TSTP Solution File: SWW207+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW207+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:15:50 EDT 2022
% Result : Theorem 28.86s 29.06s
% Output : Refutation 28.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW207+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 5 07:32:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.61/1.94 ============================== Prover9 ===============================
% 1.61/1.94 Prover9 (32) version 2009-11A, November 2009.
% 1.61/1.94 Process 876 was started by sandbox on n029.cluster.edu,
% 1.61/1.94 Sun Jun 5 07:32:35 2022
% 1.61/1.94 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_713_n029.cluster.edu".
% 1.61/1.94 ============================== end of head ===========================
% 1.61/1.94
% 1.61/1.94 ============================== INPUT =================================
% 1.61/1.94
% 1.61/1.94 % Reading from file /tmp/Prover9_713_n029.cluster.edu
% 1.61/1.94
% 1.61/1.94 set(prolog_style_variables).
% 1.61/1.94 set(auto2).
% 1.61/1.94 % set(auto2) -> set(auto).
% 1.61/1.94 % set(auto) -> set(auto_inference).
% 1.61/1.94 % set(auto) -> set(auto_setup).
% 1.61/1.94 % set(auto_setup) -> set(predicate_elim).
% 1.61/1.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.61/1.94 % set(auto) -> set(auto_limits).
% 1.61/1.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.61/1.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.61/1.94 % set(auto) -> set(auto_denials).
% 1.61/1.94 % set(auto) -> set(auto_process).
% 1.61/1.94 % set(auto2) -> assign(new_constants, 1).
% 1.61/1.94 % set(auto2) -> assign(fold_denial_max, 3).
% 1.61/1.94 % set(auto2) -> assign(max_weight, "200.000").
% 1.61/1.94 % set(auto2) -> assign(max_hours, 1).
% 1.61/1.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.61/1.94 % set(auto2) -> assign(max_seconds, 0).
% 1.61/1.94 % set(auto2) -> assign(max_minutes, 5).
% 1.61/1.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.61/1.94 % set(auto2) -> set(sort_initial_sos).
% 1.61/1.94 % set(auto2) -> assign(sos_limit, -1).
% 1.61/1.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.61/1.94 % set(auto2) -> assign(max_megs, 400).
% 1.61/1.94 % set(auto2) -> assign(stats, some).
% 1.61/1.94 % set(auto2) -> clear(echo_input).
% 1.61/1.94 % set(auto2) -> set(quiet).
% 1.61/1.94 % set(auto2) -> clear(print_initial_clauses).
% 1.61/1.94 % set(auto2) -> clear(print_given).
% 1.61/1.94 assign(lrs_ticks,-1).
% 1.61/1.94 assign(sos_limit,10000).
% 1.61/1.94 assign(order,kbo).
% 1.61/1.94 set(lex_order_vars).
% 1.61/1.94 clear(print_given).
% 1.61/1.94
% 1.61/1.94 % formulas(sos). % not echoed (1269 formulas)
% 1.61/1.94
% 1.61/1.94 ============================== end of input ==========================
% 1.61/1.94
% 1.61/1.94 % From the command line: assign(max_seconds, 300).
% 1.61/1.94
% 1.61/1.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.61/1.94
% 1.61/1.94 % Formulas that are not ordinary clauses:
% 1.61/1.94 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].
% 1.61/1.94 2 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.94 3 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2))) <-> V_a_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.94 4 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a))) # label(fact_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.94 5 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))))) # label(fact_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.94 6 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.94 7 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a))) # label(fact_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.94 8 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 9 (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r))) # label(fact_assms) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 10 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) & V_x_2 != V_y_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 11 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) | V_x_2 = V_y_2)) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 12 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))))) # label(fact_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 13 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 14 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_x_2 <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 15 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 16 (all V_x_2 all V_gb_2 all V_fa_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2)))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 17 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 18 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(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].
% 1.61/1.95 19 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 20 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(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].
% 1.61/1.95 21 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 22 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 23 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 24 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 25 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 26 (all V_x_2 all V_gb_2 all V_fa_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2)))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 27 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 28 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 29 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 30 (all V_gb_2 all V_fa_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) <-> (all B_x hBOOL(hAPP(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].
% 1.61/1.95 31 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> (V_x != V_y -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 32 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 33 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 34 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 35 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 36 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 37 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 38 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 39 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 40 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 41 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(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].
% 1.61/1.95 42 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(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].
% 1.61/1.95 43 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 44 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 45 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(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].
% 1.61/1.95 46 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 47 (all V_x_2 all V_y_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 48 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) | V_x = V_y | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 49 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) | V_x_2 = V_y_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 50 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_x_2 != V_y_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 51 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 52 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) -> (hBOOL(hAPP(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].
% 1.61/1.95 53 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))))) # label(fact_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 54 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)))) # label(fact_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 55 (all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w))) # label(fact_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 56 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a))) # label(fact_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 57 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 58 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 59 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 60 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 61 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_a != V_b -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 62 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_a != V_b -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 63 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.95 64 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 65 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 66 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 67 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 68 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 69 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 70 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 71 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 72 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 73 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 74 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 75 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 76 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 77 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 78 (all V_a_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (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].
% 1.61/1.95 79 (all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> 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].
% 1.61/1.95 80 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)))) # label(fact_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 81 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 82 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 83 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 84 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x))))) # label(fact_norm__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 85 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 86 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> 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].
% 1.61/1.95 87 (all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a))) # label(fact_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 88 (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 1.61/1.95 89 (all V_fa_2 (c_SEQ_Osubseq(V_fa_2) <-> (all B_m all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(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].
% 1.61/1.95 90 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_norm__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 91 (all V_x_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_x_2 <-> V_x_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 92 (all V_gb_2 all V_fa_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) & -hBOOL(hAPP(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].
% 1.61/1.95 93 (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].
% 1.61/1.95 94 (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].
% 1.61/1.95 95 (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].
% 1.61/1.95 96 (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].
% 1.61/1.95 97 (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].
% 1.61/1.95 98 (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].
% 1.61/1.95 99 (all V_r c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)) # label(fact_real__norm__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 100 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))))) # label(fact_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 101 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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].
% 1.61/1.95 102 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(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].
% 1.61/1.95 103 (all V_x -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x))) # label(fact_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 104 (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].
% 1.61/1.95 105 (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].
% 1.61/1.95 106 (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].
% 1.61/1.95 107 (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].
% 1.61/1.95 108 (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].
% 1.61/1.95 109 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 110 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 111 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 112 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 113 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(hAPP(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].
% 1.61/1.95 114 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/1.95 115 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/1.95 116 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 117 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 118 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 119 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 120 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> hBOOL(hAPP(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].
% 1.61/1.95 121 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 122 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 123 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.95 124 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 125 (all V_x hBOOL(hAPP(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_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))))) # label(fact_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 126 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 127 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 128 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 129 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 130 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.95 131 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.95 132 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.95 133 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 134 (all V_a_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 135 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 136 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.95 137 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(hAPP(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].
% 1.61/1.95 138 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> hBOOL(hAPP(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].
% 1.61/1.95 139 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))))) # label(fact_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 140 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 141 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.95 142 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.95 143 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.95 144 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.95 145 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.95 146 (all V_n_2 all V_fa_2 (c_SEQ_Osubseq(V_fa_2) -> hBOOL(hAPP(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].
% 1.61/1.95 147 -(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].
% 1.61/1.95 148 (all V_n -hBOOL(hAPP(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].
% 1.61/1.95 149 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(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].
% 1.61/1.95 150 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(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].
% 1.61/1.95 151 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(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].
% 1.61/1.95 152 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(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].
% 1.61/1.95 153 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(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].
% 1.61/1.95 154 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(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].
% 1.61/1.95 155 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 156 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.95 157 (all V_n hBOOL(hAPP(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].
% 1.61/1.95 158 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n))) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 159 (all V_m all V_n hBOOL(hAPP(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].
% 1.61/1.95 160 (all V_m all V_n hBOOL(hAPP(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].
% 1.61/1.95 161 (all V_n_2 all V_m_2 (hBOOL(hAPP(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].
% 1.61/1.95 162 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 163 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 164 (all V_n all V_m (V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 165 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.95 166 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.95 167 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.95 168 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k))))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 169 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (hBOOL(hAPP(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].
% 1.61/1.95 170 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(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].
% 1.61/1.95 171 (all V_n all V_k all V_m (hBOOL(hAPP(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)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 172 (all V_n all V_k all V_m (hBOOL(hAPP(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)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 173 (all V_n all V_k all V_m (hBOOL(hAPP(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)) -> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 174 (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].
% 1.61/1.95 175 (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].
% 1.61/1.95 176 (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].
% 1.61/1.95 177 (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].
% 1.61/1.95 178 (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].
% 1.61/1.95 179 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 180 (all V_n all V_m all V_l all V_k (hBOOL(hAPP(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) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 181 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(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].
% 1.61/1.95 182 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.95 183 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.95 184 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.95 185 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.95 186 (all V_i all V_j -hBOOL(hAPP(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].
% 1.61/1.95 187 (all V_j all V_i -hBOOL(hAPP(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].
% 1.61/1.95 188 (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].
% 1.61/1.95 189 (all V_y_2 all V_x_2 (V_x_2 = V_y_2 <-> hAPP(c_Complex_ORe,V_x_2) = hAPP(c_Complex_ORe,V_y_2) & hAPP(c_Complex_OIm,V_x_2) = hAPP(c_Complex_OIm,V_y_2))) # label(fact_expand__complex__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 190 (all V_n_2 all V_m_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) | hBOOL(hAPP(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].
% 1.61/1.95 191 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)))) # label(fact_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 192 (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].
% 1.61/1.95 193 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)))) # label(fact_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 194 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 195 (all V_z all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))))) # label(fact_complex__mod__triangle__sub) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 196 (all V_n_2 (hBOOL(hAPP(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].
% 1.61/1.95 197 (all V_n hBOOL(hAPP(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].
% 1.61/1.95 198 (all V_P_2 all V_n_2 all V_m_2 ((hBOOL(hAPP(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))) -> ((hBOOL(hAPP(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].
% 1.61/1.95 199 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) | V_m = V_n -> hBOOL(hAPP(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].
% 1.61/1.95 200 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (V_m != V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 201 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(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].
% 1.61/1.95 202 (all V_t all V_s (hBOOL(hAPP(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].
% 1.61/1.95 203 (all V_m all V_n (hBOOL(hAPP(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].
% 1.61/1.95 204 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 205 (all V_y all V_x (V_x != V_y -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x))))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 206 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(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].
% 1.61/1.95 207 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(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].
% 1.61/1.95 208 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) | hBOOL(hAPP(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].
% 1.61/1.95 209 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.95 210 (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].
% 1.61/1.95 211 (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].
% 1.61/1.95 212 (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].
% 1.61/1.95 213 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(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].
% 1.61/1.95 214 (all V_n all V_m (hBOOL(hAPP(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].
% 1.61/1.95 215 (all V_n -hBOOL(hAPP(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].
% 1.61/1.95 216 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(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].
% 1.61/1.95 217 (all V_n -hBOOL(hAPP(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].
% 1.61/1.96 218 (all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_abs__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 219 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 220 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(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].
% 1.61/1.96 221 (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].
% 1.61/1.96 222 (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].
% 1.61/1.96 223 (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].
% 1.61/1.96 224 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 1.61/1.96 225 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(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].
% 1.61/1.96 226 (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].
% 1.61/1.96 227 (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].
% 1.61/1.96 228 (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].
% 1.61/1.96 229 (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].
% 1.61/1.96 230 (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].
% 1.61/1.96 231 (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].
% 1.61/1.96 232 (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].
% 1.61/1.96 233 (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].
% 1.61/1.96 234 (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].
% 1.61/1.96 235 (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].
% 1.61/1.96 236 (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].
% 1.61/1.96 237 (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].
% 1.61/1.96 238 (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].
% 1.61/1.96 239 (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].
% 1.61/1.96 240 (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].
% 1.61/1.96 241 (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].
% 1.61/1.96 242 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 243 (all V_y all V_z all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z)) -> hBOOL(hAPP(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].
% 1.61/1.96 244 (all V_y all V_z all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) -> hBOOL(hAPP(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].
% 1.61/1.96 245 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 246 (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].
% 1.61/1.96 247 (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].
% 1.61/1.96 248 (all V_l_2 all V_k_2 (hBOOL(hAPP(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].
% 1.61/1.96 249 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)))))))) # label(fact_BseqD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 250 (all V_X_2 all V_K_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2)) -> ((all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 1.61/1.96 251 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 1.61/1.96 252 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2)) & (all B_i (hBOOL(hAPP(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].
% 1.61/1.96 253 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) & (V_x != c_Groups_Ozero__class_Ozero(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_norm__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 254 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a))) # label(fact_sgn__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 255 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sgn__0__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 256 (all T_a (class_Groups_Osgn__if(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 257 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 258 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 259 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_sgn__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 260 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_sgn__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 261 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))))) # label(fact_sgn__greater) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 262 (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].
% 1.61/1.96 263 (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].
% 1.61/1.96 264 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 265 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 266 (all V_a_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))))) # label(fact_sgn__1__pos) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 267 (all V_X_2 (c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2) -> ((all B_m all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))))) -> c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)))) # label(fact_Bseq__mono__convergent) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 268 (all V_x (hBOOL(hAPP(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].
% 1.61/1.96 269 (all V_x (hBOOL(hAPP(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].
% 1.61/1.96 270 (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].
% 1.61/1.96 271 (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) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(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) -> hBOOL(hAPP(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].
% 1.61/1.96 272 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_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_x_2))))) # label(fact_Bseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 273 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> 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),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))) # label(fact_norm__power) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 274 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> 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),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) # label(fact_norm__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 275 (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].
% 1.61/1.96 276 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.96 277 (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].
% 1.61/1.96 278 (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].
% 1.61/1.96 279 (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].
% 1.61/1.96 280 (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].
% 1.61/1.96 281 (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].
% 1.61/1.96 282 (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].
% 1.61/1.96 283 (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].
% 1.61/1.96 284 (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].
% 1.61/1.96 285 (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].
% 1.61/1.96 286 (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].
% 1.61/1.96 287 (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].
% 1.61/1.96 288 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))))) # label(fact_norm__power__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 289 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))))) # label(fact_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 290 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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].
% 1.61/1.96 291 (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].
% 1.61/1.96 292 (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].
% 1.61/1.96 293 (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].
% 1.61/1.96 294 (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].
% 1.61/1.96 295 (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].
% 1.61/1.96 296 (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].
% 1.61/1.96 297 (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].
% 1.61/1.96 298 (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].
% 1.61/1.96 299 (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].
% 1.61/1.96 300 (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].
% 1.61/1.96 301 (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].
% 1.61/1.96 302 (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].
% 1.61/1.96 303 (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].
% 1.61/1.96 304 (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].
% 1.61/1.96 305 (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].
% 1.61/1.96 306 (all V_z_2 all V_x_2 all V_y_2 all V_w_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_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_x_2),V_y_2)) <-> V_w_2 = V_x_2 | V_y_2 = V_z_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 307 (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].
% 1.61/1.96 308 (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].
% 1.61/1.96 309 (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].
% 1.61/1.96 310 (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].
% 1.61/1.96 311 (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].
% 1.61/1.96 312 (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].
% 1.61/1.96 313 (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].
% 1.61/1.96 314 (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].
% 1.61/1.96 315 (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].
% 1.61/1.96 316 (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].
% 1.61/1.96 317 (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].
% 1.61/1.96 318 (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].
% 1.61/1.96 319 (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].
% 1.61/1.96 320 (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].
% 1.61/1.96 321 (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].
% 1.61/1.96 322 (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].
% 1.61/1.96 323 (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].
% 1.61/1.96 324 (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].
% 1.61/1.96 325 (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].
% 1.61/1.96 326 (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].
% 1.61/1.96 327 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 328 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_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].
% 1.61/1.96 329 (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].
% 1.61/1.96 330 (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].
% 1.61/1.96 331 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(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].
% 1.61/1.96 332 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.96 333 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.96 334 (all V_m hBOOL(hAPP(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].
% 1.61/1.96 335 (all V_m hBOOL(hAPP(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].
% 1.61/1.96 336 (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].
% 1.61/1.96 337 (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].
% 1.61/1.96 338 (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].
% 1.61/1.96 339 (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].
% 1.61/1.96 340 (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].
% 1.61/1.96 341 (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].
% 1.61/1.96 342 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)))) # label(fact_sgn__times) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 343 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)))) # label(fact_sgn__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 344 (all V_x hBOOL(hAPP(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].
% 1.61/1.96 345 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 346 (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].
% 1.61/1.96 347 (all V_x_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_x_2),V_X_2))))) # label(fact_mult__right_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 348 (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,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_y_2))))) # label(fact_mult__left_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 349 (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].
% 1.61/1.96 350 (all V_x hBOOL(hAPP(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].
% 1.61/1.96 351 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 352 (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].
% 1.61/1.96 353 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(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].
% 1.61/1.96 354 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(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].
% 1.61/1.96 355 (all V_b_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(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].
% 1.61/1.96 356 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.96 357 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 358 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 359 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.96 360 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 361 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 362 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 363 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 364 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 365 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 366 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 367 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 368 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 369 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.96 370 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(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].
% 1.61/1.96 371 (all V_b_2 all V_c_2 all V_a_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(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].
% 1.61/1.96 372 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(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].
% 1.61/1.96 373 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.96 374 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.96 375 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 376 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 377 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.96 378 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.96 379 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.96 380 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.96 381 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 382 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 383 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 384 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.96 385 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 386 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.96 387 (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].
% 1.61/1.96 388 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)) -> hBOOL(hAPP(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].
% 1.61/1.96 389 (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].
% 1.61/1.96 390 (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].
% 1.61/1.96 391 (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].
% 1.61/1.96 392 (all V_d all V_b all V_c all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))))))) # label(fact_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 393 (all V_n_2 all V_m_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) & hBOOL(hAPP(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].
