44/5.67 1608 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),D)) # label(fact_divide__strict__right__mono__neg) # label(axiom). [clausify(552)].
% 5.44/5.67 1609 -class_Fields_Olinordered__field(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(c_Groups_Oabs__class_Oabs(A),C)),hAPP(c_Groups_Oabs__class_Oabs(A),B)) # label(fact_nonzero__abs__divide) # label(axiom). [clausify(553)].
% 5.44/5.67 1610 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C)) # label(fact_divide__nonneg__pos) # label(axiom). [clausify(554)].
% 5.44/5.67 1611 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__nonneg__neg) # label(axiom). [clausify(555)].
% 5.44/5.67 1612 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),E),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_frac__less2) # label(axiom). [clausify(556)].
% 5.44/5.67 1613 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),E),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_frac__less) # label(axiom). [clausify(557)].
% 5.44/5.67 1614 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),E),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_frac__le) # label(axiom). [clausify(558)].
% 5.44/5.67 1615 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__nonpos__pos) # label(axiom). [clausify(559)].
% 5.44/5.67 1616 -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),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_positive__imp__inverse__positive) # label(axiom). [clausify(712)].
% 5.44/5.67 1617 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(713)].
% 5.44/5.67 1618 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,hAPP(c_Rings_Oinverse__class_Oinverse(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_negative__imp__inverse__negative) # label(axiom). [clausify(714)].
% 5.44/5.67 1619 -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,hAPP(c_Rings_Oinverse__class_Oinverse(A),C),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_less__imp__inverse__less) # label(axiom). [clausify(715)].
% 5.44/5.67 1620 -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,hAPP(c_Rings_Oinverse__class_Oinverse(A),C),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_less__imp__inverse__less__neg) # label(axiom). [clausify(716)].
% 5.44/5.67 1621 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,hAPP(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(717)].
% 5.44/5.67 1622 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Rings_Oinverse__class_Oinverse(A),B),hAPP(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(718)].
% 5.44/5.67 1623 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,hAPP(c_Rings_Oinverse__class_Oinverse(A),B),hAPP(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(719)].
% 5.44/5.67 1624 -class_Fields_Olinordered__field(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(c_Rings_Oinverse__class_Oinverse(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_nonzero__abs__inverse) # label(axiom). [clausify(721)].
% 5.44/5.67 1625 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Rings_Oinverse__class_Oinverse(A),B),hAPP(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(793)].
% 5.44/5.67 1626 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Rings_Oinverse__class_Oinverse(A),B),hAPP(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(794)].
% 5.44/5.67 1627 -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,hAPP(c_Rings_Oinverse__class_Oinverse(A),C),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_le__imp__inverse__le__neg) # label(axiom). [clausify(795)].
% 5.44/5.67 1628 -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,hAPP(c_Rings_Oinverse__class_Oinverse(A),C),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_le__imp__inverse__le) # label(axiom). [clausify(796)].
% 5.44/5.67 1629 -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),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_one__less__inverse) # label(axiom). [clausify(799)].
% 5.44/5.67 1630 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(821)].
% 5.44/5.67 1631 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__less__divide__eq) # label(axiom). [clausify(821)].
% 5.44/5.67 1632 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__less__eq) # label(axiom). [clausify(822)].
% 5.44/5.67 1633 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | -c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__less__eq) # label(axiom). [clausify(822)].
% 5.44/5.67 1634 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) # label(fact_mult__imp__div__pos__less) # label(axiom). [clausify(823)].
% 5.44/5.67 1635 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) | c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) # label(fact_mult__imp__less__div__pos) # label(axiom). [clausify(824)].
% 5.44/5.67 1636 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | c_Orderings_Oord__class_Oless(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__less__divide__eq) # label(axiom). [clausify(825)].
% 5.44/5.67 1637 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | -c_Orderings_Oord__class_Oless(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__less__divide__eq) # label(axiom). [clausify(825)].
% 5.44/5.67 1638 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(826)].
% 5.44/5.67 1639 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__less__eq) # label(axiom). [clausify(826)].
% 5.44/5.67 1640 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) # label(fact_divide__strict__left__mono) # label(axiom). [clausify(827)].
% 5.44/5.67 1641 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C)) # label(fact_divide__strict__left__mono__neg) # label(axiom). [clausify(828)].
% 5.44/5.67 1642 -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),hAPP(c_Rings_Oinverse__class_Oinverse(A),B)) # label(fact_one__le__inverse) # label(axiom). [clausify(849)].
% 5.44/5.67 1643 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) # label(fact_divide__left__mono) # label(axiom). [clausify(854)].
% 5.44/5.67 1644 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__le__eq) # label(axiom). [clausify(855)].
% 5.44/5.67 1645 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__le__eq) # label(axiom). [clausify(855)].
% 5.44/5.67 1646 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | c_Orderings_Oord__class_Oless__eq(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__le__divide__eq) # label(axiom). [clausify(856)].
% 5.44/5.67 1647 -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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | -c_Orderings_Oord__class_Oless__eq(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__le__divide__eq) # label(axiom). [clausify(856)].
% 5.44/5.67 1648 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) | c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) # label(fact_mult__imp__le__div__pos) # label(axiom). [clausify(857)].
% 5.44/5.67 1649 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) # label(fact_mult__imp__div__pos__le) # label(axiom). [clausify(858)].
% 5.44/5.67 1650 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(859)].
% 5.44/5.67 1651 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),C),B),D) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__le__eq) # label(axiom). [clausify(859)].
% 5.44/5.67 1652 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(860)].