% 1.61/1.96 394 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(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].
% 1.61/1.96 395 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(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].
% 1.61/1.96 396 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(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].
% 1.61/1.96 397 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(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].
% 1.61/1.96 398 (all V_y_2 all V_x_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 399 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 400 (all V_y all V_x all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.96 401 (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].
% 1.61/1.96 402 (all V_y_2 all V_x_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 403 (all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x)) # label(fact_mult__sgn__abs) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 404 (all V_k all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)))) # label(fact_abs__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.96 405 (all V_x (hBOOL(hAPP(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].
% 1.61/1.97 406 (all V_x (hBOOL(hAPP(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].
% 1.61/1.97 407 (all V_b all V_a c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b))) # label(fact_expi__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 408 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 409 (all V_b_2 all V_a_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 410 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.97 411 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.97 412 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.97 413 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.97 414 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 415 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 416 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 417 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 418 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.97 419 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(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].
% 1.61/1.97 420 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.97 421 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.97 422 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = 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].
% 1.61/1.97 423 (all V_b all V_a all T_a (class_Rings_Oordered__ring__abs(T_a) -> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))) & (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))) -> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 424 (all V_y_2 all V_x_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 425 (all V_y_2 all V_x_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 426 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(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))) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(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].
% 1.61/1.97 427 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(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))) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(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].
% 1.61/1.97 428 (all V_y all V_x all V_c (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))) -> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 429 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)))) # label(fact_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 430 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 431 (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) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(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) -> hBOOL(hAPP(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].
% 1.61/1.97 432 (all V_y all V_x all V_c all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),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].
% 1.61/1.97 433 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_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_x_2))))) # label(fact_monoseq__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 434 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_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_x_2))))) # label(fact_convergent__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 435 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(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].
% 1.61/1.97 436 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(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].
% 1.61/1.97 437 (all V_y_2 all V_x_2 all V_b_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 438 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/1.97 439 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.97 440 (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) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(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].
% 1.61/1.97 441 (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].
% 1.61/1.97 442 (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].
% 1.61/1.97 443 (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].
% 1.61/1.97 444 (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].
% 1.61/1.97 445 (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].
% 1.61/1.97 446 (all V_n_2 all V_x_2 (hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))) <-> V_x_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].
% 1.61/1.97 447 (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].
% 1.61/1.97 448 (all V_n all V_m all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/1.97 449 (all V_n_2 all V_x_2 (hBOOL(hAPP(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_x_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 450 (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].
% 1.61/1.97 451 (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].
% 1.61/1.97 452 (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].
% 1.61/1.97 453 (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].
% 1.61/1.97 454 (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].
% 1.61/1.97 455 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))) # label(fact_power__abs) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 456 (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].
% 1.61/1.97 457 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 458 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 459 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 460 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 461 (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].
% 1.61/1.97 462 (all V_n_2 all V_m_2 all V_a_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(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].
% 1.61/1.97 463 (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].
% 1.61/1.97 464 (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].
% 1.61/1.97 465 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 466 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 467 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 468 (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].
% 1.61/1.97 469 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))))) # label(fact_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 470 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 471 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/1.97 472 (all V_y_2 all V_x_2 all V_b_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 473 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 474 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.97 475 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(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].
% 1.61/1.97 476 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 477 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 478 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(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].
% 1.61/1.97 479 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 480 (all V_n_2 all V_m_2 (hBOOL(hAPP(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].
% 1.61/1.97 481 (all V_n all V_m (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) -> 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].
% 1.61/1.97 482 (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].
% 1.61/1.97 483 (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].
% 1.61/1.97 484 (all V_n all V_x hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)))) # label(fact_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 485 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(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].
% 1.61/1.97 486 (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].
% 1.61/1.97 487 (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].
% 1.61/1.97 488 (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].
% 1.61/1.97 489 (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].
% 1.61/1.97 490 (all V_z_2 all V_w_2 (hBOOL(hAPP(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)))) <-> hBOOL(hAPP(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].
% 1.61/1.97 491 (all V_z_2 all V_w_2 (hBOOL(hAPP(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)))) <-> hBOOL(hAPP(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].
% 1.61/1.97 492 (all V_z_2 all V_w_2 (hBOOL(hAPP(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)) <-> hBOOL(hAPP(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].
% 1.61/1.97 493 (all V_z all V_w (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z)) -> hBOOL(hAPP(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].
% 1.61/1.97 494 (all V_w_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2)) <-> hBOOL(hAPP(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].
% 1.61/1.97 495 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y)) | V_x = V_y | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 496 (all V_z all V_z_H all V_w all V_w_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z)) -> hBOOL(hAPP(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].
% 1.61/1.97 497 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.97 498 (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].
% 1.61/1.97 499 (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].
% 1.61/1.97 500 (all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hBOOL(hAPP(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].
% 1.61/1.97 501 (all V_z_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 502 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,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].
% 1.61/1.97 503 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) <-> hBOOL(hAPP(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].
% 1.61/1.97 504 (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].
% 1.61/1.97 505 (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].
% 1.61/1.97 506 (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].
% 1.61/1.97 507 (all V_y_2 all V_x_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_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 508 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(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].
% 1.61/1.97 509 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 510 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(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].
% 1.61/1.97 511 (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 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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].
% 1.61/1.97 512 (all V_n_2 all V_x_2 (hBOOL(hAPP(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_x_2),V_n_2))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)))) # label(fact_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 513 (all V_q all V_r all V_a (hBOOL(hAPP(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)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> hBOOL(hAPP(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].
% 1.61/1.97 514 (all V_q all V_r all V_a (hBOOL(hAPP(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)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 515 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) -> hBOOL(hAPP(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].
% 1.61/1.97 516 (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].
% 1.61/1.97 517 (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].
% 1.61/1.97 518 (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].
% 1.61/1.97 519 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) -> (hBOOL(hAPP(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].
% 1.61/1.97 520 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k))))) # label(fact_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 521 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 522 (all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w))) # label(fact_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 523 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(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].
% 1.61/1.97 524 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(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].
% 1.61/1.97 525 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.97 526 (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) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.97 527 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H)) -> hBOOL(hAPP(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].
% 1.61/1.97 528 (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) -> (hBOOL(hAPP(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.97 529 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hBOOL(hAPP(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].
% 1.61/1.97 530 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.97 531 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.97 532 (all V_x_2 (-hBOOL(hAPP(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_2),V_x_2))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 533 (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))))) # label(fact_Im_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 534 (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))))) # label(fact_Re_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 535 (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))))) # label(fact_Im_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 536 (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))))) # label(fact_Re_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 537 (all T_a (class_Power_Opower(T_a) -> c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)))) # label(fact_power__power__power) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 538 (all V_a_2 all V_times_2 all V_one_2 all T_a hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2) # label(fact_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 539 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_a all B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))))) # label(fact_mult_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 540 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 541 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 542 (all V_x all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)) -> (hBOOL(hAPP(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].
% 1.61/1.97 543 (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))) # label(fact_Im_Obounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 544 (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))) # label(fact_Re_Obounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 545 (all V_n hBOOL(hAPP(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].
% 1.61/1.97 546 (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].
% 1.61/1.97 547 (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].
% 1.61/1.97 548 (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].
% 1.61/1.97 549 (all V_x c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x)) # label(fact_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 550 (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].
% 1.61/1.97 551 (all V_n -hBOOL(hAPP(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].
% 1.61/1.97 552 (all V_m_2 all V_n_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 553 (all V_m_2 all V_n_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 554 (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].
% 1.61/1.97 555 (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].
% 1.61/1.97 556 (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].
% 1.61/1.97 557 (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].
% 1.61/1.97 558 (all V_x hBOOL(hAPP(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].
% 1.61/1.97 559 (all V_n_2 (hBOOL(hAPP(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].
% 1.61/1.97 560 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(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].
% 1.61/1.97 561 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a)) -> hBOOL(hAPP(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].
% 1.61/1.97 562 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) -> hBOOL(hAPP(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].
% 1.61/1.97 563 (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].
% 1.61/1.97 564 (all V_n_2 (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.97 565 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) <-> hBOOL(hAPP(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].
% 1.61/1.97 566 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) <-> hBOOL(hAPP(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].
% 1.61/1.97 567 (all V_a_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2))))) # label(fact_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 568 (all V_a_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))))) # label(fact_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 569 (all V_x hBOOL(hAPP(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].
% 1.61/1.97 570 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n))) -> hBOOL(hAPP(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].
% 1.61/1.97 571 (all V_a all V_x (hBOOL(hAPP(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].
% 1.61/1.97 572 (all V_n all V_z (hBOOL(hAPP(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)) -> hBOOL(hAPP(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].
% 1.61/1.97 573 (all V_x all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)) -> (hBOOL(hAPP(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].
% 1.61/1.97 574 (all V_a all V_x (hBOOL(hAPP(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].
% 1.61/1.97 575 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(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].
% 1.61/1.97 576 (all V_n all V_a all V_r hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))) # label(fact_DeMoivre2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 577 (all V_a all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (exists B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a & (all B_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a -> B_y = B_x))))))) # label(fact_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 578 (all V_a all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (exists B_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a))))) # label(fact_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 579 (all V_a all V_r c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)) # label(fact_complex__mod__rcis) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 580 (all V_a c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) # label(fact_rcis__zero__mod) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 581 (all V_b all V_r2 all V_a all V_r1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b))) # label(fact_rcis__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 582 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_a all B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))))) # label(fact_mult_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 583 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 584 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))))) # label(fact_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 585 (all V_X_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> ((exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))))) <-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))))) # label(fact_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 586 (all V_X_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> ((exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))))) <-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))))) # label(fact_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.97 587 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (all B_y exists B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x)))))) # label(fact_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 588 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n)))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 589 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 590 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(V_n)))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 591 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 592 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 593 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 594 (all V_nat_H_1 c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 595 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 596 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 597 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 598 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 599 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 600 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> V_m = V_n))) # label(fact_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 601 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k))))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 602 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> (c_Nat_OSuc(V_m) != V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 603 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 604 (all V_m all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m))) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 605 (all V_m_2 all V_n_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 606 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 607 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) | V_m_2 = V_n_2)) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 608 (all V_n_2 all V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 609 (all V_y all V_x (c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 610 (all V_nat_H_2 all V_nat_2 (c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 611 (all V_n c_Nat_OSuc(V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 612 (all V_n V_n != c_Nat_OSuc(V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 613 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 614 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 615 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 616 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n))) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 617 (all V_n_2 all V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 618 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) | V_m_2 = c_Nat_OSuc(V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 619 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)))) # label(fact_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 620 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 621 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> V_m = c_Nat_OSuc(V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 622 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 623 (all V_n_2 all V_a_2 all V_times_2 all V_one_2 all T_a hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2))) # label(fact_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 624 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_power__0__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 625 (all V_n all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(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__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 626 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a))) # label(fact_power__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 627 (all V_q 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_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 628 (all V_q 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_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 629 (all V_q 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_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 630 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 631 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = c_Nat_OSuc(B_j) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)))))) # label(fact_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 632 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 633 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) <-> (exists B_m V_n_2 = c_Nat_OSuc(B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 634 (all V_n_2 all V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 635 (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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 636 (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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 637 (all V_m all V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 638 (all V_m all V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 639 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) <-> (exists B_k V_n_2 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))) # label(fact_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 640 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 641 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 642 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 643 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 644 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 645 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 646 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 647 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 648 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(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),V_m),V_n))) # label(fact_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 649 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 650 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 651 (all V_n c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 652 (all V_n c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 653 (all V_n hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_power__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 654 (all V_m_2 all V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 655 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Omonoseq(T_a,V_X_2) <-> (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n))))) | (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n))))))) # label(fact_monoseq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 656 (all V_fa_2 (c_SEQ_Osubseq(V_fa_2) <-> (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n))))))) # label(fact_subseq__Suc__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 657 (all V_n_2 c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2))) # label(fact_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 658 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)))))) # label(fact_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 659 (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),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> V_a = V_b))))) # label(fact_power__inject__base) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 660 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(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),c_Nat_OSuc(V_n))))))) # label(fact_power__gt1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 661 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))))) # label(fact_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 662 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))))) # label(fact_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 663 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))))) # label(fact_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 664 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)))) # label(fact_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 665 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))))) # label(fact_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 666 (all V_n c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = 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))) # label(fact_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 667 (all V_n all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))))) # label(fact_nat__one__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 668 (all V_n all V_r all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n))),V_r)))))) # label(fact_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 669 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),c_Groups_Oone__class_Oone(T_a))))))) # label(fact_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 670 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))))) # label(fact_Bseq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 671 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))))) # label(fact_Bseq__iff1a) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 672 (all V_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))))) # label(fact_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 673 (all V_a all V_n c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)))) # label(fact_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 674 (all V_x all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y)),V_x)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y)))))))) # label(fact_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 675 (all V_b all V_a hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b))) # label(fact_cis__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 676 (all V_a c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a)) # label(fact_cis__rcis__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 677 (all V_n all V_a hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))) # label(fact_DeMoivre) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 678 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)))) # label(fact_ln__realpow) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 679 (all V_a all V_n c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n))) # label(fact_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 680 (all V_a all V_n c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n))) # label(fact_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 681 (all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) # label(fact_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 682 (all V_y all V_x c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y)))) # label(fact_sin__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 683 (all V_x (c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_sin__zero__abs__cos__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 684 (all V_x (c_Transcendental_Ocos(V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) -> c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 685 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_cos__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 686 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_sin__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 687 (all V_a hAPP(c_Complex_OIm,c_Complex_Ocis(V_a)) = c_Transcendental_Osin(V_a)) # label(fact_Im__cis) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 688 (all V_a hAPP(c_Complex_ORe,c_Complex_Ocis(V_a)) = c_Transcendental_Ocos(V_a)) # label(fact_Re__cis) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 689 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x)))) # label(fact_ln__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 690 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) -> (c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_ln__inj__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 691 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)))))) # label(fact_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 692 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_abs__sin__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 693 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_abs__cos__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 694 (all V_a all V_r hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a))) # label(fact_Im__rcis) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 695 (all V_a all V_r hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a))) # label(fact_Re__rcis) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 696 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)))))) # label(fact_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 697 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))))) # label(fact_ln__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 698 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))))) # label(fact_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 699 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))))) # label(fact_ln__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 700 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 701 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 702 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))))) # label(fact_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 703 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))))) # label(fact_ln__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 704 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))))) # label(fact_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 705 (all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))))) # label(fact_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 706 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y))))) # label(fact_ln__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 707 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x)))) # label(fact_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 708 (all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y)) = V_y)) # label(fact_cos__arccos__abs) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 709 (all V_n all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) -> (exists B_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n)) = V_a)))) # label(fact_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 710 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))) # label(fact_mult__left_Obounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 711 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_a all B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))) # label(fact_mult_Obounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 712 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))) # label(fact_mult__right_Obounded) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 713 (all V_x all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> (hBOOL(hAPP(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),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].
% 1.61/1.98 714 (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),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].
% 1.61/1.98 715 (all V_k all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 716 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 717 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))))) # label(fact_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 718 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))) <-> hBOOL(hAPP(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].
% 1.61/1.98 719 (all V_n all V_m all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 720 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_m_2 = V_n_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 721 (all V_n all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,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].
% 1.61/1.98 722 (all V_l all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 723 (all V_l all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 724 (all V_n all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m))) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 725 (all V_n all V_k all V_m 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)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 726 (all V_n all V_m all V_k 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)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 727 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,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].
% 1.61/1.98 728 (all V_m all V_n 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].
% 1.61/1.98 729 (all V_n all V_m 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].
% 1.61/1.98 730 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 731 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> 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].
% 1.61/1.98 732 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) <-> hBOOL(hAPP(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].
% 1.61/1.98 733 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))))) # label(fact_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 734 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) # label(fact_norm__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 735 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 736 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = 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].
% 1.61/1.98 737 (all V_n all V_k all V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k)))) # label(fact_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 738 (all V_l all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 739 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) # label(fact_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 740 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 741 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 742 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 743 (all V_n all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (c_Groups_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].
% 1.61/1.98 744 (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),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = 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].
% 1.61/1.98 745 (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),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = 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].
% 1.61/1.98 746 (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),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = 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].
% 1.61/1.98 747 (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),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = 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].
% 1.61/1.98 748 (all V_d_2 all V_c_2 all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) <-> hBOOL(hAPP(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].
% 1.61/1.98 749 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 750 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 751 (all V_b_2 all V_a_2 all T_a (class_Groups_Oab__group__add(T_a) -> (V_a_2 = V_b_2 <-> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 752 (all V_b_2 all V_a_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_a_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 753 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.61/1.98 754 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = 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].
% 1.61/1.98 755 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 756 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 757 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.61/1.98 758 (all V_i_2 all V_k_2 all V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2)) <-> hBOOL(hAPP(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].
% 1.61/1.98 759 (all V_m all V_n all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),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].
% 1.61/1.98 760 (all V_m all V_n (hBOOL(hAPP(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),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].
% 1.61/1.98 761 (all V_i all V_j all V_k (hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = 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].
% 1.61/1.98 762 (all V_i_2 all V_j_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))) <-> hBOOL(hAPP(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].
% 1.61/1.98 763 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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].
% 1.61/1.98 764 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) -> (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].
% 1.61/1.98 765 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 766 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.61/1.98 767 (all V_i all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> 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),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].
% 1.61/1.98 768 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))) <-> hBOOL(hAPP(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].
% 1.61/1.98 769 (all V_c all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 770 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))) <-> hBOOL(hAPP(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].
% 1.61/1.98 771 (all V_n all V_m (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),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].
% 1.61/1.98 772 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 773 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 774 (all V_n_2 all V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(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].
% 1.61/1.98 775 (all V_m all V_n 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].
% 1.61/1.98 776 (all V_n all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m)))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 777 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m))))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 778 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))) <-> hBOOL(hAPP(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].
% 1.61/1.98 779 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))))) # label(fact_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 780 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))))) # label(fact_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 781 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))))) # label(fact_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 782 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> 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),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 783 (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),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].
% 1.61/1.98 784 (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),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].
% 1.61/1.98 785 (all V_b all V_a all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> 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),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))))) # label(fact_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 786 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 787 (all V_b_2 all V_a_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.98 788 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.98 789 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.98 790 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.98 791 (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) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.99 792 (all V_x all T_a (class_Rings_Oring__1(T_a) -> 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))),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].
% 1.61/1.99 793 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))))) # label(fact_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 794 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,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),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))))) # label(fact_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 795 (all V_ra_2 all V_a_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_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].
% 1.61/1.99 796 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))))) # label(fact_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 797 (all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n)) # label(fact_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 798 (all V_i all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i))),V_n)))) # label(fact_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 799 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) <-> -(hBOOL(hAPP(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].
% 1.61/1.99 800 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) <-> (hBOOL(hAPP(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].
% 1.61/1.99 801 (all V_m all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 802 (all V_m all V_j all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)))) # label(fact_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 803 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.99 804 (all V_n all V_m all V_u all V_i all V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i)) -> 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)) = 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),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].
% 1.61/1.99 805 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (hBOOL(hAPP(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),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].
% 1.61/1.99 806 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.99 807 (all V_n all V_m all V_u all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> 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)) = 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),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].
% 1.61/1.99 808 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (hBOOL(hAPP(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),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].
% 1.61/1.99 809 (all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))))) # label(fact_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 810 (all V_y all V_n all V_p all T_a (class_Groups_Omonoid__mult(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p),V_n)) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y)))) # label(fact_lemma__realpow__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 811 (all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 812 (all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n)) # label(fact_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 813 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))))) # label(fact_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 814 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.99 815 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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),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].
% 1.61/1.99 816 (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),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].
% 1.61/1.99 817 (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),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].
% 1.61/1.99 818 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)))) # label(fact_realpow__two__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 819 (all V_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r)) & hBOOL(hAPP(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].
% 1.61/1.99 820 (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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))))))))) # label(fact_lemmaCauchy) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 821 (all V_y all V_x hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = 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].
% 1.61/1.99 822 (all V_y all V_x hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = 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].
% 1.61/1.99 823 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,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].
% 1.61/1.99 824 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = 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].
% 1.61/1.99 825 (all V_l_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 826 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 827 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))) # label(fact_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 828 (all V_y all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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].
% 1.61/1.99 829 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(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].
% 1.61/1.99 830 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 831 (all V_y all V_x c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x)))) # label(fact_sin__diff2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 832 (all V_y all V_x c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y)))) # label(fact_sin__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 833 (all V_a all V_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)))) # label(fact_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 834 (all V_y all V_x c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y)))) # label(fact_cos__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 835 (all V_y all V_x c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y)))) # label(fact_cos__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 836 (all V_y all V_x c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x)))) # label(fact_cos__diff2) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 837 (all V_x all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x)) -> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = 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].
% 1.61/1.99 838 (all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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].
% 1.61/1.99 839 (all V_x all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x)) -> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = 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].
% 1.61/1.99 840 (all V_y all V_x hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = 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].
% 1.61/1.99 841 (all V_z all V_x all V_d (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)))) # label(fact_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 842 (all V_x all V_z all V_d (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) -> hBOOL(hAPP(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))))) # label(fact_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 843 (all V_z (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_unimodular__reduce__norm) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 844 (all V_x all V_y ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) -> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)) & (-hBOOL(hAPP(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].
% 1.61/1.99 845 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.99 846 (all V_x all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) -> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y))) # label(fact_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 847 (all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_int__power__div__base) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 848 (all V_d all V_b all V_c all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,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),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)))) # label(fact_Deriv_Oadd__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 849 (all V_k all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(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].
% 1.61/1.99 850 (all V_b all V_a all V_c (hBOOL(hAPP(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].
% 1.61/1.99 851 (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].
% 1.61/1.99 852 (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].
% 1.61/1.99 853 (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].
% 1.61/1.99 854 (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].
% 1.61/1.99 855 (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].
% 1.61/1.99 856 (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].
% 1.61/1.99 857 (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].
% 1.61/1.99 858 (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].
% 1.61/1.99 859 (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].
% 1.61/1.99 860 (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].
% 1.61/1.99 861 (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].
% 1.61/1.99 862 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.99 863 (all V_a_2 all V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.99 864 (all V_a_2 all V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.99 865 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(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].
% 1.61/1.99 866 (all V_b all V_a_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(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].
% 1.61/1.99 867 (all V_b all V_a_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.99 868 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(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].
% 1.61/1.99 869 (all V_b all V_b_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.99 870 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.99 871 (all V_a_2 all V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.99 872 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(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].
% 1.61/1.99 873 (all V_b all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(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].
% 1.61/1.99 874 (all V_b all V_b_H all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(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].
% 1.61/1.99 875 (all V_b_2 all V_a_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2)) & hBOOL(hAPP(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].
% 1.61/1.99 876 (all V_i_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.99 877 (all V_a_2 all V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) -> (hBOOL(hAPP(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))) <-> hBOOL(hAPP(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].
% 1.61/1.99 878 (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) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & hBOOL(hAPP(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].
% 1.61/1.99 879 (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].
% 1.61/1.99 880 (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].
% 1.61/1.99 881 (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].
% 1.61/1.99 882 (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].
% 1.61/1.99 883 (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) -> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1)) & hBOOL(hAPP(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].
% 1.61/1.99 884 (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)))) & (hBOOL(hAPP(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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(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))))) & (hBOOL(hAPP(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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j)) & hBOOL(hAPP(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].
% 1.61/1.99 885 (all V_y all V_x hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(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].
% 1.61/1.99 886 (all V_b all V_x all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_b)) -> (exists B_d (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_d)) & (all B_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y))),B_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a),B_y)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y),V_b))))))))) # label(fact_lemma__interval) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 887 (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].
% 1.61/1.99 888 (all V_k all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(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].
% 1.61/1.99 889 (all V_n all V_m hBOOL(hAPP(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].
% 1.61/1.99 890 (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].
% 1.61/1.99 891 (all V_n all V_m (hBOOL(hAPP(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].
% 1.61/1.99 892 (all V_m c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m) # label(fact_div__1) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 893 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> hBOOL(hAPP(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].
% 1.61/1.99 894 (all V_m all V_n (hBOOL(hAPP(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].
% 1.61/1.99 895 (all V_m all V_n (hBOOL(hAPP(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].
% 1.61/1.99 896 (all V_n all V_m all V_k (hBOOL(hAPP(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].
% 1.61/1.99 897 (all V_k all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(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].
% 1.61/1.99 898 (all V_d all V_c all V_b all V_a c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d))) # label(fact_complex__diff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 899 (all V_z 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].
% 1.61/1.99 900 (all V_real2_H_2 all V_real1_H_2 all V_real2_2 all V_real1_2 (c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = 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].
% 1.61/1.99 901 (all V_y all V_x hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_y) # label(fact_Im) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 902 (all V_y all V_x hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_x) # label(fact_Re) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 903 (all V_d all V_c all V_b all V_a hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = 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].
% 1.61/1.99 904 (all V_b_2 all V_a_2 (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].
% 1.61/1.99 905 (all V_y_2 all V_x_2 (c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) = c_Complex_Oii <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) & V_y_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_Complex__eq__i) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 906 (all V_b_2 all V_a_2 (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].
% 1.61/1.99 907 (all V_a c_Complex_Ocis(V_a) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) # label(fact_cis__def) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 908 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (-hBOOL(hAPP(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_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))))) # label(fact_div__geq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 909 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(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)) & (-hBOOL(hAPP(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_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))))) # label(fact_div__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 910 (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 (hBOOL(hAPP(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].
% 1.61/1.99 911 (all V_d all V_c all V_b all V_a hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(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].
% 1.61/1.99 912 (all V_a c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) # label(fact_cmod__unit__one) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 913 (all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = 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].
% 1.61/1.99 914 (all V_m_2 all V_q_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))) <-> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_split__div__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 915 (all V_n_2 all V_m_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_q (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))) & hBOOL(hAPP(V_P_2,B_q)))))) # label(fact_split__div_H) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 916 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))))) # label(fact_le__div__geq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 917 (all V_real2 all V_real1 c_Complex_Ocomplex_Ocomplex__size(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].
% 1.61/1.99 918 (all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) -> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 919 (all V_y (V_y != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_cos__arg__i__mult__zero) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 920 (all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 921 (all V_real2 all V_real1 c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,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].
% 1.61/1.99 922 (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,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].
% 1.61/1.99 923 (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,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].
% 1.61/1.99 924 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(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].
% 1.61/1.99 925 (all V_x c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) # label(fact_real__sgn__eq) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 926 (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].
% 1.61/1.99 927 (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].
% 1.61/1.99 928 (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].
% 1.61/1.99 929 (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].
% 1.61/1.99 930 (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].
% 1.61/1.99 931 (all V_y_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_y_2))))) # label(fact_divide_Oconvergent) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 932 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_RealVector_Oreal__normed__field(T_a) -> 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),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))) # label(fact_norm__divide) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 933 (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].
% 1.61/1.99 934 (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].
% 1.61/1.99 935 (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].
% 1.61/1.99 936 (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].
% 1.61/1.99 937 (all V_a all V_b all T_a (class_RealVector_Oreal__normed__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_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),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b))))) # label(fact_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 938 (all V_y_2 all V_x_2 (hBOOL(hAPP(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_x_2),V_y_2))) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))) & (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))))) # label(fact_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.61/1.99 939 (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].
% 1.61/1.99 940 (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].
% 1.61/1.99 941 (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].
% 1.61/1.99 942 (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].
% 1.61/1.99 943 (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].
% 1.61/1.99 944 (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].
% 1.61/1.99 945 (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].
% 1.61/1.99 946 (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].
% 1.61/1.99 947 (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].
% 1.61/1.99 948 (all V_z hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) # label(fact_Im__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.00 949 (all V_z hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) # label(fact_Re__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.00 950 (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),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = 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].
% 1.61/2.00 951 (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),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_c) = 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].
% 1.61/2.00 952 (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),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),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),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].
% 1.61/2.00 953 (all V_b_2 all V_a_2 all V_fa_2 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_a_2)) = 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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2))) # label(fact_lemma__MVT) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.00 954 (all V_x all V_n hBOOL(hAPP(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].
% 1.61/2.00 955 (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) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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].
% 1.61/2.00 956 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) -> c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y))))) # label(fact_ln__div) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.00 957 (all V_x all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),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].
% 1.61/2.00 958 (all V_x all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 1.61/2.00 959 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/2.00 960 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(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))) -> hBOOL(hAPP(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].
% 1.61/2.00 961 (all V_b all V_a hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_b))) # label(fact_cis__divide) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.00 962 (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].
% 1.61/2.00 963 (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].
% 1.61/2.00 964 (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].
% 1.61/2.00 965 (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].
% 1.61/2.00 966 (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].
% 1.61/2.00 967 (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].
% 1.61/2.00 968 (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].
% 1.61/2.00 969 (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].
% 1.61/2.00 970 (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].
% 1.61/2.00 971 (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].
% 1.61/2.00 972 (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].
% 1.61/2.00 973 (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].
% 1.61/2.00 974 (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].
% 1.61/2.00 975 (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].
% 1.61/2.00 976 (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].
% 1.61/2.00 977 (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].
% 1.61/2.00 978 (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].
% 1.61/2.00 979 (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].
% 1.61/2.00 980 (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].
% 1.61/2.00 981 (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].
% 1.61/2.00 982 (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].
% 1.61/2.00 983 (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].
% 1.61/2.00 984 (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].
% 1.61/2.00 985 (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].
% 1.61/2.00 986 (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].
% 1.61/2.00 987 (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].
% 1.61/2.00 988 (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].
% 1.61/2.00 989 (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].
% 1.61/2.00 990 (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].
% 1.61/2.00 991 (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].
% 1.61/2.00 992 (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].
% 1.61/2.00 993 (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].
% 1.61/2.00 994 (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].
% 1.61/2.00 995 (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].
% 1.61/2.00 996 (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].
% 1.61/2.00 997 (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].
% 1.61/2.00 998 (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].
% 1.61/2.00 999 (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].
% 1.61/2.00 1000 (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].
% 1.61/2.00 1001 (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].
% 1.61/2.00 1002 (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].
% 1.61/2.00 1003 (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].
% 1.61/2.00 1004 (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].
% 1.61/2.00 1005 (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].
% 1.61/2.00 1006 (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].
% 1.61/2.00 1007 (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].
% 1.61/2.00 1008 (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].
% 1.61/2.00 1009 (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].
% 1.61/2.00 1010 (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].
% 1.61/2.00 1011 (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].
% 1.61/2.00 1012 (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].
% 1.61/2.00 1013 (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].
% 1.61/2.00 1014 (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].
% 1.61/2.00 1015 (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].
% 1.61/2.00 1016 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Osgn__if) # label(axiom) # label(non_clause). [assumption].
% 1.61/2.00 1017 (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].
% 1.61/2.00 1018 (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].
% 1.61/2.00 1019 (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].
% 1.61/2.00 1020 (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].
% 1.61/2.00 1021 (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].
% 1.61/2.00 1022 (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].
% 1.61/2.00 1023 (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].
% 1.61/2.00 1024 (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].
% 1.61/2.04 1025 (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].
% 1.61/2.04 1026 -(exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.61/2.04
% 1.61/2.04 ============================== end of process non-clausal formulas ===
% 1.61/2.04
% 1.61/2.04 ============================== PROCESS INITIAL CLAUSES ===============
% 1.61/2.04
% 1.61/2.04 ============================== PREDICATE ELIMINATION =================
% 1.61/2.04 1027 -c_SEQ_Osubseq(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,C))) # label(fact_subseq__def) # label(axiom). [clausify(89)].
% 1.61/2.04 1028 c_SEQ_Osubseq(v_f____) # label(fact_f_I1_J) # label(axiom). [assumption].
% 1.61/2.04 1029 c_SEQ_Osubseq(v_ga____) # label(fact_g_I1_J) # label(axiom). [assumption].
% 1.61/2.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A)),hAPP(v_f____,B))). [resolve(1027,a,1028,a)].
% 1.61/2.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,A)),hAPP(v_ga____,B))). [resolve(1027,a,1029,a)].
% 1.61/2.04 1030 c_SEQ_Osubseq(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,f3(A)),f4(A))) # label(fact_subseq__def) # label(axiom). [clausify(89)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,f3(A)),f4(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,C))). [resolve(1030,a,1027,a)].
% 1.61/2.04 1031 c_SEQ_Osubseq(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f3(A))),hAPP(A,f4(A)))) # label(fact_subseq__def) # label(axiom). [clausify(89)].
% 1.61/2.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f3(A))),hAPP(A,f4(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,C))). [resolve(1031,a,1027,a)].
% 1.61/2.04 1032 -c_SEQ_Osubseq(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(A,B))) # label(fact_seq__suble) # label(axiom). [clausify(146)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),hAPP(v_f____,A))). [resolve(1032,a,1028,a)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),hAPP(v_ga____,A))). [resolve(1032,a,1029,a)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),hAPP(B,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,f3(B)),f4(B))). [resolve(1032,a,1030,a)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),hAPP(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(B,f3(B))),hAPP(B,f4(B)))). [resolve(1032,a,1031,a)].
% 1.61/2.04 1033 c_SEQ_Osubseq(c1) # 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(147)].
% 1.61/2.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c1,A)),hAPP(c1,B))). [resolve(1033,a,1027,a)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),hAPP(c1,A))). [resolve(1033,a,1032,a)].
% 1.61/2.04 1034 -c_SEQ_Osubseq(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,c_Nat_OSuc(B)))) # label(fact_subseq__Suc__iff) # label(axiom). [clausify(656)].
% 1.61/2.04 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A)),hAPP(v_f____,c_Nat_OSuc(A)))). [resolve(1034,a,1028,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,A)),hAPP(v_ga____,c_Nat_OSuc(A)))). [resolve(1034,a,1029,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,c_Nat_OSuc(B)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,f3(A)),f4(A))). [resolve(1034,a,1030,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,c_Nat_OSuc(B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f3(A))),hAPP(A,f4(A)))). [resolve(1034,a,1031,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c1,A)),hAPP(c1,c_Nat_OSuc(A)))). [resolve(1034,a,1033,a)].
% 1.61/2.21 1035 c_SEQ_Osubseq(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f46(A))),hAPP(A,c_Nat_OSuc(f46(A))))) # label(fact_subseq__Suc__iff) # label(axiom). [clausify(656)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f46(A))),hAPP(A,c_Nat_OSuc(f46(A))))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,C))). [resolve(1035,a,1027,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f46(A))),hAPP(A,c_Nat_OSuc(f46(A))))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(A,B))). [resolve(1035,a,1032,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,f46(A))),hAPP(A,c_Nat_OSuc(f46(A))))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,c_Nat_OSuc(B)))). [resolve(1035,a,1034,a)].
% 1.61/2.21 1036 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.61/2.21 1037 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_abs__not__less__zero) # label(axiom). [clausify(2)].
% 1.61/2.21 1038 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oabs__class_Oabs(A,B))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(3)].
% 1.61/2.21 1039 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oabs__class_Oabs(A,B))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(3)].
% 1.61/2.21 1040 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__of__pos) # label(axiom). [clausify(4)].
% 1.61/2.21 1041 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oabs__class_Oabs(A,B))) # label(fact_abs__ge__zero) # label(axiom). [clausify(5)].
% 1.61/2.21 1042 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,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(6)].
% 1.61/2.21 1043 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,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(6)].
% 1.61/2.21 1044 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__of__nonneg) # label(axiom). [clausify(7)].