% 5.44/5.67 1653 -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(hAPP(c_Rings_Oinverse__class_Odivide(A),D),B)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__le__divide__eq) # label(axiom). [clausify(860)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(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(1599,a,1600,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(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(1599,a,1601,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)). [resolve(1599,a,1602,a)].
% 5.44/5.67 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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1599,a,1607,a)].
% 5.44/5.67 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),C)). [resolve(1599,a,1608,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B)). [resolve(1599,a,1610,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1599,a,1611,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1599,a,1612,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1599,a,1613,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),D),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1599,a,1614,a)].
% 5.44/5.67 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1599,a,1615,a)].
% 5.44/5.67 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,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1599,a,1619,a)].
% 5.44/5.67 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,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1599,a,1620,a)].
% 5.44/5.68 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(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(1599,a,1622,a)].
% 5.44/5.68 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(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(1599,a,1623,a)].
% 5.44/5.68 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(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(1599,a,1625,a)].
% 5.44/5.68 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(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(1599,a,1626,a)].
% 5.44/5.68 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,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1599,a,1627,a)].
% 5.44/5.68 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,hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)). [resolve(1599,a,1628,a)].
% 5.44/5.68 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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)). [resolve(1599,a,1636,a)].
% 5.44/5.68 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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)). [resolve(1599,a,1637,a)].
% 5.44/5.68 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B). [resolve(1599,a,1638,a)].
% 5.44/5.68 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B). [resolve(1599,a,1639,a)].
% 5.44/5.68 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)). [resolve(1599,a,1640,a)].
% 5.61/5.81 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),B)). [resolve(1599,a,1641,a)].
% 5.61/5.81 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)). [resolve(1599,a,1643,a)].
% 5.61/5.81 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B). [resolve(1599,a,1644,a)].
% 5.61/5.81 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(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B). [resolve(1599,a,1645,a)].
% 5.61/5.81 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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)). [resolve(1599,a,1646,a)].
% 5.61/5.81 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,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)). [resolve(1599,a,1647,a)].
% 5.61/5.81 1654 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 5.61/5.81 1655 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self1) # label(axiom). [clausify(577)].
% 5.61/5.81 1656 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__0) # label(axiom). [clausify(598)].
% 5.61/5.81 1657 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__by__0) # label(axiom). [clausify(599)].
% 5.61/5.81 1658 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_div__by__1) # label(axiom). [clausify(600)].
% 5.61/5.81 1659 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_div__self) # label(axiom). [clausify(603)].
% 5.61/5.81 1660 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self2) # label(axiom). [clausify(605)].
% 5.61/5.81 1661 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult1) # label(axiom). [clausify(776)].
% 5.61/5.81 1662 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult2) # label(axiom). [clausify(777)].
% 5.61/5.81 1663 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = C # label(fact_div__mult__self1__is__id) # label(axiom). [clausify(778)].
% 5.61/5.81 1664 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),B) = C # label(fact_div__mult__self2__is__id) # label(axiom). [clausify(779)].
% 5.61/5.81 1665 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__mult__mult1__if) # label(axiom). [clausify(780)].
% 5.61/5.81 1666 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult1__if) # label(axiom). [clausify(780)].
% 5.61/5.81 1667 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__self2) # label(axiom). [clausify(842)].
% 5.61/5.81 1668 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__self1) # label(axiom). [clausify(843)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1654,a,1655,a)].
% 5.61/5.81 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1654,a,1656,a)].
% 5.61/5.81 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1654,a,1657,a)].
% 5.61/5.81 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1654,a,1658,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1654,a,1659,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1654,a,1660,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C). [resolve(1654,a,1661,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C). [resolve(1654,a,1662,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = B. [resolve(1654,a,1663,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),A) = B. [resolve(1654,a,1664,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1654,a,1665,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1654,a,1667,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1654,a,1668,a)].
% 5.61/5.81 1669 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1669,a,1655,a)].
% 5.61/5.81 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1669,a,1656,a)].
% 5.61/5.81 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1669,a,1657,a)].
% 5.61/5.81 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1669,a,1658,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,A) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1669,a,1659,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1669,a,1660,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C). [resolve(1669,a,1661,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C). [resolve(1669,a,1662,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = B. [resolve(1669,a,1663,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),A) = B. [resolve(1669,a,1664,a)].
% 5.61/5.81 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1669,a,1665,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1669,a,1667,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1669,a,1668,a)].
% 5.61/5.87 1670 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1507,a,1491,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))). [resolve(1670,a,1655,a)].
% 5.61/5.87 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1670,a,1656,a)].
% 5.61/5.87 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1670,a,1657,a)].
% 5.61/5.87 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = A. [resolve(1670,a,1658,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1670,a,1659,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))). [resolve(1670,a,1660,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C). [resolve(1670,a,1661,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C). [resolve(1670,a,1662,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = B. [resolve(1670,a,1663,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),A) = B. [resolve(1670,a,1664,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(1670,a,1665,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)). [resolve(1670,a,1667,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)). [resolve(1670,a,1668,a)].
% 5.61/5.87 1671 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1507,a,1506,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(1671,a,1655,a)].
% 5.61/5.87 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1671,a,1656,a)].
% 5.61/5.87 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1671,a,1657,a)].
% 5.61/5.87 Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = A. [resolve(1671,a,1658,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1671,a,1659,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(1671,a,1660,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1671,a,1661,a)].
% 5.61/5.87 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1671,a,1662,a)].
% 5.73/5.93 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),A) = B. [resolve(1671,a,1663,a)].