% 1.61/2.21 1045 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Oabs__class_Oabs(A,B))) # label(fact_abs__ge__self) # label(axiom). [clausify(12)].
% 1.61/2.21 1046 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) # label(fact_abs__le__D1) # label(axiom). [clausify(13)].
% 1.61/2.21 1047 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,B) # label(fact_abs__idempotent) # label(axiom). [clausify(56)].
% 1.61/2.21 1048 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__eq__0) # label(axiom). [clausify(78)].
% 1.61/2.21 1049 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__eq__0) # label(axiom). [clausify(78)].
% 1.61/2.21 1050 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_abs__zero) # label(axiom). [clausify(79)].
% 1.61/2.21 1051 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__add__abs) # label(axiom). [clausify(124)].
% 1.61/2.21 1052 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)))) # label(fact_abs__triangle__ineq) # label(axiom). [clausify(139)].
% 1.61/2.21 1053 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)) # label(fact_abs__minus__commute) # label(axiom). [clausify(739)].
% 1.61/2.21 1054 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)))) # label(fact_abs__triangle__ineq2__sym) # label(axiom). [clausify(779)].
% 1.61/2.21 1055 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)))) # label(fact_abs__triangle__ineq2) # label(axiom). [clausify(780)].
% 1.61/2.21 1056 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)))) # label(fact_abs__triangle__ineq3) # label(axiom). [clausify(781)].
% 1.61/2.21 1057 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)))) # label(fact_abs__triangle__ineq4) # label(axiom). [clausify(793)].
% 1.61/2.21 1058 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,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),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,D))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,E))))) # label(fact_abs__diff__triangle__ineq) # label(axiom). [clausify(794)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1036,a,1037,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1036,a,1038,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1036,a,1039,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A. [resolve(1036,a,1040,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A))). [resolve(1036,a,1041,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1036,a,1042,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1036,a,1043,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A. [resolve(1036,a,1044,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A))). [resolve(1036,a,1045,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)). [resolve(1036,a,1046,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,A). [resolve(1036,a,1047,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1036,a,1048,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1036,a,1049,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1036,a,1050,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1036,a,1051,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)))). [resolve(1036,a,1052,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A)). [resolve(1036,a,1053,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A)))). [resolve(1036,a,1054,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)))). [resolve(1036,a,1055,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)))). [resolve(1036,a,1056,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)))). [resolve(1036,a,1057,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,D))))). [resolve(1036,a,1058,a)].
% 1.61/2.21 1059 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1059,a,1037,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1059,a,1038,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1059,a,1039,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A. [resolve(1059,a,1040,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A))). [resolve(1059,a,1041,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1059,a,1042,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1059,a,1043,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A. [resolve(1059,a,1044,a)].
% 1.61/2.21 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A))). [resolve(1059,a,1045,a)].
% 1.61/2.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)). [resolve(1059,a,1046,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A). [resolve(1059,a,1047,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1059,a,1048,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1059,a,1049,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1059,a,1050,a)].
% 1.61/2.21 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1059,a,1051,a)].
% 1.61/2.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)))). [resolve(1059,a,1052,a)].
% 1.61/2.22 Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)). [resolve(1059,a,1053,a)].
% 1.61/2.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)))). [resolve(1059,a,1054,a)].
% 1.61/2.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)))). [resolve(1059,a,1055,a)].
% 1.61/2.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)))). [resolve(1059,a,1056,a)].
% 1.61/2.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)))). [resolve(1059,a,1057,a)].
% 1.61/2.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,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),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D))))). [resolve(1059,a,1058,a)].
% 1.61/2.22 1060 -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(976)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1060,b,1037,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1060,b,1038,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1060,b,1039,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B) = B. [resolve(1060,b,1040,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B))). [resolve(1060,b,1041,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),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(1060,b,1042,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),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(1060,b,1043,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B) = B. [resolve(1060,b,1044,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B))). [resolve(1060,b,1045,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)). [resolve(1060,b,1046,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)) = c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B). [resolve(1060,b,1047,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | 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(1060,b,1048,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | 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(1060,b,1049,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1060,b,1050,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)). [resolve(1060,b,1051,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),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)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)))). [resolve(1060,b,1052,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)) = c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,B)). [resolve(1060,b,1053,a)].
% 1.61/2.22 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,B)))). [resolve(1060,b,1054,a)].
% 2.18/2.40 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)))). [resolve(1060,b,1055,a)].
% 2.18/2.40 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)))). [resolve(1060,b,1056,a)].
% 2.18/2.40 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)))). [resolve(1060,b,1057,a)].
% 2.18/2.40 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),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)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,D))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,E))))). [resolve(1060,b,1058,a)].
% 2.18/2.40 1061 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.18/2.40 1062 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__le__cases) # label(axiom). [clausify(15)].
% 2.18/2.40 1063 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__linear) # label(axiom). [clausify(29)].
% 2.18/2.40 1064 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | C = B | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__cases) # label(axiom). [clausify(31)].
% 2.18/2.40 1065 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) # label(fact_linorder__neqE) # label(axiom). [clausify(46)].
% 2.18/2.40 1066 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) | C = B # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(47)].
% 2.18/2.40 1067 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) | C != B # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(47)].
% 2.18/2.40 1068 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | C = B | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__less__linear) # label(axiom). [clausify(48)].
% 2.18/2.40 1069 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) | B = C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(49)].
% 2.18/2.40 1070 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(49)].
% 2.18/2.40 1071 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | B != C # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(49)].
% 2.18/2.40 1072 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(50)].
% 2.18/2.40 1073 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(50)].
% 2.18/2.40 1074 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(50)].
% 2.18/2.40 1075 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | B = C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(64)].
% 2.18/2.40 1076 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | B != C # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(64)].
% 2.18/2.40 1077 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_leD) # label(axiom). [clausify(66)].
% 2.18/2.40 1078 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | B = C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(69)].
% 2.18/2.40 1079 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | B != C # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(69)].
% 2.18/2.40 1080 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_not__leE) # label(axiom). [clausify(70)].
% 2.18/2.40 1081 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_leI) # label(axiom). [clausify(71)].
% 2.18/2.40 1082 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(75)].
% 2.18/2.40 1083 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__not__le) # label(axiom). [clausify(76)].
% 2.18/2.40 1084 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__not__le) # label(axiom). [clausify(76)].
% 2.18/2.40 1085 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__not__less) # label(axiom). [clausify(77)].
% 2.18/2.40 1086 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_linorder__not__less) # label(axiom). [clausify(77)].
% 2.18/2.40 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1061,a,1062,a)].
% 2.18/2.40 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | B = A | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1061,a,1064,a)].
% 2.18/2.40 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)) | B != A. [resolve(1061,a,1067,a)].
% 2.18/2.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1061,a,1070,a)].
% 2.18/2.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | A != B. [resolve(1061,a,1071,a)].
% 2.18/2.40 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1061,a,1074,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | A = B. [resolve(1061,a,1075,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1061,a,1077,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | A != B. [resolve(1061,a,1079,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1061,a,1080,a)].
% 2.18/2.42 1087 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A)). [resolve(1087,a,1062,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | B = A | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1087,a,1064,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)) | B != A. [resolve(1087,a,1067,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1087,a,1070,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | A != B. [resolve(1087,a,1071,a)].
% 2.18/2.42 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1087,a,1074,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | A = B. [resolve(1087,a,1075,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1087,a,1077,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | A != B. [resolve(1087,a,1079,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1087,a,1080,a)].
% 2.18/2.42 1088 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1062,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | B = A | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1064,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)) | B != A. [resolve(1088,a,1067,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1070,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | A != B. [resolve(1088,a,1071,a)].
% 2.18/2.42 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1074,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | A = B. [resolve(1088,a,1075,a)].
% 2.18/2.42 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1077,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | A != B. [resolve(1088,a,1079,a)].
% 2.18/2.42 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1080,a)].
% 2.29/2.54 1089 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1006)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),B)). [resolve(1089,b,1062,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | C = B | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1089,b,1064,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)) | C != B. [resolve(1089,b,1067,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1089,b,1070,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | B != C. [resolve(1089,b,1071,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1089,b,1074,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | B = C. [resolve(1089,b,1075,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1089,b,1077,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | B != C. [resolve(1089,b,1079,a)].
% 2.29/2.54 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1089,b,1080,a)].
% 2.29/2.54 1090 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.29/2.54 1091 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__norm__iff) # label(axiom). [clausify(81)].
% 2.29/2.54 1092 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__norm__iff) # label(axiom). [clausify(81)].
% 2.29/2.54 1093 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(82)].
% 2.29/2.54 1094 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(82)].
% 2.29/2.54 1095 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_norm__not__less__zero) # label(axiom). [clausify(83)].
% 2.29/2.54 1096 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))) # label(fact_norm__ge__zero) # label(axiom). [clausify(84)].
% 2.29/2.54 1097 -class_RealVector_Oreal__normed__vector(A) | 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__eq__zero) # label(axiom). [clausify(85)].
% 2.29/2.54 1098 -class_RealVector_Oreal__normed__vector(A) | 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__eq__zero) # label(axiom). [clausify(85)].
% 2.29/2.54 1099 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) # label(fact_norm__zero) # label(axiom). [clausify(86)].
% 2.29/2.54 1100 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,B) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)) # label(fact_abs__norm__cancel) # label(axiom). [clausify(87)].
% 2.29/2.54 1101 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))) # label(fact_norm__triangle__ineq) # label(axiom). [clausify(100)].
% 2.29/2.54 1102 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D)),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(101)].
% 2.29/2.54 1103 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f12(B,A))) # label(fact_Bseq__def) # label(axiom). [clausify(224)].
% 2.29/2.54 1104 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f12(B,A))) # label(fact_Bseq__def) # label(axiom). [clausify(224)].
% 2.29/2.54 1105 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f13(B,A,C)))),C)) # label(fact_Bseq__def) # label(axiom). [clausify(224)].
% 2.29/2.54 1106 -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(233)].
% 2.29/2.54 1107 -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(234)].
% 2.29/2.54 1108 -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(235)].
% 2.29/2.54 1109 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f17(B,A))) # label(fact_BseqD) # label(axiom). [clausify(249)].
% 2.29/2.54 1110 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f17(B,A))) # label(fact_BseqD) # label(axiom). [clausify(249)].
% 2.29/2.54 1111 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f18(C,B,A)))),B)) | c_SEQ_OBseq(A,C) # label(fact_BseqI) # label(axiom). [clausify(250)].
% 2.29/2.54 1112 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),f19(C,D,B,A))) | c_SEQ_OBseq(A,D) # label(fact_BseqI2_H) # label(axiom). [clausify(251)].
% 2.29/2.54 1113 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f19(C,B,D,A)))),C)) | c_SEQ_OBseq(A,B) # label(fact_BseqI2_H) # label(axiom). [clausify(251)].
% 2.29/2.54 1114 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) != B | c_RealVector_Onorm__class_Onorm(A,c_Groups_Osgn__class_Osgn(A,B)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) # label(fact_norm__sgn) # label(axiom). [clausify(253)].
% 2.29/2.54 1115 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Osgn__class_Osgn(A,B)) # label(fact_norm__sgn) # label(axiom). [clausify(253)].
% 2.29/2.54 1116 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sgn__zero__iff) # label(axiom). [clausify(257)].
% 2.29/2.54 1117 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sgn__zero__iff) # label(axiom). [clausify(257)].
% 2.29/2.54 1118 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__zero) # label(axiom). [clausify(258)].
% 2.29/2.54 1119 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_RealVector_Onorm__class_Onorm(A,D)))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_norm__ratiotest__lemma) # label(axiom). [clausify(432)].
% 2.29/2.54 1120 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f32(C,A,B)))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f33(C,A))))) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(585)].
% 2.29/2.54 1121 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f34(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f35(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(585)].
% 2.29/2.54 1122 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f34(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f35(B,A,D)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(D)))) # label(fact_lemma__NBseq__def2) # label(axiom). [clausify(585)].
% 2.29/2.54 1123 -class_RealVector_Oreal__normed__vector(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f36(C,A,B)))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f37(C,A))))) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(586)].
% 2.29/2.54 1124 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f38(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f39(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(586)].
% 2.29/2.54 1125 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),f38(B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f39(B,A,D)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(D)))) # label(fact_lemma__NBseq__def) # label(axiom). [clausify(586)].
% 2.29/2.54 1126 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f47(B,A))))) # label(fact_Bseq__iff) # label(axiom). [clausify(670)].
% 2.29/2.54 1127 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f48(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))) # label(fact_Bseq__iff) # label(axiom). [clausify(670)].
% 2.29/2.54 1128 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f49(B,A))))) # label(fact_Bseq__iff1a) # label(axiom). [clausify(671)].
% 2.29/2.54 1129 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f50(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))) # label(fact_Bseq__iff1a) # label(axiom). [clausify(671)].
% 2.29/2.54 1130 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)))) # label(fact_norm__triangle__ineq3) # label(axiom). [clausify(717)].
% 2.29/2.54 1131 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)))) # label(fact_norm__triangle__ineq2) # label(axiom). [clausify(733)].
% 2.29/2.54 1132 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,B)) # label(fact_norm__minus__commute) # label(axiom). [clausify(734)].
% 2.29/2.54 1133 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))) # label(fact_norm__triangle__ineq4) # label(axiom). [clausify(796)].
% 2.29/2.54 1134 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,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),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,D))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,E))))) # label(fact_norm__diff__triangle__ineq) # label(axiom). [clausify(809)].
% 2.29/2.54 1135 -class_RealVector_Oreal__normed__vector(A) | -class_Orderings_Oord(B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(B,C),f60(D,C,B,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(B,C),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(A,hAPP(D,C))))) # label(fact_lemmaCauchy) # label(axiom). [clausify(820)].
% 2.29/2.54 1136 -class_RealVector_Oreal__normed__vector(A) | -class_Orderings_Oord(B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(C,D),hAPP(C,f60(C,D,B,A))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(B,D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))))) # label(fact_lemmaCauchy) # label(axiom). [clausify(820)].
% 2.29/2.54 1137 -class_RealVector_Oreal__normed__vector(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)))) # label(fact_norm__diff__ineq) # label(axiom). [clausify(827)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1090,a,1091,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1090,a,1092,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1090,a,1093,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1090,a,1094,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1090,a,1095,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A))). [resolve(1090,a,1096,a)].
% 2.29/2.54 Derived: 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(1090,a,1097,a)].
% 2.29/2.54 Derived: 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(1090,a,1098,a)].
% 2.29/2.54 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1090,a,1099,a)].
% 2.29/2.54 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)). [resolve(1090,a,1100,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)))). [resolve(1090,a,1101,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(1090,a,1102,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f12(A,tc_RealDef_Oreal))). [resolve(1090,a,1103,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f12(A,tc_RealDef_Oreal))). [resolve(1090,a,1104,a)].
% 2.29/2.54 Derived: c_SEQ_OBseq(tc_RealDef_Oreal,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f13(A,tc_RealDef_Oreal,B)))),B)). [resolve(1090,a,1105,a)].
% 2.29/2.54 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(1090,a,1106,a)].
% 2.29/2.54 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(1090,a,1107,a)].
% 2.29/2.54 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(1090,a,1108,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f17(A,tc_RealDef_Oreal))). [resolve(1090,a,1109,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f17(A,tc_RealDef_Oreal))). [resolve(1090,a,1110,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f18(B,A,tc_RealDef_Oreal)))),A)) | c_SEQ_OBseq(tc_RealDef_Oreal,B). [resolve(1090,a,1111,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),f19(B,C,A,tc_RealDef_Oreal))) | c_SEQ_OBseq(tc_RealDef_Oreal,C). [resolve(1090,a,1112,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f19(B,A,C,tc_RealDef_Oreal)))),B)) | c_SEQ_OBseq(tc_RealDef_Oreal,A). [resolve(1090,a,1113,a)].
% 2.29/2.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1090,a,1114,a)].
% 2.29/2.54 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)). [resolve(1090,a,1115,a)].
% 2.29/2.54 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(1090,a,1116,a)].
% 2.29/2.54 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A. [resolve(1090,a,1117,a)].
% 2.29/2.54 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1090,a,1118,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C)))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1090,a,1119,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f32(B,tc_RealDef_Oreal,A)))),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f33(B,tc_RealDef_Oreal))))). [resolve(1090,a,1120,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f34(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f35(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1090,a,1121,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f34(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f35(A,tc_RealDef_Oreal,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))). [resolve(1090,a,1122,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f36(B,tc_RealDef_Oreal,A)))),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f37(B,tc_RealDef_Oreal))))). [resolve(1090,a,1123,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f38(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f39(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1090,a,1124,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),f38(A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f39(A,tc_RealDef_Oreal,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))). [resolve(1090,a,1125,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f47(A,tc_RealDef_Oreal))))). [resolve(1090,a,1126,a)].
% 2.29/2.54 Derived: c_SEQ_OBseq(tc_RealDef_Oreal,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f48(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1090,a,1127,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f49(A,tc_RealDef_Oreal))))). [resolve(1090,a,1128,a)].
% 2.29/2.54 Derived: c_SEQ_OBseq(tc_RealDef_Oreal,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f50(A,tc_RealDef_Oreal,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1090,a,1129,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)))). [resolve(1090,a,1130,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)))). [resolve(1090,a,1131,a)].
% 2.29/2.54 Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)). [resolve(1090,a,1132,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)))). [resolve(1090,a,1133,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D))))). [resolve(1090,a,1134,a)].
% 2.29/2.54 Derived: -class_Orderings_Oord(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),f60(C,B,A,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(C,B))))). [resolve(1090,a,1135,a)].
% 2.29/2.54 Derived: -class_Orderings_Oord(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(B,C),hAPP(B,f60(B,C,A,tc_RealDef_Oreal))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,C))))). [resolve(1090,a,1136,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)))). [resolve(1090,a,1137,a)].
% 2.29/2.54 1138 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1138,a,1091,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1138,a,1092,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1138,a,1093,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1138,a,1094,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1138,a,1095,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A))). [resolve(1138,a,1096,a)].