% 5.73/5.93 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),A) = B. [resolve(1671,a,1664,a)].
% 5.73/5.93 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1671,a,1665,a)].
% 5.73/5.93 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)). [resolve(1671,a,1667,a)].
% 5.73/5.93 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)). [resolve(1671,a,1668,a)].
% 5.73/5.93 1672 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.73/5.93 1673 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C) # label(fact_power__mult__distrib) # label(axiom). [clausify(631)].
% 5.73/5.93 1674 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1) # label(axiom). [clausify(693)].
% 5.73/5.93 1675 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom). [clausify(695)].
% 5.73/5.93 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(1672,a,1673,a)].
% 5.73/5.93 1676 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.73/5.93 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),B). [resolve(1676,a,1673,a)].
% 5.73/5.93 1677 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.82/6.06 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),B). [resolve(1677,a,1673,a)].
% 5.82/6.06 1678 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.82/6.06 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(1678,a,1673,a)].
% 5.82/6.06 1679 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) # label(axiom). [clausify(998)].
% 5.82/6.06 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),C). [resolve(1679,b,1673,a)].
% 5.82/6.06 1680 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 5.82/6.06 1681 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(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(651)].
% 5.82/6.06 1682 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(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(651)].
% 5.82/6.06 1683 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(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(651)].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(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(1680,a,1681,a)].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1680,a,1682,a)].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1680,a,1683,a)].
% 5.82/6.06 1684 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(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(1684,a,1681,a)].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1684,a,1682,a)].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1684,a,1683,a)].
% 5.82/6.06 1685 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 5.82/6.06 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(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(1685,a,1681,a)].
% 6.00/6.19 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1685,a,1682,a)].
% 6.00/6.19 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1685,a,1683,a)].
% 6.00/6.19 1686 -class_Rings_Oidom(A) | class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) # label(axiom). [clausify(990)].
% 6.00/6.19 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1686,b,1681,a)].
% 6.00/6.19 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1686,b,1682,a)].
% 6.00/6.19 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1686,b,1683,a)].
% 6.00/6.19 1687 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 6.00/6.19 1688 -class_Groups_Oab__semigroup__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(670)].
% 6.00/6.19 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(1687,a,1688,a)].
% 6.00/6.19 1689 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 6.00/6.19 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1689,a,1688,a)].
% 6.00/6.19 1690 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 6.00/6.19 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(1690,a,1688,a)].
% 6.00/6.19 1691 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 6.00/6.19 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(1691,a,1688,a)].
% 6.00/6.19 1692 -class_Rings_Ocomm__semiring__0(A) | class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) # label(axiom). [clausify(997)].
% 6.00/6.19 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(1692,b,1688,a)].
% 6.21/6.44 1693 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 6.21/6.44 1694 -class_Rings_Osemiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),E)) # label(fact_combine__common__factor) # label(axiom). [clausify(682)].
% 6.21/6.44 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),D)). [resolve(1693,a,1694,a)].
% 6.21/6.44 1695 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 6.21/6.44 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),D)). [resolve(1695,a,1694,a)].
% 6.21/6.44 1696 class_Rings_Osemiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring) # label(axiom). [assumption].
% 6.21/6.44 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)),D)). [resolve(1696,a,1694,a)].
% 6.21/6.44 1697 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom). [assumption].
% 6.21/6.44 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)),D)). [resolve(1697,a,1694,a)].
% 6.21/6.44 1698 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom). [clausify(1020)].
% 6.21/6.44 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)),E)). [resolve(1698,b,1694,a)].
% 6.21/6.44 1699 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 6.21/6.44 1700 -class_Rings_Ocomm__semiring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(683)].
% 6.21/6.44 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(1699,a,1700,a)].
% 6.34/6.57 1701 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 6.34/6.57 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1701,a,1700,a)].
% 6.34/6.57 1702 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 6.34/6.57 1703 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 6.34/6.57 1704 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1008)].
% 6.34/6.57 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(1704,b,1700,a)].
% 6.34/6.57 1705 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.34/6.57 1706 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(724)].
% 6.34/6.57 1707 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(724)].
% 6.34/6.57 1708 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonpos__nonneg) # label(axiom). [clausify(734)].
% 6.34/6.57 1709 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos2) # label(axiom). [clausify(735)].
% 6.34/6.57 1710 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos) # label(axiom). [clausify(736)].
% 6.34/6.57 1711 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__nonneg__nonneg) # label(axiom). [clausify(737)].
% 6.34/6.57 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_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1705,a,1706,a)].
% 6.34/6.57 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_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1705,a,1707,a)].
% 6.34/6.57 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,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)). [resolve(1705,a,1711,a)].
% 6.34/6.57 1712 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.34/6.57 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1712,a,1706,a)].
% 6.34/6.57 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1712,a,1707,a)].
% 6.34/6.57 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)). [resolve(1712,a,1711,a)].
% 6.34/6.57 1713 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.34/6.57 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_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1713,a,1706,a)].
% 6.34/6.57 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_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1713,a,1707,a)].
% 6.34/6.57 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1713,a,1711,a)].
% 6.34/6.57 1714 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) # label(axiom). [clausify(988)].
% 6.34/6.57 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1714,b,1706,a)].
% 6.51/6.69 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1714,b,1707,a)].
% 6.51/6.69 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)). [resolve(1714,b,1711,a)].
% 6.51/6.69 1715 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 6.51/6.69 1716 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(725)].
% 6.51/6.69 1717 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(725)].
% 6.51/6.69 1718 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_mult__left__mono__neg) # label(axiom). [clausify(728)].