% 2.29/2.54 Derived: 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(1138,a,1097,a)].
% 2.29/2.54 Derived: 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(1138,a,1098,a)].
% 2.29/2.54 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1138,a,1099,a)].
% 2.29/2.54 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)). [resolve(1138,a,1100,a)].
% 2.29/2.54 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)))). [resolve(1138,a,1101,a)].
% 2.29/2.54 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(1138,a,1102,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f12(A,tc_Complex_Ocomplex))). [resolve(1138,a,1103,a)].
% 2.29/2.54 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f12(A,tc_Complex_Ocomplex))). [resolve(1138,a,1104,a)].
% 2.29/2.54 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f13(A,tc_Complex_Ocomplex,B)))),B)). [resolve(1138,a,1105,a)].
% 2.29/2.54 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(1138,a,1106,a)].
% 2.29/2.54 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(1138,a,1107,a)].
% 2.29/2.54 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(1138,a,1108,a)].
% 2.29/2.55 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f17(A,tc_Complex_Ocomplex))). [resolve(1138,a,1109,a)].
% 2.29/2.55 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f17(A,tc_Complex_Ocomplex))). [resolve(1138,a,1110,a)].
% 2.29/2.55 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f18(B,A,tc_Complex_Ocomplex)))),A)) | c_SEQ_OBseq(tc_Complex_Ocomplex,B). [resolve(1138,a,1111,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),f19(B,C,A,tc_Complex_Ocomplex))) | c_SEQ_OBseq(tc_Complex_Ocomplex,C). [resolve(1138,a,1112,a)].
% 2.29/2.55 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f19(B,A,C,tc_Complex_Ocomplex)))),B)) | c_SEQ_OBseq(tc_Complex_Ocomplex,A). [resolve(1138,a,1113,a)].
% 2.29/2.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1138,a,1114,a)].
% 2.29/2.55 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A)). [resolve(1138,a,1115,a)].
% 2.29/2.55 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1138,a,1116,a)].
% 2.29/2.55 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1138,a,1117,a)].
% 2.29/2.55 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1138,a,1118,a)].
% 2.29/2.55 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C)))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1138,a,1119,a)].
% 2.29/2.55 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f32(B,tc_Complex_Ocomplex,A)))),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f33(B,tc_Complex_Ocomplex))))). [resolve(1138,a,1120,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f34(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f35(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1138,a,1121,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f34(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f35(A,tc_Complex_Ocomplex,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))). [resolve(1138,a,1122,a)].
% 2.29/2.55 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f36(B,tc_Complex_Ocomplex,A)))),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f37(B,tc_Complex_Ocomplex))))). [resolve(1138,a,1123,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f38(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f39(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1138,a,1124,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),f38(A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f39(A,tc_Complex_Ocomplex,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))). [resolve(1138,a,1125,a)].
% 2.29/2.55 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f47(A,tc_Complex_Ocomplex))))). [resolve(1138,a,1126,a)].
% 2.29/2.55 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f48(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1138,a,1127,a)].
% 2.29/2.55 Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(f49(A,tc_Complex_Ocomplex))))). [resolve(1138,a,1128,a)].
% 2.29/2.55 Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f50(A,tc_Complex_Ocomplex,B)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B)))). [resolve(1138,a,1129,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)))). [resolve(1138,a,1130,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)))). [resolve(1138,a,1131,a)].
% 2.29/2.55 Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,A)). [resolve(1138,a,1132,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)))). [resolve(1138,a,1133,a)].
% 2.29/2.55 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D))))). [resolve(1138,a,1134,a)].
% 2.45/2.68 Derived: -class_Orderings_Oord(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),f60(C,B,A,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(C,B))))). [resolve(1138,a,1135,a)].
% 2.45/2.68 Derived: -class_Orderings_Oord(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(B,C),hAPP(B,f60(B,C,A,tc_Complex_Ocomplex))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,C))))). [resolve(1138,a,1136,a)].
% 2.45/2.68 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)))). [resolve(1138,a,1137,a)].
% 2.45/2.68 1139 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 2.45/2.68 1140 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A)) # label(fact_norm__one) # label(axiom). [clausify(90)].
% 2.45/2.68 1141 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__one) # label(axiom). [clausify(259)].
% 2.45/2.68 1142 -class_RealVector_Oreal__normed__algebra__1(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,B)),C))) # label(fact_norm__power__ineq) # label(axiom). [clausify(288)].
% 2.45/2.68 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). [resolve(1139,a,1140,a)].
% 2.45/2.68 Derived: c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal). [resolve(1139,a,1141,a)].
% 2.45/2.68 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B))). [resolve(1139,a,1142,a)].
% 2.45/2.68 1143 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 2.45/2.68 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(1143,a,1140,a)].
% 2.45/2.68 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1143,a,1141,a)].
% 2.45/2.68 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B))). [resolve(1143,a,1142,a)].
% 2.67/2.89 1144 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.89 1145 -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(93)].
% 2.67/2.89 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(1144,a,1145,a)].
% 2.67/2.89 1146 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.89 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(1146,a,1145,a)].
% 2.67/2.89 1147 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.89 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(1147,a,1145,a)].
% 2.67/2.89 1148 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.89 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(1148,a,1145,a)].
% 2.67/2.89 1149 -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(992)].
% 2.67/2.89 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(1149,b,1145,a)].
% 2.67/2.89 1150 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.67/2.89 1151 -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(94)].
% 2.67/2.89 1152 -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(94)].
% 2.67/2.89 1153 -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(95)].
% 2.67/2.89 1154 -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(95)].
% 2.67/2.89 1155 -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(96)].
% 2.67/2.89 1156 -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(98)].
% 2.67/2.90 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(1150,a,1151,a)].
% 2.67/2.90 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(1150,a,1152,a)].
% 2.67/2.90 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(1150,a,1153,a)].
% 2.67/2.90 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(1150,a,1154,a)].
% 2.67/2.90 1157 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.67/2.90 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(1157,a,1151,a)].
% 2.67/2.90 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(1157,a,1152,a)].
% 2.67/2.90 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(1157,a,1153,a)].
% 2.67/2.90 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(1157,a,1154,a)].
% 2.67/2.90 1158 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.67/2.90 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(1158,a,1151,a)].
% 2.67/2.90 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(1158,a,1152,a)].
% 2.67/2.90 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(1158,a,1153,a)].
% 2.67/2.90 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(1158,a,1154,a)].
% 2.67/2.90 1159 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.67/2.90 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(1159,a,1151,a)].
% 2.67/2.90 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(1159,a,1152,a)].
% 2.67/2.90 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(1159,a,1153,a)].
% 2.67/2.90 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(1159,a,1154,a)].
% 2.67/2.90 1160 -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(987)].
% 2.67/2.90 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(1160,b,1151,a)].
% 2.67/2.90 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(1160,b,1152,a)].
% 2.67/2.90 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(1160,b,1153,a)].
% 2.90/3.18 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(1160,b,1154,a)].
% 2.90/3.18 1161 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.90/3.18 1162 -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(97)].
% 2.90/3.18 1163 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.90/3.18 1164 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.90/3.18 1165 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.90/3.18 1166 -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(979)].
% 2.90/3.18 1167 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.90/3.18 1168 -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(104)].
% 2.90/3.18 1169 -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(107)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(1167,a,1168,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1167,a,1169,a)].
% 2.90/3.18 1170 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A. [resolve(1170,a,1168,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1170,a,1169,a)].
% 2.90/3.18 1171 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A. [resolve(1171,a,1168,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1171,a,1169,a)].
% 2.90/3.18 1172 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(1172,a,1168,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1172,a,1169,a)].
% 2.90/3.18 1173 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom). [clausify(1009)].
% 2.90/3.18 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(1173,b,1168,a)].
% 2.90/3.18 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(1173,b,1169,a)].
% 2.90/3.18 1174 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 2.90/3.18 1175 -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(106)].
% 2.90/3.18 1176 -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(106)].
% 2.90/3.18 1177 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | hBOOL(hAPP(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(126)].
% 2.90/3.18 1178 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(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(126)].
% 2.90/3.18 1179 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(127)].
% 2.90/3.18 1180 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(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(127)].
% 2.90/3.18 1181 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | hBOOL(hAPP(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(133)].
% 2.90/3.18 1182 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(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(133)].
% 2.90/3.18 1183 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(134)].
% 2.90/3.18 1184 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(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(134)].
% 2.90/3.18 1185 -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(210)].
% 2.90/3.18 1186 -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(210)].
% 2.90/3.18 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(1174,a,1175,a)].
% 2.90/3.18 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(1174,a,1176,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1174,a,1177,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1174,a,1178,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1174,a,1179,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1174,a,1180,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1174,a,1181,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1174,a,1182,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1174,a,1183,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1174,a,1184,a)].
% 2.90/3.18 1187 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 2.90/3.18 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(1187,a,1175,a)].
% 2.90/3.18 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(1187,a,1176,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1187,a,1177,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1187,a,1178,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1187,a,1179,a)].
% 2.98/3.19 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1187,a,1180,a)].
% 2.98/3.19 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1187,a,1181,a)].
% 2.98/3.19 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1187,a,1182,a)].
% 2.98/3.19 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1187,a,1183,a)].
% 2.98/3.19 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1187,a,1184,a)].
% 2.98/3.19 1188 -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(978)].
% 2.98/3.19 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(1188,b,1175,a)].
% 2.98/3.19 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(1188,b,1176,a)].
% 2.98/3.19 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1188,b,1177,a)].
% 2.98/3.19 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1188,b,1178,a)].
% 2.98/3.19 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1188,b,1179,a)].
% 2.98/3.19 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1188,b,1180,a)].
% 2.98/3.19 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1188,b,1181,a)].
% 3.08/3.28 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1188,b,1182,a)].
% 3.08/3.28 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1188,b,1183,a)].
% 3.08/3.28 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1188,b,1184,a)].
% 3.08/3.28 1189 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].
% 3.08/3.28 1190 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__cancel__right) # label(axiom). [clausify(109)].
% 3.08/3.28 1191 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__cancel__right) # label(axiom). [clausify(109)].
% 3.08/3.28 1192 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__cancel__left) # label(axiom). [clausify(110)].
% 3.08/3.28 1193 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__cancel__left) # label(axiom). [clausify(110)].
% 3.08/3.28 1194 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_add__le__imp__le__right) # label(axiom). [clausify(114)].
% 3.08/3.28 1195 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_add__le__imp__le__left) # label(axiom). [clausify(115)].
% 3.08/3.28 1196 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_add__less__cancel__right) # label(axiom). [clausify(116)].
% 3.08/3.28 1197 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_add__less__cancel__right) # label(axiom). [clausify(116)].
% 3.08/3.28 1198 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_add__less__cancel__left) # label(axiom). [clausify(117)].
% 3.08/3.28 1199 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_add__less__cancel__left) # label(axiom). [clausify(117)].
% 3.08/3.28 1200 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_add__less__imp__less__right) # label(axiom). [clausify(121)].
% 3.08/3.28 1201 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_add__less__imp__less__left) # label(axiom). [clausify(122)].
% 3.08/3.28 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1189,a,1190,a)].
% 3.08/3.28 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1189,a,1191,a)].
% 3.08/3.28 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1189,a,1192,a)].
% 3.08/3.28 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1189,a,1193,a)].
% 3.08/3.28 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)). [resolve(1189,a,1196,a)].
% 3.08/3.28 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)). [resolve(1189,a,1197,a)].
% 3.08/3.28 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)). [resolve(1189,a,1198,a)].
% 3.08/3.28 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)). [resolve(1189,a,1199,a)].
% 3.08/3.28 1202 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].
% 3.08/3.28 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1202,a,1190,a)].
% 3.08/3.28 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1202,a,1191,a)].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1202,a,1192,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1202,a,1193,a)].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)). [resolve(1202,a,1196,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)). [resolve(1202,a,1197,a)].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1202,a,1198,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1202,a,1199,a)].
% 3.08/3.29 1203 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].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1203,a,1190,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1203,a,1191,a)].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1203,a,1192,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1203,a,1193,a)].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)). [resolve(1203,a,1196,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)). [resolve(1203,a,1197,a)].
% 3.08/3.29 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)). [resolve(1203,a,1198,a)].
% 3.08/3.29 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)). [resolve(1203,a,1199,a)].
% 3.12/3.38 1204 -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(971)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1204,b,1190,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1204,b,1191,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1204,b,1192,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1204,b,1193,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)). [resolve(1204,b,1196,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)). [resolve(1204,b,1197,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)). [resolve(1204,b,1198,a)].
% 3.12/3.38 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)). [resolve(1204,b,1199,a)].
% 3.12/3.38 1205 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.12/3.38 1206 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(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(111)].
% 3.12/3.38 1207 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(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(112)].
% 3.22/3.48 1208 -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(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(113)].
% 3.22/3.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | hBOOL(hAPP(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(1205,a,1208,a)].
% 3.22/3.48 1209 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(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(1209,a,1208,a)].
% 3.22/3.48 1210 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(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(1210,a,1208,a)].
% 3.22/3.48 1211 -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(975)].
% 3.22/3.48 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(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(1211,b,1208,a)].
% 3.22/3.48 1212 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.48 1213 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(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(118)].
% 3.22/3.48 1214 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(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(119)].
% 3.22/3.48 1215 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | hBOOL(hAPP(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(120)].
% 3.22/3.48 1216 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(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(137)].
% 3.22/3.48 1217 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | hBOOL(hAPP(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(138)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | hBOOL(hAPP(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(1212,a,1215,a)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | hBOOL(hAPP(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(1212,a,1216,a)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | hBOOL(hAPP(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(1212,a,1217,a)].
% 3.22/3.49 1218 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) | hBOOL(hAPP(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(1218,a,1215,a)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(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(1218,a,1216,a)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) | hBOOL(hAPP(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(1218,a,1217,a)].
% 3.22/3.49 1219 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(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(1219,a,1215,a)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(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(1219,a,1216,a)].
% 3.22/3.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(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(1219,a,1217,a)].
% 3.22/3.49 1220 -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(970)].
% 3.22/3.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(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(1220,b,1215,a)].
% 3.38/3.59 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(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(1220,b,1216,a)].
% 3.38/3.59 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(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(1220,b,1217,a)].
% 3.38/3.59 1221 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.38/3.59 1222 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(128)].
% 3.38/3.59 1223 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(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(129)].
% 3.38/3.59 1224 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(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(129)].
% 3.38/3.59 1225 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(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(129)].
% 3.38/3.59 1226 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(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(130)].
% 3.38/3.59 1227 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(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(131)].
% 3.38/3.59 1228 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(132)].
% 3.38/3.59 1229 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(135)].
% 3.38/3.59 1230 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(136)].
% 3.38/3.59 1231 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(140)].
% 3.38/3.59 1232 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(141)].
% 3.38/3.59 1233 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) | hBOOL(hAPP(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(142)].
% 3.38/3.59 1234 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) | hBOOL(hAPP(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(143)].
% 3.38/3.59 1235 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(144)].
% 3.38/3.59 1236 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(145)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(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(1221,a,1222,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(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(1221,a,1223,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(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(1221,a,1224,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(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(1221,a,1225,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1221,a,1226,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A))). [resolve(1221,a,1227,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1221,a,1228,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(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(1221,a,1229,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1221,a,1230,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(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(1221,a,1231,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(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(1221,a,1232,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1221,a,1233,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1221,a,1234,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1221,a,1235,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1221,a,1236,a)].
% 3.38/3.59 1237 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1237,a,1222,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(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(1237,a,1223,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(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(1237,a,1224,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(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(1237,a,1225,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1237,a,1226,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A))). [resolve(1237,a,1227,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(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(1237,a,1228,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1237,a,1229,a)].
% 3.38/3.59 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(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(1237,a,1230,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1237,a,1231,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1237,a,1232,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1237,a,1233,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1237,a,1234,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(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(1237,a,1235,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(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(1237,a,1236,a)].
% 3.38/3.60 1238 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(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(1238,a,1222,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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(1238,a,1223,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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(1238,a,1224,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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(1238,a,1225,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1238,a,1226,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),A))). [resolve(1238,a,1227,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1238,a,1228,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(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(1238,a,1229,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1238,a,1230,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(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(1238,a,1231,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(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(1238,a,1232,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1238,a,1233,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1238,a,1234,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1238,a,1235,a)].
% 3.38/3.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1238,a,1236,a)].
% 3.38/3.60 1239 -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(977)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(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(1239,b,1222,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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(1239,b,1223,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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(1239,b,1224,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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(1239,b,1225,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(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(1239,b,1226,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(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(1239,b,1227,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1239,b,1228,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(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(1239,b,1229,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1239,b,1230,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(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(1239,b,1231,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(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(1239,b,1232,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1239,b,1233,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1239,b,1234,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1239,b,1235,a)].
% 3.38/3.60 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1239,b,1236,a)].
% 3.49/3.70 1240 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.49/3.70 1241 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(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(149)].
% 3.49/3.70 1242 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(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(150)].
% 3.49/3.70 1243 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(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(151)].
% 3.49/3.70 1244 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(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(152)].
% 3.49/3.70 1245 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(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(153)].
% 3.49/3.70 1246 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(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(154)].
% 3.49/3.70 1247 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) | hBOOL(hAPP(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(156)].
% 3.49/3.70 1248 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),C)) | hBOOL(hAPP(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(388)].
% 3.49/3.70 1249 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D)) | hBOOL(hAPP(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(435)].
% 3.49/3.70 1250 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(436)].
% 3.49/3.70 1251 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) # label(fact_power__increasing__iff) # label(axiom). [clausify(437)].
% 3.49/3.70 1252 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) # label(fact_power__increasing__iff) # label(axiom). [clausify(437)].
% 3.49/3.70 1253 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) # label(fact_power__le__imp__le__exp) # label(axiom). [clausify(438)].