% 6.51/6.69 1719 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult__right__mono__neg) # label(axiom). [clausify(729)].
% 6.51/6.69 1720 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__nonpos__nonpos) # label(axiom). [clausify(733)].
% 6.51/6.69 1721 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | c_Orderings_Oord__class_Oless__eq(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F)) # label(fact_le__add__iff2) # label(axiom). [clausify(815)].
% 6.51/6.69 1722 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | -c_Orderings_Oord__class_Oless__eq(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F)) # label(fact_le__add__iff2) # label(axiom). [clausify(815)].
% 6.51/6.69 1723 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D),F) # label(fact_le__add__iff1) # label(axiom). [clausify(816)].
% 6.51/6.69 1724 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D),F) # label(fact_le__add__iff1) # label(axiom). [clausify(816)].
% 6.51/6.69 1725 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | c_Orderings_Oord__class_Oless(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F)) # label(fact_less__add__iff2) # label(axiom). [clausify(817)].
% 6.51/6.69 1726 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | -c_Orderings_Oord__class_Oless(A,D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F)) # label(fact_less__add__iff2) # label(axiom). [clausify(817)].
% 6.51/6.69 1727 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D),F) # label(fact_less__add__iff1) # label(axiom). [clausify(818)].
% 6.51/6.69 1728 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D),F) # label(fact_less__add__iff1) # label(axiom). [clausify(818)].
% 6.51/6.69 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_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)). [resolve(1715,a,1717,a)].
% 6.51/6.69 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)). [resolve(1715,a,1718,a)].
% 6.51/6.69 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(1715,a,1719,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E)). [resolve(1715,a,1721,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E)). [resolve(1715,a,1722,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),E). [resolve(1715,a,1723,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),E). [resolve(1715,a,1724,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E)). [resolve(1715,a,1725,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E)). [resolve(1715,a,1726,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),E). [resolve(1715,a,1727,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),E). [resolve(1715,a,1728,a)].
% 6.51/6.70 1729 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom). [assumption].
% 6.51/6.70 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_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1729,a,1717,a)].
% 6.51/6.70 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)). [resolve(1729,a,1718,a)].
% 6.51/6.70 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1729,a,1719,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E)). [resolve(1729,a,1721,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E)). [resolve(1729,a,1722,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C),E). [resolve(1729,a,1723,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C),E). [resolve(1729,a,1724,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E)). [resolve(1729,a,1725,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E)). [resolve(1729,a,1726,a)].
% 6.51/6.70 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C),E). [resolve(1729,a,1727,a)].
% 6.51/6.70 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C),E). [resolve(1729,a,1728,a)].
% 6.51/6.70 1730 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom). [clausify(1011)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)). [resolve(1730,b,1717,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)). [resolve(1730,b,1718,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)). [resolve(1730,b,1719,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F)). [resolve(1730,b,1721,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F)). [resolve(1730,b,1722,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D),F). [resolve(1730,b,1723,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D),F). [resolve(1730,b,1724,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F)). [resolve(1730,b,1725,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F)). [resolve(1730,b,1726,a)].
% 6.51/6.70 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D),F). [resolve(1730,b,1727,a)].
% 6.65/6.83 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D),F). [resolve(1730,b,1728,a)].
% 6.65/6.83 1731 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.65/6.83 1732 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__mono) # label(axiom). [clausify(726)].
% 6.65/6.83 1733 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__mono_H) # label(axiom). [clausify(727)].
% 6.65/6.83 1734 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_mult__left__mono) # label(axiom). [clausify(731)].
% 6.65/6.83 1735 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__right__mono) # label(axiom). [clausify(732)].
% 6.65/6.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(1731,a,1732,a)].
% 6.65/6.83 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(1731,a,1733,a)].
% 6.65/6.83 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)). [resolve(1731,a,1734,a)].
% 6.65/6.83 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(1731,a,1735,a)].
% 6.65/6.84 1736 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(1736,a,1732,a)].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(1736,a,1733,a)].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)). [resolve(1736,a,1734,a)].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1736,a,1735,a)].
% 6.65/6.84 1737 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1737,a,1732,a)].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1737,a,1733,a)].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)). [resolve(1737,a,1734,a)].
% 6.65/6.84 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(1737,a,1735,a)].
% 6.65/6.84 1738 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom). [clausify(1000)].
% 6.65/6.84 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)). [resolve(1738,b,1732,a)].
% 6.89/7.09 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)). [resolve(1738,b,1733,a)].
% 6.89/7.09 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)). [resolve(1738,b,1734,a)].
% 6.89/7.09 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(1738,b,1735,a)].
% 6.89/7.09 1739 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.89/7.09 1740 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_comm__mult__left__mono) # label(axiom). [clausify(730)].
% 6.89/7.09 1741 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.89/7.09 1742 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.89/7.09 1743 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) # label(axiom). [clausify(991)].
% 6.89/7.09 1744 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 6.89/7.09 1745 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(738)].
% 6.89/7.09 1746 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(738)].
% 6.89/7.09 1747 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(738)].
% 6.89/7.09 1748 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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(738)].
% 6.89/7.09 1749 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(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(738)].
% 6.89/7.09 1750 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(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(738)].
% 6.89/7.09 1751 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(739)].
% 6.89/7.09 1752 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(739)].
% 6.89/7.09 1753 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(739)].
% 6.89/7.09 1754 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(739)].
% 6.89/7.09 1755 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(739)].
% 6.89/7.09 1756 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(739)].
% 6.89/7.09 1757 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(741)].
% 6.89/7.09 1758 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(742)].
% 6.89/7.09 1759 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__neg__neg) # label(axiom). [clausify(746)].
% 6.89/7.09 1760 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(748)].
% 6.89/7.09 1761 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(748)].
% 6.89/7.09 1762 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(754)].
% 6.89/7.09 1763 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(754)].
% 6.89/7.09 1764 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(755)].
% 6.89/7.09 1765 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(755)].
% 6.89/7.09 1766 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(755)].
% 6.89/7.09 1767 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(755)].
% 6.89/7.09 1768 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(755)].
% 6.89/7.09 1769 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(755)].
% 6.89/7.09 1770 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(756)].
% 6.89/7.09 1771 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(756)].
% 6.89/7.09 1772 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(756)].
% 6.89/7.09 1773 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(756)].
% 6.89/7.09 1774 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(756)].
% 6.89/7.09 1775 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(756)].
% 6.89/7.09 1776 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(811)].
% 6.89/7.09 1777 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(811)].
% 6.89/7.09 1778 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(812)].
% 6.89/7.09 1779 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(812)].
% 6.89/7.09 1780 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(942)].
% 6.89/7.09 1781 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(942)].
% 6.89/7.09 1782 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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__eq__zero__iff) # label(axiom). [clausify(942)].
% 6.89/7.09 1783 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(943)].
% 6.89/7.09 1784 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(943)].
% 6.89/7.09 1785 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(943)].
% 6.89/7.09 1786 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(945)].
% 6.89/7.09 1787 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(945)].
% 6.89/7.09 1788 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(945)].
% 6.89/7.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1744,a,1746,a)].
% 6.89/7.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1744,a,1747,a)].
% 6.89/7.09 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1744,a,1752,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1744,a,1753,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)). [resolve(1744,a,1757,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(1744,a,1758,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)). [resolve(1744,a,1759,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B). [resolve(1744,a,1760,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1744,a,1762,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). [resolve(1744,a,1763,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1764,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1765,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1766,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1767,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1770,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1771,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1772,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1773,a)].
% 6.89/7.10 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1744,a,1774,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B). [resolve(1744,a,1776,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B). [resolve(1744,a,1777,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1744,a,1778,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C). [resolve(1744,a,1779,a)].
% 6.89/7.10 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1744,a,1780,a)].
% 6.89/7.10 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1744,a,1781,a)].
% 6.89/7.10 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(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(1744,a,1782,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(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(1744,a,1783,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(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(1744,a,1784,a)].
% 6.89/7.10 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(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(1744,a,1785,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(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(1744,a,1786,a)].
% 6.89/7.10 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1744,a,1787,a)].
% 6.89/7.10 Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1744,a,1788,a)].
% 6.89/7.10 1789 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1789,a,1746,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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(1789,a,1747,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1789,a,1752,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1789,a,1753,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)). [resolve(1789,a,1757,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1789,a,1758,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1789,a,1759,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B). [resolve(1789,a,1760,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1789,a,1762,a)].
% 6.89/7.10 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C). [resolve(1789,a,1763,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1764,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1765,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1766,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1767,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1770,a)].
% 6.89/7.10 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1771,a)].
% 6.89/7.11 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1772,a)].
% 6.89/7.11 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1773,a)].
% 6.89/7.11 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1789,a,1774,a)].
% 6.89/7.11 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B). [resolve(1789,a,1776,a)].
% 6.89/7.11 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B). [resolve(1789,a,1777,a)].
% 6.89/7.11 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1789,a,1778,a)].
% 6.89/7.11 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C). [resolve(1789,a,1779,a)].
% 6.89/7.11 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1789,a,1780,a)].
% 6.89/7.11 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1789,a,1781,a)].
% 6.89/7.11 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(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(1789,a,1782,a)].
% 6.89/7.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(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(1789,a,1783,a)].
% 6.89/7.11 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(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(1789,a,1784,a)].
% 6.89/7.11 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(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(1789,a,1785,a)].
% 6.89/7.11 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(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(1789,a,1786,a)].
% 6.89/7.11 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1789,a,1787,a)].
% 6.89/7.11 Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1789,a,1788,a)].
% 6.89/7.11 1790 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) # label(axiom). [clausify(989)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1790,b,1746,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1747,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1752,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1753,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)). [resolve(1790,b,1757,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)). [resolve(1790,b,1758,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)). [resolve(1790,b,1759,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1790,b,1760,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1790,b,1762,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1790,b,1763,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1764,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1790,b,1765,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1766,a)].
% 6.89/7.11 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1790,b,1767,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1770,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B). [resolve(1790,b,1771,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1790,b,1772,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B). [resolve(1790,b,1773,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1790,b,1774,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C). [resolve(1790,b,1776,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C). [resolve(1790,b,1777,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1790,b,1778,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1790,b,1779,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1790,b,1780,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1790,b,1781,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1790,b,1782,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1790,b,1783,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1790,b,1784,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1790,b,1785,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1790,b,1786,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1790,b,1787,a)].
% 6.93/7.12 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1790,b,1788,a)].
% 7.03/7.25 1791 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 7.03/7.25 1792 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)) # label(fact_zero__le__square) # label(axiom). [clausify(740)].
% 7.03/7.25 1793 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__square__less__zero) # label(axiom). [clausify(757)].
% 7.03/7.25 1794 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))) # label(fact_sum__squares__ge__zero) # label(axiom). [clausify(944)].
% 7.03/7.25 1795 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(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(946)].
% 7.03/7.25 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)). [resolve(1791,a,1792,a)].
% 7.03/7.25 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1791,a,1793,a)].