% 3.49/3.70 1254 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(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(439)].
% 3.49/3.70 1255 -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) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(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(440)].
% 3.49/3.70 1256 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(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(457)].
% 3.49/3.70 1257 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(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(458)].
% 3.49/3.70 1258 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(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(459)].
% 3.49/3.70 1259 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(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(460)].
% 3.49/3.70 1260 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(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(462)].
% 3.49/3.70 1261 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(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(462)].
% 3.49/3.70 1262 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_power__less__imp__less__base) # label(axiom). [clausify(465)].
% 3.49/3.70 1263 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(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(466)].
% 3.49/3.70 1264 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(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(467)].
% 3.49/3.70 1265 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),D)) | hBOOL(hAPP(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(470)].
% 3.49/3.70 1266 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) # label(fact_power__less__imp__less__exp) # label(axiom). [clausify(471)].
% 3.49/3.70 1267 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(472)].
% 3.49/3.70 1268 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(472)].
% 3.49/3.70 1269 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A)),D)) | hBOOL(hAPP(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(473)].
% 3.49/3.70 1270 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(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(474)].
% 3.49/3.70 1271 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(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(475)].
% 3.49/3.70 1272 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Nat_OSuc(C)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_power__le__imp__le__base) # label(axiom). [clausify(658)].
% 3.49/3.70 1273 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Nat_OSuc(C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | B = D # label(fact_power__inject__base) # label(axiom). [clausify(659)].
% 3.49/3.71 1274 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)))) # label(fact_power__gt1) # label(axiom). [clausify(660)].
% 3.49/3.71 1275 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))),B)) # label(fact_realpow__Suc__le__self) # label(axiom). [clausify(668)].
% 3.49/3.71 1276 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))),c_Groups_Oone__class_Oone(A))) # label(fact_power__Suc__less__one) # label(axiom). [clausify(669)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1240,a,1241,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1240,a,1242,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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(1240,a,1243,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1240,a,1244,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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(1240,a,1245,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1240,a,1246,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(1240,a,1247,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)) | hBOOL(hAPP(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(1240,a,1248,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1240,a,1249,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1240,a,1250,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1240,a,1251,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1240,a,1252,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(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(1240,a,1254,a)].
% 3.49/3.71 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) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(1240,a,1255,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(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(1240,a,1256,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(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(1240,a,1257,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(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(1240,a,1258,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(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(1240,a,1259,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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(1240,a,1260,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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(1240,a,1261,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)). [resolve(1240,a,1262,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(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(1240,a,1263,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(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(1240,a,1264,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1240,a,1265,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1240,a,1266,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1240,a,1269,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(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(1240,a,1270,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(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(1240,a,1271,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Nat_OSuc(B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),c_Nat_OSuc(B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1240,a,1272,a)].
% 3.49/3.71 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Nat_OSuc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),c_Nat_OSuc(B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | A = C. [resolve(1240,a,1273,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(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),c_Nat_OSuc(B)))). [resolve(1240,a,1274,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Nat_OSuc(B))),A)). [resolve(1240,a,1275,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Nat_OSuc(B))),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1240,a,1276,a)].
% 3.49/3.71 1277 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1277,a,1241,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1277,a,1242,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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(1277,a,1243,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1277,a,1244,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(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(1277,a,1245,a)].
% 3.49/3.71 Derived: hBOOL(hAPP(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(1277,a,1246,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(1277,a,1247,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1277,a,1248,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1277,a,1249,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1277,a,1250,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1277,a,1251,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1277,a,1252,a)].
% 3.49/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(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(1277,a,1254,a)].
% 3.51/3.71 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) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(1277,a,1255,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(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(1277,a,1256,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(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(1277,a,1257,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(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(1277,a,1258,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(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(1277,a,1259,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(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(1277,a,1260,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(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(1277,a,1261,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)). [resolve(1277,a,1262,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(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(1277,a,1263,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(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(1277,a,1264,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1277,a,1265,a)].
% 3.51/3.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1277,a,1266,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1277,a,1269,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(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(1277,a,1270,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(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(1277,a,1271,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Nat_OSuc(B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),c_Nat_OSuc(B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1277,a,1272,a)].
% 3.51/3.72 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Nat_OSuc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),c_Nat_OSuc(B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | A = C. [resolve(1277,a,1273,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(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),c_Nat_OSuc(B)))). [resolve(1277,a,1274,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Nat_OSuc(B))),A)). [resolve(1277,a,1275,a)].
% 3.51/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Nat_OSuc(B))),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1277,a,1276,a)].
% 3.51/3.72 1278 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 3.51/3.72 Derived: hBOOL(hAPP(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(1278,a,1241,a)].
% 3.51/3.72 Derived: hBOOL(hAPP(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(1278,a,1242,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(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(1278,a,1243,a)].
% 3.52/3.72 Derived: hBOOL(hAPP(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(1278,a,1244,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(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(1278,a,1245,a)].
% 3.52/3.72 Derived: hBOOL(hAPP(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(1278,a,1246,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))). [resolve(1278,a,1247,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(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(1278,a,1248,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1278,a,1249,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1278,a,1250,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1278,a,1251,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1278,a,1252,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1278,a,1254,a)].
% 3.52/3.72 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) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(1278,a,1255,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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(1278,a,1256,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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(1278,a,1257,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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(1278,a,1258,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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(1278,a,1259,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(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(1278,a,1260,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(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(1278,a,1261,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)). [resolve(1278,a,1262,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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(1278,a,1263,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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(1278,a,1264,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1278,a,1265,a)].
% 3.52/3.72 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1278,a,1266,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1278,a,1269,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1278,a,1270,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1278,a,1271,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Nat_OSuc(B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),c_Nat_OSuc(B)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1278,a,1272,a)].
% 3.52/3.73 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Nat_OSuc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),c_Nat_OSuc(B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | A = C. [resolve(1278,a,1273,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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),c_Nat_OSuc(B)))). [resolve(1278,a,1274,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Nat_OSuc(B))),A)). [resolve(1278,a,1275,a)].
% 3.52/3.73 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Nat_OSuc(B))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1278,a,1276,a)].
% 3.52/3.73 1279 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(989)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1279,b,1241,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1279,b,1242,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1279,b,1243,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1279,b,1244,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1279,b,1245,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1279,b,1246,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D))). [resolve(1279,b,1247,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(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(1279,b,1248,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D)) | hBOOL(hAPP(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(1279,b,1249,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1279,b,1250,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)). [resolve(1279,b,1251,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)). [resolve(1279,b,1252,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1279,b,1254,a)].
% 3.52/3.73 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) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | B = D. [resolve(1279,b,1255,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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(1279,b,1256,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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(1279,b,1257,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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(1279,b,1258,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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(1279,b,1259,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1279,b,1260,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1279,b,1261,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)). [resolve(1279,b,1262,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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(1279,b,1263,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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(1279,b,1264,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1279,b,1265,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)). [resolve(1279,b,1266,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1279,b,1269,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1279,b,1270,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1279,b,1271,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Nat_OSuc(C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),c_Nat_OSuc(C)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1279,b,1272,a)].
% 3.52/3.73 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Nat_OSuc(C)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),c_Nat_OSuc(C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | B = D. [resolve(1279,b,1273,a)].
% 3.60/3.84 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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_Nat_OSuc(C)))). [resolve(1279,b,1274,a)].
% 3.60/3.84 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Nat_OSuc(C))),B)). [resolve(1279,b,1275,a)].
% 3.60/3.84 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Nat_OSuc(C))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1279,b,1276,a)].
% 3.60/3.84 1280 class_Rings_Ozero__neq__one(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.60/3.84 1281 -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(211)].
% 3.60/3.84 1282 -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(212)].
% 3.60/3.84 1283 -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(461)].
% 3.60/3.84 1284 -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(461)].
% 3.60/3.84 1285 -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(461)].
% 3.60/3.84 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1280,a,1281,a)].
% 3.60/3.84 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(1280,a,1283,d)].
% 3.60/3.84 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(1280,a,1284,d)].
% 3.60/3.84 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(1280,a,1285,d)].
% 3.60/3.85 1286 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.60/3.85 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1286,a,1281,a)].
% 3.60/3.85 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(1286,a,1283,d)].
% 3.60/3.85 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(1286,a,1284,d)].
% 3.60/3.85 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(1286,a,1285,d)].
% 3.60/3.85 1287 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.60/3.85 Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1287,a,1281,a)].
% 3.60/3.85 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(1287,a,1283,d)].
% 3.60/3.85 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(1287,a,1284,d)].
% 3.60/3.85 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(1287,a,1285,d)].
% 3.60/3.85 1288 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 3.60/3.85 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1288,a,1281,a)].
% 3.60/3.85 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(1288,a,1283,d)].
% 3.60/3.85 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(1288,a,1284,d)].
% 3.60/3.85 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(1288,a,1285,d)].
% 3.83/4.08 1289 -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(1003)].
% 3.83/4.08 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(1289,b,1281,a)].
% 3.83/4.08 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(1289,b,1283,d)].
% 3.83/4.08 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(1289,b,1284,d)].
% 3.83/4.08 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(1289,b,1285,d)].
% 3.83/4.08 1290 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f10(B,A)),f11(B,A))) # label(fact_decseq__def) # label(axiom). [clausify(220)].
% 3.83/4.08 1291 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D)),hAPP(B,C))) # label(fact_decseq__def) # label(axiom). [clausify(220)].
% 3.83/4.08 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f10(B,A)),f11(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D)),hAPP(B,C))). [resolve(1290,b,1291,b)].
% 3.83/4.08 1292 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f11(B,A))),hAPP(B,f10(B,A)))) # label(fact_decseq__def) # label(axiom). [clausify(220)].
% 3.83/4.08 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f11(B,A))),hAPP(B,f10(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D)),hAPP(B,C))). [resolve(1292,b,1291,b)].
% 3.83/4.08 1293 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | c_SEQ_Omonoseq(A,B) # label(fact_decseq__imp__monoseq) # label(axiom). [clausify(247)].
% 3.83/4.08 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f10(B,A)),f11(B,A))). [resolve(1293,b,1290,b)].
% 3.83/4.08 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f11(B,A))),hAPP(B,f10(B,A)))). [resolve(1293,b,1292,b)].
% 3.83/4.08 1294 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) # label(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.83/4.08 1295 -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(221)].
% 3.83/4.08 1296 -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(221)].
% 3.83/4.08 1297 -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),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(303)].
% 3.83/4.08 1298 -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),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(303)].
% 3.83/4.08 1299 -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(303)].
% 3.83/4.08 1300 -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(306)].
% 3.83/4.08 1301 -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(306)].
% 3.83/4.08 1302 -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(306)].
% 3.83/4.08 1303 -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),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(387)].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1294,a,1295,a)].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1294,a,1296,a)].
% 3.83/4.08 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(1294,a,1297,a)].
% 3.83/4.08 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(1294,a,1298,a)].
% 3.83/4.08 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D),A)). [resolve(1294,a,1299,a)].
% 3.83/4.08 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(1294,a,1300,a)].
% 3.83/4.08 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(1294,a,1301,a)].
% 3.83/4.08 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),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),E)). [resolve(1294,a,1303,a)].
% 3.83/4.08 1304 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) # label(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1304,a,1295,a)].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1304,a,1296,a)].
% 3.83/4.08 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(1304,a,1297,a)].
% 3.83/4.08 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(1304,a,1298,a)].
% 3.83/4.08 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D),A)). [resolve(1304,a,1299,a)].
% 3.83/4.08 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(1304,a,1300,a)].
% 3.83/4.08 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(1304,a,1301,a)].
% 3.83/4.08 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),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),E)). [resolve(1304,a,1303,a)].
% 3.83/4.08 1305 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B. [resolve(1305,a,1295,a)].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B. [resolve(1305,a,1296,a)].
% 3.83/4.08 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1305,a,1297,a)].
% 3.83/4.08 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(1305,a,1298,a)].
% 3.83/4.08 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),D),B)) = 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)). [resolve(1305,a,1299,a)].
% 3.83/4.08 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(1305,a,1300,a)].
% 3.83/4.08 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(1305,a,1301,a)].
% 3.83/4.08 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),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),E)). [resolve(1305,a,1303,a)].
% 3.83/4.08 1306 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].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1306,a,1295,a)].
% 3.83/4.08 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1306,a,1296,a)].
% 3.83/4.08 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(1306,a,1297,a)].
% 3.83/4.09 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(1306,a,1298,a)].
% 3.83/4.09 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)) = 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)). [resolve(1306,a,1299,a)].
% 3.83/4.09 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)) | A = C | B = D. [resolve(1306,a,1300,a)].
% 3.83/4.09 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)) | A != C. [resolve(1306,a,1301,a)].
% 3.83/4.09 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),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),E)). [resolve(1306,a,1303,a)].
% 3.83/4.09 1307 -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(969)].
% 3.83/4.09 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(1307,b,1295,a)].
% 3.83/4.09 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(1307,b,1296,a)].
% 3.83/4.09 Derived: -class_Rings_Oidom(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)),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)). [resolve(1307,b,1297,a)].
% 3.83/4.09 Derived: -class_Rings_Oidom(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)). [resolve(1307,b,1298,a)].
% 3.83/4.09 Derived: -class_Rings_Oidom(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)),E),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)),E),B)). [resolve(1307,b,1299,a)].
% 4.09/4.33 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(1307,b,1300,a)].
% 4.09/4.33 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(1307,b,1301,a)].
% 4.09/4.33 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),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),F)). [resolve(1307,b,1303,a)].
% 4.09/4.33 1308 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f14(B,A)),f15(B,A))) # label(fact_incseq__def) # label(axiom). [clausify(225)].
% 4.09/4.33 1309 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))) # label(fact_incseq__def) # label(axiom). [clausify(225)].
% 4.09/4.33 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f14(B,A)),f15(B,A))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))). [resolve(1308,b,1309,b)].
% 4.09/4.33 1310 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f14(B,A))),hAPP(B,f15(B,A)))) # label(fact_incseq__def) # label(axiom). [clausify(225)].
% 4.09/4.33 Derived: -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f14(B,A))),hAPP(B,f15(B,A)))) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C)),hAPP(B,D))). [resolve(1310,b,1309,b)].
% 4.09/4.33 1311 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | c_SEQ_Omonoseq(A,B) # label(fact_incseq__imp__monoseq) # label(axiom). [clausify(246)].
% 4.09/4.33 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f14(B,A)),f15(B,A))). [resolve(1311,b,1308,b)].
% 4.09/4.33 Derived: -class_Orderings_Oorder(A) | c_SEQ_Omonoseq(A,B) | -class_Orderings_Oorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f14(B,A))),hAPP(B,f15(B,A)))). [resolve(1311,b,1310,b)].
% 4.09/4.33 1312 class_RealVector_Ometric__space(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Ometric__space) # label(axiom). [assumption].
% 4.09/4.33 1313 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(A,c_COMBK(A,tc_Nat_Onat,B)) # label(fact_convergent__const) # label(axiom). [clausify(231)].
% 4.09/4.33 Derived: c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBK(tc_RealDef_Oreal,tc_Nat_Onat,A)). [resolve(1312,a,1313,a)].
% 4.09/4.33 1314 class_RealVector_Ometric__space(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Ometric__space) # label(axiom). [assumption].
% 4.26/4.56 Derived: c_SEQ_Oconvergent(tc_Complex_Ocomplex,c_COMBK(tc_Complex_Ocomplex,tc_Nat_Onat,A)). [resolve(1314,a,1313,a)].
% 4.26/4.56 1315 class_Groups_Osgn__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Osgn__if) # label(axiom). [assumption].
% 4.26/4.56 1316 -class_Groups_Osgn__if(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn0) # label(axiom). [clausify(256)].
% 4.26/4.56 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1315,a,1316,a)].
% 4.26/4.56 1317 class_Groups_Osgn__if(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Osgn__if) # label(axiom). [assumption].
% 4.26/4.56 1318 -class_Rings_Olinordered__idom(A) | class_Groups_Osgn__if(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Osgn__if) # label(axiom). [clausify(1016)].
% 4.26/4.56 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1318,b,1316,a)].
% 4.26/4.56 1319 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 4.26/4.56 1320 -class_Rings_Olinordered__semiring__1__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),E)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(271)].
% 4.26/4.56 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(1319,a,1320,a)].
% 4.26/4.56 1321 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 4.26/4.56 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),D)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(1321,a,1320,a)].
% 4.26/4.56 1322 -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(973)].
% 4.26/4.56 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),E)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(1322,b,1320,a)].
% 4.58/4.79 1323 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 4.58/4.79 1324 -class_RealVector_Oreal__normed__div__algebra(A) | 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),c_RealVector_Onorm__class_Onorm(A,B)),C) # label(fact_norm__power) # label(axiom). [clausify(273)].
% 4.58/4.79 1325 -class_RealVector_Oreal__normed__div__algebra(A) | 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),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)) # label(fact_norm__mult) # label(axiom). [clausify(274)].
% 4.58/4.79 1326 -class_RealVector_Oreal__normed__div__algebra(A) | c_Groups_Osgn__class_Osgn(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C)) # label(fact_sgn__mult) # label(axiom). [clausify(343)].
% 4.58/4.79 Derived: 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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B). [resolve(1323,a,1324,a)].
% 4.58/4.79 Derived: 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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)). [resolve(1323,a,1325,a)].
% 4.58/4.79 Derived: c_Groups_Osgn__class_Osgn(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_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,B)). [resolve(1323,a,1326,a)].
% 4.58/4.79 1327 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 4.58/4.79 Derived: 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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B). [resolve(1327,a,1324,a)].
% 4.58/4.79 Derived: 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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)). [resolve(1327,a,1325,a)].
% 4.58/4.79 Derived: c_Groups_Osgn__class_Osgn(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_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A)),c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,B)). [resolve(1327,a,1326,a)].
% 4.58/4.79 1328 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.58/4.79 1329 -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(275)].
% 4.70/4.91 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(1328,a,1329,a)].
% 4.70/4.91 1330 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.70/4.91 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(1330,a,1329,a)].
% 4.70/4.91 1331 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.70/4.91 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(1331,a,1329,a)].
% 4.70/4.91 1332 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.70/4.91 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(1332,a,1329,a)].
% 4.70/4.91 1333 -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(990)].
% 4.70/4.91 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(1333,b,1329,a)].
% 4.70/4.91 1334 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 4.70/4.91 1335 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))) # label(fact_norm__mult__ineq) # label(axiom). [clausify(289)].
% 4.70/4.91 1336 -class_RealVector_Oreal__normed__algebra(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D)),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(290)].
% 4.70/4.91 1337 -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(293)].
% 4.70/4.91 1338 -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(294)].
% 4.70/4.91 1339 -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(295)].
% 4.70/4.91 1340 -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(296)].
% 4.70/4.91 1341 -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(307)].
% 4.70/4.91 1342 -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(308)].
% 4.70/4.91 1343 -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(309)].
% 4.70/4.91 1344 -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(310)].
% 4.70/4.91 1345 -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(347)].
% 4.70/4.91 1346 -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(348)].
% 4.70/4.91 1347 -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(349)].
% 4.70/4.91 1348 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f24(A))) # label(fact_mult_Opos__bounded) # label(axiom). [clausify(539)].
% 4.70/4.91 1349 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f24(A)))) # label(fact_mult_Opos__bounded) # label(axiom). [clausify(539)].
% 4.70/4.91 1350 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f25(B,A))) # label(fact_mult__right_Opos__bounded) # label(axiom). [clausify(540)].
% 4.70/4.91 1351 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,C)),f25(B,A)))) # label(fact_mult__right_Opos__bounded) # label(axiom). [clausify(540)].
% 4.70/4.91 1352 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f26(B,A))) # label(fact_mult__left_Opos__bounded) # label(axiom). [clausify(541)].
% 4.70/4.91 1353 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,B)),f26(C,A)))) # label(fact_mult__left_Opos__bounded) # label(axiom). [clausify(541)].
% 4.70/4.91 1354 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f29(A))) # label(fact_mult_Ononneg__bounded) # label(axiom). [clausify(582)].
% 4.70/4.91 1355 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f29(A)))) # label(fact_mult_Ononneg__bounded) # label(axiom). [clausify(582)].
% 4.70/4.91 1356 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f30(B,A))) # label(fact_mult__right_Ononneg__bounded) # label(axiom). [clausify(583)].
% 4.70/4.91 1357 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,C)),f30(B,A)))) # label(fact_mult__right_Ononneg__bounded) # label(axiom). [clausify(583)].
% 4.70/4.91 1358 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f31(B,A))) # label(fact_mult__left_Ononneg__bounded) # label(axiom). [clausify(584)].
% 4.70/4.91 1359 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,B)),f31(C,A)))) # label(fact_mult__left_Ononneg__bounded) # label(axiom). [clausify(584)].
% 4.70/4.91 1360 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,B)),f54(C,A)))) # label(fact_mult__left_Obounded) # label(axiom). [clausify(710)].
% 4.70/4.91 1361 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f55(A)))) # label(fact_mult_Obounded) # label(axiom). [clausify(711)].
% 4.70/4.91 1362 -class_RealVector_Oreal__normed__algebra(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(A,C)),f56(B,A)))) # label(fact_mult__right_Obounded) # label(axiom). [clausify(712)].
% 4.70/4.91 1363 -class_RealVector_Oreal__normed__algebra(A) | 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult_Odiff__right) # label(axiom). [clausify(744)].
% 4.70/4.91 1364 -class_RealVector_Oreal__normed__algebra(A) | 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult__right_Odiff) # label(axiom). [clausify(745)].
% 4.70/4.91 1365 -class_RealVector_Oreal__normed__algebra(A) | 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),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),C) # label(fact_mult_Odiff__left) # label(axiom). [clausify(746)].
% 4.70/4.91 1366 -class_RealVector_Oreal__normed__algebra(A) | 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),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),C) # label(fact_mult__left_Odiff) # label(axiom). [clausify(747)].
% 4.70/4.91 1367 -class_RealVector_Oreal__normed__algebra(A) | 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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),c_Groups_Ominus__class_Ominus(A,C,E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),c_Groups_Ominus__class_Ominus(A,C,E))) # label(fact_mult_Oprod__diff__prod) # label(axiom). [clausify(785)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)))). [resolve(1334,a,1335,a)].
% 4.70/4.91 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(1334,a,1336,a)].
% 4.70/4.91 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(1334,a,1337,a)].
% 4.70/4.91 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(1334,a,1339,a)].
% 4.70/4.91 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(1334,a,1341,a)].
% 4.70/4.91 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(1334,a,1343,a)].
% 4.70/4.91 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(1334,a,1345,a)].
% 4.70/4.91 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(1334,a,1346,a)].
% 4.70/4.91 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(1334,a,1347,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f24(tc_RealDef_Oreal))). [resolve(1334,a,1348,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f24(tc_RealDef_Oreal)))). [resolve(1334,a,1349,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f25(A,tc_RealDef_Oreal))). [resolve(1334,a,1350,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f25(A,tc_RealDef_Oreal)))). [resolve(1334,a,1351,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f26(A,tc_RealDef_Oreal))). [resolve(1334,a,1352,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f26(B,tc_RealDef_Oreal)))). [resolve(1334,a,1353,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f29(tc_RealDef_Oreal))). [resolve(1334,a,1354,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f29(tc_RealDef_Oreal)))). [resolve(1334,a,1355,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f30(A,tc_RealDef_Oreal))). [resolve(1334,a,1356,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f30(A,tc_RealDef_Oreal)))). [resolve(1334,a,1357,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f31(A,tc_RealDef_Oreal))). [resolve(1334,a,1358,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f31(B,tc_RealDef_Oreal)))). [resolve(1334,a,1359,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f54(B,tc_RealDef_Oreal)))). [resolve(1334,a,1360,a)].
% 4.70/4.91 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f55(tc_RealDef_Oreal)))). [resolve(1334,a,1361,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f56(A,tc_RealDef_Oreal)))). [resolve(1334,a,1362,a)].
% 4.70/4.92 Derived: 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C)). [resolve(1334,a,1363,a)].
% 4.70/4.92 Derived: 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),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),B). [resolve(1334,a,1365,a)].
% 4.70/4.92 Derived: 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)) = 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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D))). [resolve(1334,a,1367,a)].
% 4.70/4.92 1368 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)))). [resolve(1368,a,1335,a)].
% 4.70/4.92 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C)),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(1368,a,1336,a)].
% 4.70/4.92 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(1368,a,1337,a)].
% 4.70/4.92 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(1368,a,1339,a)].
% 4.70/4.92 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(1368,a,1341,a)].
% 4.70/4.92 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(1368,a,1343,a)].
% 4.70/4.92 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(1368,a,1345,a)].
% 4.70/4.92 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(1368,a,1346,a)].
% 4.70/4.92 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(1368,a,1347,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f24(tc_Complex_Ocomplex))). [resolve(1368,a,1348,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f24(tc_Complex_Ocomplex)))). [resolve(1368,a,1349,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f25(A,tc_Complex_Ocomplex))). [resolve(1368,a,1350,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f25(A,tc_Complex_Ocomplex)))). [resolve(1368,a,1351,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f26(A,tc_Complex_Ocomplex))). [resolve(1368,a,1352,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f26(B,tc_Complex_Ocomplex)))). [resolve(1368,a,1353,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f29(tc_Complex_Ocomplex))). [resolve(1368,a,1354,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f29(tc_Complex_Ocomplex)))). [resolve(1368,a,1355,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f30(A,tc_Complex_Ocomplex))). [resolve(1368,a,1356,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f30(A,tc_Complex_Ocomplex)))). [resolve(1368,a,1357,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),f31(A,tc_Complex_Ocomplex))). [resolve(1368,a,1358,a)].
% 4.70/4.92 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f31(B,tc_Complex_Ocomplex)))). [resolve(1368,a,1359,a)].
% 4.75/5.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f54(B,tc_Complex_Ocomplex)))). [resolve(1368,a,1360,a)].
% 4.75/5.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f55(tc_Complex_Ocomplex)))). [resolve(1368,a,1361,a)].
% 4.75/5.03 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f56(A,tc_Complex_Ocomplex)))). [resolve(1368,a,1362,a)].
% 4.75/5.03 Derived: 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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C)). [resolve(1368,a,1363,a)].
% 4.75/5.03 Derived: 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),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),B). [resolve(1368,a,1365,a)].
% 4.75/5.03 Derived: 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)) = 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),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D))). [resolve(1368,a,1367,a)].
% 4.75/5.03 1369 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 4.75/5.03 1370 -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(299)].
% 4.75/5.03 1371 -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(299)].
% 4.75/5.03 1372 -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(299)].
% 4.75/5.03 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(1369,a,1370,a)].
% 4.75/5.03 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(1369,a,1371,a)].
% 4.90/5.16 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(1369,a,1372,a)].
% 4.90/5.16 1373 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 4.90/5.16 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(1373,a,1370,a)].
% 4.90/5.16 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(1373,a,1371,a)].
% 4.90/5.16 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(1373,a,1372,a)].
% 4.90/5.16 1374 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 4.90/5.16 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(1374,a,1370,a)].
% 4.90/5.16 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(1374,a,1371,a)].
% 4.90/5.16 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(1374,a,1372,a)].
% 4.90/5.16 1375 -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(983)].
% 4.90/5.16 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(1375,b,1370,a)].
% 4.90/5.16 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(1375,b,1371,a)].
% 4.90/5.16 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(1375,b,1372,a)].
% 4.90/5.16 1376 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 4.90/5.16 1377 -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(311)].
% 4.90/5.16 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(1376,a,1377,a)].
% 4.90/5.16 1378 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 4.90/5.16 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(1378,a,1377,a)].
% 5.06/5.28 1379 class_Rings_Osemiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring) # label(axiom). [assumption].
% 5.06/5.28 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(1379,a,1377,a)].
% 5.06/5.28 1380 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom). [assumption].
% 5.06/5.28 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(1380,a,1377,a)].
% 5.06/5.28 1381 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom). [clausify(1014)].
% 5.06/5.28 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(1381,b,1377,a)].
% 5.06/5.28 1382 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.06/5.28 1383 -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(312)].
% 5.06/5.28 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(1382,a,1383,a)].
% 5.06/5.28 1384 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.06/5.28 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(1384,a,1383,a)].
% 5.06/5.28 1385 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.06/5.28 1386 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 5.06/5.28 1387 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1001)].
% 5.06/5.28 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(1387,b,1383,a)].
% 5.18/5.39 1388 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 5.18/5.39 1389 -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(315)].
% 5.18/5.39 1390 -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(317)].
% 5.18/5.39 1391 -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(450)].
% 5.18/5.39 1392 -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(452)].
% 5.18/5.39 1393 -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(454)].
% 5.18/5.39 1394 -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(456)].
% 5.18/5.39 1395 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = 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)) # label(fact_power__add) # label(axiom). [clausify(464)].
% 5.18/5.39 1396 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(fact_power__Suc2) # label(axiom). [clausify(626)].
% 5.18/5.39 1397 -class_Groups_Omonoid__mult(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C) # label(fact_realpow__minus__mult) # label(axiom). [clausify(713)].
% 5.18/5.39 1398 -class_Groups_Omonoid__mult(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B))),D) # label(fact_lemma__realpow__diff) # label(axiom). [clausify(810)].
% 5.18/5.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(1388,a,1389,a)].
% 5.18/5.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1388,a,1390,a)].
% 5.18/5.39 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(1388,a,1391,a)].
% 5.18/5.39 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(1388,a,1392,a)].
% 5.18/5.39 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(1388,a,1393,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1388,a,1394,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = 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)). [resolve(1388,a,1395,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Nat_OSuc(B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A). [resolve(1388,a,1396,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B). [resolve(1388,a,1397,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))),C). [resolve(1388,a,1398,a)].
% 5.18/5.40 1399 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 5.18/5.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(1399,a,1389,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1399,a,1390,a)].
% 5.18/5.40 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(1399,a,1391,a)].
% 5.18/5.40 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(1399,a,1392,a)].
% 5.18/5.40 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(1399,a,1393,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1399,a,1394,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = 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)). [resolve(1399,a,1395,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Nat_OSuc(B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A). [resolve(1399,a,1396,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B). [resolve(1399,a,1397,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))),C). [resolve(1399,a,1398,a)].
% 5.18/5.40 1400 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom). [assumption].
% 5.18/5.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A) = A. [resolve(1400,a,1389,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1400,a,1390,a)].
% 5.18/5.40 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(1400,a,1391,a)].
% 5.18/5.40 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(1400,a,1392,a)].
% 5.18/5.40 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(1400,a,1393,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1400,a,1394,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = 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)). [resolve(1400,a,1395,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Nat_OSuc(B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A). [resolve(1400,a,1396,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B). [resolve(1400,a,1397,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))),C). [resolve(1400,a,1398,a)].
% 5.18/5.40 1401 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom). [assumption].
% 5.18/5.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(1401,a,1389,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1401,a,1390,a)].
% 5.18/5.40 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(1401,a,1391,a)].
% 5.18/5.40 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(1401,a,1392,a)].
% 5.18/5.40 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(1401,a,1393,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1401,a,1394,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = 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)). [resolve(1401,a,1395,a)].
% 5.18/5.40 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Nat_OSuc(B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(1401,a,1396,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B). [resolve(1401,a,1397,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))),C). [resolve(1401,a,1398,a)].
% 5.18/5.40 1402 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1007)].
% 5.18/5.40 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(1402,b,1389,a)].
% 5.18/5.40 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(1402,b,1390,a)].
% 5.18/5.40 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(1402,b,1391,a)].
% 5.18/5.40 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(1402,b,1392,a)].
% 5.18/5.40 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(1402,b,1393,a)].
% 5.18/5.40 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(1402,b,1394,a)].
% 5.18/5.40 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = 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)). [resolve(1402,b,1395,a)].
% 5.18/5.40 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Nat_OSuc(C)) = 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). [resolve(1402,b,1396,a)].
% 5.18/5.40 Derived: -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C). [resolve(1402,b,1397,a)].
% 5.43/5.65 Derived: -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B))),D). [resolve(1402,b,1398,a)].
% 5.43/5.65 1403 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.43/5.65 1404 -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(316)].
% 5.43/5.65 1405 -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(318)].
% 5.43/5.65 1406 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__mult__distrib) # label(axiom). [clausify(453)].
% 5.43/5.65 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(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),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(1403,a,1406,a)].
% 5.43/5.65 1407 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.43/5.65 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(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),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(1407,a,1406,a)].
% 5.43/5.65 1408 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.43/5.65 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(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),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(1408,a,1406,a)].
% 5.43/5.65 1409 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.43/5.65 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(1409,a,1406,a)].
% 5.43/5.65 1410 -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(991)].
% 5.43/5.65 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(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)),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(1410,b,1406,a)].
% 5.43/5.65 1411 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 5.43/5.65 1412 -class_Rings_Olinordered__ring(A) | hBOOL(hAPP(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(353)].
% 5.43/5.66 1413 -class_Rings_Olinordered__ring(A) | -hBOOL(hAPP(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(370)].
% 5.43/5.66 1414 -class_Rings_Olinordered__ring(A) | -hBOOL(hAPP(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(478)].
% 5.43/5.66 1415 -class_Rings_Olinordered__ring(A) | hBOOL(hAPP(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(510)].
% 5.43/5.66 Derived: hBOOL(hAPP(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(1411,a,1412,a)].
% 5.43/5.66 Derived: -hBOOL(hAPP(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(1411,a,1413,a)].
% 5.43/5.66 Derived: -hBOOL(hAPP(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(1411,a,1414,a)].
% 5.43/5.66 Derived: hBOOL(hAPP(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(1411,a,1415,a)].
% 5.43/5.66 1416 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom). [assumption].
% 5.43/5.66 Derived: hBOOL(hAPP(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(1416,a,1412,a)].
% 5.43/5.66 Derived: -hBOOL(hAPP(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(1416,a,1413,a)].
% 5.43/5.66 Derived: -hBOOL(hAPP(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(1416,a,1414,a)].
% 5.43/5.66 Derived: hBOOL(hAPP(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(1416,a,1415,a)].
% 5.43/5.66 1417 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom). [clausify(997)].
% 5.43/5.66 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1417,b,1412,a)].
% 5.43/5.66 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1417,b,1413,a)].
% 5.43/5.66 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1417,b,1414,a)].
% 5.58/5.78 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1417,b,1415,a)].
% 5.58/5.78 1418 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 5.58/5.78 1419 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(354)].
% 5.58/5.78 1420 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(354)].
% 5.58/5.78 1421 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(354)].
% 5.58/5.78 1422 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(354)].
% 5.58/5.78 1423 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(354)].
% 5.58/5.78 1424 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(354)].
% 5.58/5.78 1425 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(355)].
% 5.58/5.78 1426 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(355)].
% 5.58/5.78 1427 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(355)].
% 5.58/5.78 1428 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(355)].
% 5.58/5.78 1429 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(355)].
% 5.58/5.78 1430 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(355)].
% 5.58/5.78 1431 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(371)].
% 5.58/5.78 1432 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(371)].
% 5.58/5.78 1433 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(371)].
% 5.58/5.78 1434 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(371)].
% 5.58/5.78 1435 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(371)].
% 5.58/5.78 1436 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(371)].
% 5.58/5.78 1437 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(372)].
% 5.58/5.78 1438 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(372)].
% 5.58/5.78 1439 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(372)].
% 5.58/5.78 1440 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(372)].
% 5.58/5.78 1441 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(372)].
% 5.58/5.78 1442 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(372)].
% 5.58/5.78 1443 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(373)].
% 5.58/5.78 1444 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(373)].