% 7.03/7.25 Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))). [resolve(1791,a,1794,a)].
% 7.03/7.25 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1791,a,1795,a)].
% 7.03/7.25 1796 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom). [assumption].
% 7.03/7.25 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)). [resolve(1796,a,1792,a)].
% 7.03/7.25 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1796,a,1793,a)].
% 7.03/7.25 Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))). [resolve(1796,a,1794,a)].
% 7.03/7.25 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1796,a,1795,a)].
% 7.03/7.25 1797 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom). [clausify(1004)].
% 7.03/7.25 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)). [resolve(1797,b,1792,a)].
% 7.03/7.25 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1797,b,1793,a)].
% 7.03/7.25 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))). [resolve(1797,b,1794,a)].
% 7.32/7.52 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1797,b,1795,a)].
% 7.32/7.52 1798 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 7.32/7.52 1799 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(743)].
% 7.32/7.52 1800 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)). [resolve(1800,a,1799,a)].
% 7.32/7.52 1801 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 7.32/7.52 1802 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) # label(axiom). [clausify(979)].
% 7.32/7.52 1803 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 7.32/7.52 1804 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(744)].
% 7.32/7.52 1805 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(745)].
% 7.32/7.52 1806 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__neg__pos) # label(axiom). [clausify(747)].
% 7.32/7.52 1807 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(749)].
% 7.32/7.52 1808 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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(750)].
% 7.32/7.52 1809 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg2) # label(axiom). [clausify(751)].
% 7.32/7.52 1810 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg) # label(axiom). [clausify(752)].
% 7.32/7.52 1811 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__pos__pos) # label(axiom). [clausify(753)].
% 7.32/7.52 1812 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(801)].
% 7.32/7.52 1813 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(802)].
% 7.32/7.52 1814 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(803)].
% 7.32/7.52 1815 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(805)].
% 7.32/7.52 1816 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__le__less__imp__less) # label(axiom). [clausify(807)].
% 7.32/7.52 1817 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__less__le__imp__less) # label(axiom). [clausify(808)].
% 7.32/7.52 1818 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__strict__mono_H) # label(axiom). [clausify(809)].
% 7.32/7.52 1819 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__strict__mono) # label(axiom). [clausify(810)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1803,a,1806,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1803,a,1807,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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(1803,a,1808,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1803,a,1810,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)). [resolve(1803,a,1811,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1803,a,1813,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1803,a,1814,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(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(1803,a,1815,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(1803,a,1816,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(1803,a,1817,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(1803,a,1818,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(1803,a,1819,a)].
% 7.32/7.52 1820 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1820,a,1805,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1820,a,1806,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(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(1820,a,1807,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(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(1820,a,1808,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1820,a,1810,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)). [resolve(1820,a,1811,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(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(1820,a,1812,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(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(1820,a,1813,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(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(1820,a,1814,a)].
% 7.32/7.52 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(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(1820,a,1815,a)].
% 7.32/7.52 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(1820,a,1816,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(1820,a,1817,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(1820,a,1818,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(1820,a,1819,a)].
% 7.32/7.53 1821 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1821,a,1806,a)].
% 7.32/7.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1821,a,1807,a)].
% 7.32/7.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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(1821,a,1808,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1821,a,1810,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(1821,a,1811,a)].
% 7.32/7.53 Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1821,a,1813,a)].
% 7.32/7.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1821,a,1814,a)].
% 7.32/7.53 Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(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(1821,a,1815,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1821,a,1816,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1821,a,1817,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1821,a,1818,a)].
% 7.32/7.53 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(1821,a,1819,a)].
% 7.32/7.53 1822 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) # label(axiom). [clausify(981)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1822,b,1806,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1822,b,1807,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1822,b,1808,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1822,b,1810,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)). [resolve(1822,b,1811,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1822,b,1813,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1822,b,1814,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1822,b,1815,a)].
% 7.32/7.53 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)). [resolve(1822,b,1816,a)].
% 7.47/7.67 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)). [resolve(1822,b,1817,a)].
% 7.47/7.67 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)). [resolve(1822,b,1818,a)].
% 7.47/7.67 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)). [resolve(1822,b,1819,a)].
% 7.47/7.67 1823 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption].
% 7.47/7.67 1824 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) = D # label(fact_eq__add__iff2) # label(axiom). [clausify(760)].
% 7.47/7.67 1825 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) != D # label(fact_eq__add__iff2) # label(axiom). [clausify(760)].
% 7.47/7.67 1826 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(fact_eq__add__iff1) # label(axiom). [clausify(761)].
% 7.47/7.67 1827 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) != F # label(fact_eq__add__iff1) # label(axiom). [clausify(761)].
% 7.47/7.67 1828 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),D)) # label(fact_mult__diff__mult) # label(axiom). [clausify(762)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E) = C. [resolve(1823,a,1824,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E) != C. [resolve(1823,a,1825,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) = E. [resolve(1823,a,1826,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) != E. [resolve(1823,a,1827,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),C)). [resolve(1823,a,1828,a)].
% 7.47/7.67 1829 class_Rings_Oring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring) # label(axiom). [assumption].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E) = C. [resolve(1829,a,1824,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),D),A)),B)),E) != C. [resolve(1829,a,1825,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C) = E. [resolve(1829,a,1826,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),B)),C) != E. [resolve(1829,a,1827,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),D)),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),C)). [resolve(1829,a,1828,a)].
% 7.47/7.67 1830 class_Rings_Oring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring) # label(axiom). [assumption].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B)),E) = C. [resolve(1830,a,1824,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B)),E) != C. [resolve(1830,a,1825,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C) = E. [resolve(1830,a,1826,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C) != E. [resolve(1830,a,1827,a)].
% 7.47/7.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),C)). [resolve(1830,a,1828,a)].
% 7.47/7.67 1831 -class_Rings_Ocomm__ring(A) | class_Rings_Oring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom). [clausify(1025)].
% 7.47/7.67 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F) = D. [resolve(1831,b,1824,a)].
% 7.69/7.95 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F) != D. [resolve(1831,b,1825,a)].
% 7.69/7.95 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D) = F. [resolve(1831,b,1826,a)].
% 7.69/7.95 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D) != F. [resolve(1831,b,1827,a)].
% 7.69/7.95 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),D)). [resolve(1831,b,1828,a)].
% 7.69/7.95 1832 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 7.69/7.95 1833 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(804)].
% 7.69/7.95 1834 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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(806)].
% 7.69/7.95 1835 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 7.69/7.95 1836 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 7.69/7.95 1837 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom). [clausify(995)].
% 7.69/7.95 1838 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 7.69/7.95 1839 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Oone__class_Oone(A))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Oone__class_Oone(A)) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(829)].
% 7.84/8.07 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1838,a,1839,a)].
% 7.84/8.07 1840 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption].
% 7.84/8.07 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1840,a,1839,a)].
% 7.84/8.07 1841 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom). [assumption].
% 7.84/8.07 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1841,a,1839,a)].
% 7.84/8.07 1842 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom). [clausify(1022)].
% 7.84/8.07 Derived: -class_Rings_Ocomm__ring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1842,b,1839,a)].
% 7.84/8.07 1843 class_Rings_Oordered__ring__abs(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 7.84/8.07 1844 -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) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(835)].
% 7.84/8.07 1845 -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)) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(835)].
% 7.84/8.07 1846 -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) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(835)].
% 7.84/8.08 1847 -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)) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(835)].
% 7.84/8.08 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) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(1843,a,1844,a)].
% 7.84/8.08 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)) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(1843,a,1845,a)].
% 7.84/8.08 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) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(1843,a,1846,a)].
% 7.84/8.08 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)) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(1843,a,1847,a)].
% 7.84/8.08 1848 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 7.84/8.08 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) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(1848,a,1844,a)].
% 7.84/8.08 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)) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(1848,a,1845,a)].
% 7.84/8.08 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) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(1848,a,1846,a)].
% 8.01/8.21 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)) | hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(1848,a,1847,a)].
% 8.01/8.21 1849 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring__abs) # label(axiom). [clausify(1001)].
% 8.01/8.21 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)). [resolve(1849,b,1844,a)].
% 8.01/8.21 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)). [resolve(1849,b,1845,a)].
% 8.01/8.21 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)). [resolve(1849,b,1846,a)].
% 8.01/8.21 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A)),C)). [resolve(1849,b,1847,a)].
% 8.01/8.21 1850 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption].
% 8.01/8.21 1851 -class_RealVector_Oreal__field(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))),F) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E)),F))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),F)),E)) # label(fact_DERIV__mult__lemma) # label(axiom). [clausify(844)].
% 8.14/8.35 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D))),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),B),D)),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal),A),C)),E)),D)). [resolve(1850,a,1851,a)].
% 8.14/8.35 1852 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 8.14/8.35 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D))),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),E)),D)). [resolve(1852,a,1851,a)].
% 8.14/8.35 1853 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 8.14/8.35 1854 -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_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C) # label(fact_convex__bound__le) # label(axiom). [clausify(852)].
% 8.14/8.35 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_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),D),E) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C)),B). [resolve(1853,a,1854,a)].
% 8.14/8.35 1855 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 8.14/8.35 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_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),D),E) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C)),B). [resolve(1855,a,1854,a)].
% 8.14/8.35 1856 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) # label(axiom). [clausify(992)].
% 8.24/8.49 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),E),F) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),D)),C). [resolve(1856,b,1854,a)].
% 8.24/8.49 1857 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 8.24/8.49 1858 -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_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C) # label(fact_convex__bound__lt) # label(axiom). [clausify(866)].
% 8.24/8.49 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_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),D),E) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C)),B). [resolve(1857,a,1858,a)].
% 8.24/8.49 1859 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 8.24/8.49 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_Oone__class_Oone(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C)),B). [resolve(1859,a,1858,a)].
% 8.24/8.49 1860 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) # label(axiom). [clausify(980)].
% 8.24/8.49 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),E),F) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),D)),C). [resolve(1860,b,1858,a)].
% 8.52/8.76 1861 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_ga____)). [resolve(1043,c,1033,a)].
% 8.52/8.76 1862 class_SEQ_Ocomplete__space(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__SEQ_Ocomplete__space) # label(axiom). [assumption].
% 8.52/8.76 1863 class_SEQ_Ocomplete__space(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__SEQ_Ocomplete__space) # label(axiom). [assumption].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,v_ga____)). [resolve(1861,a,1862,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,v_ga____)). [resolve(1861,a,1863,a)].
% 8.52/8.76 1864 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,v_f____)). [resolve(1043,c,1034,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,v_f____)). [resolve(1864,a,1862,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,v_f____)). [resolve(1864,a,1863,a)].
% 8.52/8.76 1865 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))). [resolve(1043,c,1035,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))). [resolve(1865,a,1862,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))). [resolve(1865,a,1863,a)].
% 8.52/8.76 1866 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(C),f3(C)). [resolve(1043,c,1037,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(B),f3(B)). [resolve(1866,a,1862,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,f2(B),f3(B)). [resolve(1866,a,1863,a)].
% 8.52/8.76 1867 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(C,f2(C)),hAPP(C,f3(C))). [resolve(1043,c,1038,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(B,f2(B)),hAPP(B,f3(B))). [resolve(1867,a,1862,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(B,f2(B)),hAPP(B,f3(B))). [resolve(1867,a,1863,a)].
% 8.52/8.76 1868 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c1)). [resolve(1043,c,1039,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c1)). [resolve(1868,a,1862,a)].
% 8.52/8.76 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c1)). [resolve(1868,a,1863,a)].
% 8.52/8.76 1869 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c2)). [resolve(1043,c,1040,a)].
% 13.02/13.25 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c2)). [resolve(1869,a,1862,a)].
% 13.02/13.25 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c2)). [resolve(1869,a,1863,a)].
% 13.02/13.25 1870 -class_SEQ_Ocomplete__space(A) | -c_SEQ_Oconvergent(A,B) | c_SEQ_Oconvergent(A,c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B,c3)). [resolve(1043,c,1041,a)].
% 13.02/13.25 Derived: -c_SEQ_Oconvergent(tc_RealDef_Oreal,A) | c_SEQ_Oconvergent(tc_RealDef_Oreal,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,A,c3)). [resolve(1870,a,1862,a)].
% 13.02/13.25 Derived: -c_SEQ_Oconvergent(tc_Complex_Ocomplex,A) | c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_Fun_Ocomp(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,A,c3)). [resolve(1870,a,1863,a)].
% 13.02/13.25
% 13.02/13.25 ============================== end predicate elimination =============
% 13.02/13.25
% 13.02/13.25 Auto_denials: (non-Horn, no changes).
% 13.02/13.25
% 13.02/13.25 Term ordering decisions:
% 13.02/13.25 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Nat_Onat=1. tc_Int_Oint=1. tc_Complex_Ocomplex=1. c_Limits_Osequentially=1. c_Complex_OIm=1. c_Complex_ORe=1. c_Complex_Ocomplex_OComplex=1. v_f____=1. v_ga____=1. v_s=1. c_Complex_Oii=1. v_r=1. tc_HOL_Obool=1. v_x____=1. v_y____=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. hAPP=1. c_RealDef_Oreal=1. tc_fun=1. c_Nat__Transfer_Otsub=1. c_SEQ_Olim=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Nat_Osize__class_Osize=1. f1=1. f5=1. f6=1. f7=1. f9=1. f10=1. f12=1. f13=1. f14=1. f15=1. f16=1. f23=1. f27=1. f35=1. f37=1. f44=1. f45=1. c_Groups_Ozero__class_Ozero=1. c_Groups_Otimes__class_Otimes=1. tc_Polynomial_Opoly=1. c_Groups_Oplus__class_Oplus=1. c_Groups_Ominus__class_Ominus=1. c_Groups_Oone__class_Oone=1. c_Power_Opower__class_Opower=1. c_Rings_Oinverse__class_Odivide=1. c_Groups_Oabs__class_Oabs=1. c_RealVector_Onorm__class_Onorm=1. c_Rings_Oinverse__class_Oinverse=1. c_RComplete_Onatfloor=1. c_RComplete_Onatceiling=1. tc_Limits_Onet=1. c_Complex_Ocomplex_Ocomplex__size=1. f2=1. f3=1. f11=1. f19=1. f20=1. f36=1. c_Divides_Odiv__class_Odiv=1. c_COMBK=1. c_Complex_Ocomplex_Ocomplex__case=1. c_Complex_Ocomplex_Ocomplex__rec=1. f8=1. f17=1. f21=1. f22=1. f28=1. f29=1. f31=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f46=1. f4=1. f18=1. f24=1. f25=1. f30=1. f32=1. f33=1. f34=1. c_COMBB=1. c_Fun_Ocomp=1. c_COMBC=1. c_COMBS=1. f26=1.
% 13.02/13.25
% 13.02/13.25 ============================== end of process initial clauses ========
% 13.02/13.25
% 13.02/13.25 ============================== CLAUSES FOR SEARCH ====================
% 13.02/13.25
% 13.02/13.25 ============================== end of clauses for search =============
% 13.02/13.25
% 13.02/13.25 ============================== SEARCH ================================
% 13.02/13.25
% 13.02/13.25 % Starting search at 7.51 seconds.
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=58.000, iters=3681
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=43.000, iters=3396
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=38.000, iters=3339
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=37.000, iters=3393
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=36.000, iters=3356
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=34.000, iters=3375
% 13.02/13.25
% 13.02/13.25 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 50 (0.00 of 7.81 sec).
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=33.000, iters=3337
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=32.000, iters=3342
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=31.000, iters=3348
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=30.000, iters=3339
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=29.000, iters=3348
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=28.000, iters=3454
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=27.000, iters=3336
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=26.000, iters=3383
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=25.000, iters=3398
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=24.000, iters=3338
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=23.000, iters=3366
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=22.000, iters=3333
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=21.000, iters=3363
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=20.000, iters=3346
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=19.000, iters=3351
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=18.000, iters=3359
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=17.000, iters=3334
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=16.000, iters=3333
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=15.000, iters=3342
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=14.000, iters=3334
% 13.02/13.25
% 13.02/13.25 Low Water (keep): wt=13.000, iters=3334
% 13.02/13.25
% 13.02/13.25 Low Water (displace): id=17326, wt=12.000
% 13.02/13.25
% 13.02/13.25 Low Water (displace): idCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------