% 5.58/5.78 1445 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(379)].
% 5.58/5.78 1446 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(379)].
% 5.58/5.78 1447 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(381)].
% 5.58/5.78 1448 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(385)].
% 5.58/5.78 1449 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(386)].
% 5.58/5.78 1450 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(408)].
% 5.58/5.78 1451 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(408)].
% 5.58/5.78 1452 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),C)) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(409)].
% 5.58/5.78 1453 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),C)) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(409)].
% 5.58/5.78 1454 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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(477)].
% 5.58/5.78 1455 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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(477)].
% 5.58/5.78 1456 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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(477)].
% 5.58/5.78 1457 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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(479)].
% 5.58/5.78 1458 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(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(479)].
% 5.58/5.78 1459 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(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(479)].
% 5.58/5.78 1460 -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(507)].
% 5.58/5.78 1461 -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(507)].
% 5.58/5.78 1462 -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(507)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1420,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1421,a)].
% 5.58/5.78 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1418,a,1423,a)].
% 5.58/5.78 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1424,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1418,a,1426,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1427,a)].
% 5.58/5.78 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1429,a)].
% 5.58/5.78 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1418,a,1430,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1431,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A)). [resolve(1418,a,1432,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1433,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A)). [resolve(1418,a,1434,a)].
% 5.58/5.78 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)). [resolve(1418,a,1435,a)].
% 5.58/5.78 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A)). [resolve(1418,a,1436,a)].
% 5.58/5.78 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1437,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),B)). [resolve(1418,a,1438,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1418,a,1439,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),B)). [resolve(1418,a,1440,a)].
% 5.58/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)). [resolve(1418,a,1441,a)].
% 5.58/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),B)). [resolve(1418,a,1442,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)). [resolve(1418,a,1443,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),B)). [resolve(1418,a,1445,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1418,a,1447,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1418,a,1450,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),C)). [resolve(1418,a,1451,a)].
% 5.58/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),B)). [resolve(1418,a,1452,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),B)). [resolve(1418,a,1453,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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(1418,a,1454,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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(1418,a,1455,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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(1418,a,1456,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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(1418,a,1457,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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(1418,a,1458,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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(1418,a,1459,a)].
% 5.60/5.79 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(1418,a,1460,a)].
% 5.60/5.79 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(1418,a,1461,a)].
% 5.60/5.79 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(1418,a,1462,a)].
% 5.60/5.79 1463 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1420,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1421,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1463,a,1423,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1424,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1463,a,1426,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1427,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1429,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1463,a,1430,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1431,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),A)). [resolve(1463,a,1432,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1433,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),A)). [resolve(1463,a,1434,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)). [resolve(1463,a,1435,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),A)). [resolve(1463,a,1436,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1437,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),B)). [resolve(1463,a,1438,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1463,a,1439,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),B)). [resolve(1463,a,1440,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)). [resolve(1463,a,1441,a)].
% 5.60/5.79 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),B)). [resolve(1463,a,1442,a)].
% 5.60/5.79 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)). [resolve(1463,a,1443,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),B)). [resolve(1463,a,1445,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1463,a,1447,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1463,a,1450,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),C)). [resolve(1463,a,1451,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),B)). [resolve(1463,a,1452,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),B)). [resolve(1463,a,1453,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(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(1463,a,1454,a)].
% 5.60/5.80 Derived: hBOOL(hAPP(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(1463,a,1455,a)].
% 5.60/5.80 Derived: hBOOL(hAPP(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(1463,a,1456,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(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(1463,a,1457,a)].
% 5.60/5.80 Derived: -hBOOL(hAPP(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(1463,a,1458,a)].
% 5.60/5.80 Derived: hBOOL(hAPP(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(1463,a,1459,a)].
% 5.60/5.80 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(1463,a,1460,a)].
% 5.60/5.80 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(1463,a,1461,a)].
% 5.60/5.80 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(1463,a,1462,a)].
% 5.60/5.80 1464 -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(982)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1420,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1421,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1464,b,1423,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1424,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1464,b,1426,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1427,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1429,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1464,b,1430,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1431,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),B)). [resolve(1464,b,1432,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1433,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),B)). [resolve(1464,b,1434,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)). [resolve(1464,b,1435,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),B)). [resolve(1464,b,1436,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1437,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),C)). [resolve(1464,b,1438,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1464,b,1439,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),C)). [resolve(1464,b,1440,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)). [resolve(1464,b,1441,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),C)). [resolve(1464,b,1442,a)].
% 5.60/5.80 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)). [resolve(1464,b,1443,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),C)). [resolve(1464,b,1445,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1464,b,1447,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1464,b,1450,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),D)). [resolve(1464,b,1451,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),C)). [resolve(1464,b,1452,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),C)). [resolve(1464,b,1453,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1464,b,1454,a)].
% 5.60/5.81 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1464,b,1455,a)].
% 5.72/5.93 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1464,b,1456,a)].
% 5.72/5.93 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1464,b,1457,a)].
% 5.72/5.93 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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(1464,b,1458,a)].
% 5.72/5.93 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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(1464,b,1459,a)].
% 5.72/5.93 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(1464,b,1460,a)].
% 5.72/5.93 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(1464,b,1461,a)].
% 5.72/5.93 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(1464,b,1462,a)].
% 5.72/5.93 1465 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 5.72/5.93 1466 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(356)].
% 5.72/5.93 1467 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(357)].
% 5.88/6.07 1468 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(358)].
% 5.88/6.07 1469 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(359)].
% 5.88/6.07 1470 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(369)].
% 5.88/6.07 1471 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(369)].
% 5.88/6.07 1472 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 5.88/6.07 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1472,a,1466,a)].
% 5.88/6.07 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(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(1472,a,1467,a)].
% 5.88/6.07 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1472,a,1468,a)].
% 5.88/6.07 1473 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 5.88/6.07 1474 -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(981)].
% 5.88/6.07 1475 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 5.88/6.07 1476 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(360)].
% 5.88/6.07 1477 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(364)].
% 5.88/6.07 1478 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(365)].
% 5.88/6.07 1479 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(368)].
% 5.88/6.07 1480 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(368)].
% 5.88/6.07 1481 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(788)].
% 5.88/6.07 1482 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(788)].
% 5.88/6.07 1483 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(789)].
% 5.88/6.07 1484 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(789)].
% 5.88/6.07 1485 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(790)].
% 5.88/6.07 1486 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(790)].
% 5.88/6.07 1487 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(791)].
% 5.88/6.07 1488 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(791)].
% 5.88/6.07 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1475,a,1477,a)].
% 5.88/6.07 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1475,a,1478,a)].
% 5.88/6.07 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B)),E))). [resolve(1475,a,1481,a)].
% 5.88/6.07 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B)),E))). [resolve(1475,a,1482,a)].
% 5.88/6.07 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B)),C)),E)). [resolve(1475,a,1483,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B)),C)),E)). [resolve(1475,a,1484,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B)),E))). [resolve(1475,a,1485,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B)),E))). [resolve(1475,a,1486,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B)),C)),E)). [resolve(1475,a,1487,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B)),C)),E)). [resolve(1475,a,1488,a)].
% 5.88/6.08 1489 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom). [assumption].
% 5.88/6.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1489,a,1477,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1489,a,1478,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B)),E))). [resolve(1489,a,1481,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B)),E))). [resolve(1489,a,1482,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B)),C)),E)). [resolve(1489,a,1483,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B)),C)),E)). [resolve(1489,a,1484,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B)),E))). [resolve(1489,a,1485,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B)),E))). [resolve(1489,a,1486,a)].
% 5.88/6.08 Derived: -hBOOL(hAPP(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))) | hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B)),C)),E)). [resolve(1489,a,1487,a)].
% 5.88/6.08 Derived: hBOOL(hAPP(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))) | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B)),C)),E)). [resolve(1489,a,1488,a)].
% 5.88/6.08 1490 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom). [clausify(1004)].
% 5.88/6.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1490,b,1477,a)].
% 5.88/6.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1490,b,1478,a)].
% 5.88/6.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C)),F))). [resolve(1490,b,1481,a)].
% 5.88/6.08 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C)),F))). [resolve(1490,b,1482,a)].
% 5.88/6.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C)),D)),F)). [resolve(1490,b,1483,a)].
% 5.88/6.08 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C)),D)),F)). [resolve(1490,b,1484,a)].
% 5.95/6.20 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C)),F))). [resolve(1490,b,1485,a)].
% 5.95/6.20 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C)),F))). [resolve(1490,b,1486,a)].
% 5.95/6.20 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C)),D)),F)). [resolve(1490,b,1487,a)].
% 5.95/6.20 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(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))) | -hBOOL(hAPP(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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C)),D)),F)). [resolve(1490,b,1488,a)].
% 5.95/6.20 1491 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 5.95/6.20 1492 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(361)].
% 5.95/6.20 1493 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(362)].
% 5.95/6.20 1494 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(366)].
% 5.95/6.21 1495 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(367)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1491,a,1492,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1491,a,1493,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1491,a,1494,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1491,a,1495,a)].
% 5.95/6.21 1496 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1496,a,1492,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1496,a,1493,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1496,a,1494,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1496,a,1495,a)].
% 5.95/6.21 1497 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom). [assumption].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1497,a,1492,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1497,a,1493,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1497,a,1494,a)].
% 5.95/6.21 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1497,a,1495,a)].
% 5.95/6.21 1498 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom). [clausify(993)].
% 5.95/6.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1498,b,1492,a)].
% 5.95/6.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1498,b,1493,a)].
% 5.95/6.21 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1498,b,1494,a)].
% 6.24/6.47 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1498,b,1495,a)].
% 6.24/6.47 1499 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.24/6.47 1500 -class_Rings_Oordered__comm__semiring(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(363)].
% 6.24/6.47 1501 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.24/6.47 1502 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.24/6.47 1503 -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(984)].
% 6.24/6.47 1504 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.24/6.47 1505 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(374)].
% 6.24/6.47 1506 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(375)].
% 6.24/6.47 1507 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(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(376)].
% 6.24/6.47 1508 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_zero__less__mult__pos) # label(axiom). [clausify(377)].
% 6.24/6.47 1509 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__mult__pos2) # label(axiom). [clausify(378)].
% 6.24/6.47 1510 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(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(380)].
% 6.24/6.47 1511 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(382)].
% 6.24/6.47 1512 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(383)].
% 6.24/6.47 1513 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(410)].
% 6.24/6.47 1514 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(411)].
% 6.24/6.47 1515 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(412)].
% 6.24/6.47 1516 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(413)].
% 6.24/6.47 1517 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_mult__less__imp__less__right) # label(axiom). [clausify(415)].
% 6.24/6.48 1518 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_mult__less__imp__less__left) # label(axiom). [clausify(417)].
% 6.24/6.48 1519 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),D)) # label(fact_mult__right__le__imp__le) # label(axiom). [clausify(418)].
% 6.24/6.48 1520 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),D)) # label(fact_mult__left__le__imp__le) # label(axiom). [clausify(419)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(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(1504,a,1505,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(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(1504,a,1506,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1504,a,1507,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1504,a,1508,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1504,a,1509,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1504,a,1513,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1504,a,1514,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1504,a,1515,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(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(1504,a,1516,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C)). [resolve(1504,a,1517,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),C)). [resolve(1504,a,1518,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),C)). [resolve(1504,a,1519,a)].
% 6.24/6.48 1521 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(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(1521,a,1505,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(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(1521,a,1506,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1521,a,1507,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(1521,a,1508,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(1521,a,1509,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1521,a,1511,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1521,a,1512,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1521,a,1513,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1521,a,1514,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1521,a,1515,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(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(1521,a,1516,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)). [resolve(1521,a,1517,a)].
% 6.24/6.48 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1521,a,1518,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C)). [resolve(1521,a,1519,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1521,a,1520,a)].
% 6.24/6.49 1522 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(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(1522,a,1505,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(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(1522,a,1506,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1522,a,1507,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)). [resolve(1522,a,1508,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)). [resolve(1522,a,1509,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1522,a,1513,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1522,a,1514,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1522,a,1515,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | hBOOL(hAPP(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(1522,a,1516,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),C)). [resolve(1522,a,1517,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)). [resolve(1522,a,1518,a)].
% 6.24/6.49 Derived: -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),C)). [resolve(1522,a,1519,a)].
% 6.24/6.49 1523 -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(974)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(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(1523,b,1505,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(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(1523,b,1506,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1523,b,1507,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1523,b,1508,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1523,b,1509,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1523,b,1513,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1523,b,1514,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1523,b,1515,a)].
% 6.24/6.49 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),D)) | hBOOL(hAPP(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(1523,b,1516,a)].
% 6.55/6.77 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),D)). [resolve(1523,b,1517,a)].
% 6.55/6.77 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),D)). [resolve(1523,b,1518,a)].
% 6.55/6.77 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),D)). [resolve(1523,b,1519,a)].
% 6.55/6.77 1524 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.55/6.77 1525 -class_Rings_Olinordered__comm__semiring__strict(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(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(384)].
% 6.55/6.77 1526 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.55/6.77 1527 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.55/6.77 1528 -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(972)].
% 6.55/6.77 1529 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.55/6.77 1530 -class_Rings_Olinordered__semiring(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)) # label(fact_mult__right__less__imp__less) # label(axiom). [clausify(414)].
% 6.55/6.77 1531 -class_Rings_Olinordered__semiring(A) | -hBOOL(hAPP(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))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)) # label(fact_mult__left__less__imp__less) # label(axiom). [clausify(416)].
% 6.55/6.77 1532 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.55/6.77 1533 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.55/6.77 1534 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom). [clausify(988)].
% 6.72/6.90 1535 class_Rings_Oordered__ring__abs(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 6.72/6.90 1536 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(423)].
% 6.72/6.90 1537 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(423)].
% 6.72/6.90 1538 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(423)].
% 6.72/6.90 1539 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(423)].
% 6.72/6.90 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1535,a,1536,a)].
% 6.72/6.90 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1535,a,1537,a)].
% 6.72/6.90 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1535,a,1538,a)].
% 6.72/6.91 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)). [resolve(1535,a,1539,a)].
% 6.72/6.91 1540 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 6.72/6.91 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1540,a,1536,a)].
% 6.72/6.91 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1540,a,1537,a)].
% 6.72/6.91 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1540,a,1538,a)].
% 6.72/6.91 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)). [resolve(1540,a,1539,a)].
% 6.72/6.91 1541 -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(994)].
% 6.72/6.91 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | 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)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)). [resolve(1541,b,1536,a)].
% 6.72/6.91 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | 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)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)). [resolve(1541,b,1537,a)].
% 6.72/6.91 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | 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)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)). [resolve(1541,b,1538,a)].
% 6.80/7.04 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | 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)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)). [resolve(1541,b,1539,a)].
% 6.80/7.04 1542 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 6.80/7.04 1543 -class_Rings_Olinordered__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),E)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(431)].
% 6.80/7.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(1542,a,1543,a)].
% 6.80/7.04 1544 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 6.80/7.04 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),D)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(1544,a,1543,a)].
% 6.80/7.04 1545 -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(985)].
% 6.80/7.04 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),E)) | -hBOOL(hAPP(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) | hBOOL(hAPP(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(1545,b,1543,a)].
% 7.10/7.31 1546 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 7.10/7.31 1547 -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(451)].
% 7.10/7.31 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(1546,a,1547,a)].
% 7.10/7.31 1548 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 7.10/7.31 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(1548,a,1547,a)].
% 7.10/7.31 1549 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 7.10/7.31 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(1549,a,1547,a)].
% 7.10/7.31 1550 -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(980)].
% 7.10/7.31 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(1550,b,1547,a)].
% 7.10/7.31 1551 class_Rings_Osemiring__0(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.10/7.31 1552 -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(468)].
% 7.10/7.31 1553 -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(468)].
% 7.10/7.31 1554 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),c_Nat_OSuc(B)) # label(fact_power__0__Suc) # label(axiom). [clausify(624)].
% 7.10/7.31 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(1551,a,1552,b)].
% 7.10/7.31 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(1551,a,1553,b)].
% 7.10/7.31 Derived: -class_Power_Opower(tc_Int_Oint) | 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)),c_Nat_OSuc(A)). [resolve(1551,a,1554,b)].
% 7.10/7.31 1555 class_Rings_Osemiring__0(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.10/7.31 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(1555,a,1552,b)].
% 7.10/7.31 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(1555,a,1553,b)].
% 7.26/7.45 Derived: -class_Power_Opower(tc_Nat_Onat) | 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)),c_Nat_OSuc(A)). [resolve(1555,a,1554,b)].
% 7.26/7.45 1556 class_Rings_Osemiring__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.26/7.45 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(1556,a,1552,b)].
% 7.26/7.45 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(1556,a,1553,b)].
% 7.26/7.45 Derived: -class_Power_Opower(tc_RealDef_Oreal) | 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)),c_Nat_OSuc(A)). [resolve(1556,a,1554,b)].
% 7.26/7.45 1557 class_Rings_Osemiring__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring__0) # label(axiom). [assumption].
% 7.26/7.45 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(1557,a,1552,b)].
% 7.26/7.45 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(1557,a,1553,b)].
% 7.26/7.45 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | 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)),c_Nat_OSuc(A)). [resolve(1557,a,1554,b)].
% 7.26/7.45 1558 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom). [clausify(1010)].
% 7.26/7.45 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(1558,b,1552,b)].
% 7.26/7.45 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(1558,b,1553,b)].
% 7.26/7.45 Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | 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))),c_Nat_OSuc(B)). [resolve(1558,b,1554,b)].
% 7.26/7.45 1559 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 7.26/7.45 1560 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,B,C)),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(730)].
% 7.26/7.45 1561 -class_Groups_Ogroup__add(A) | 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(731)].
% 7.26/7.45 1562 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(749)].
% 7.26/7.46 1563 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_diff__self) # label(axiom). [clausify(750)].
% 7.26/7.46 1564 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | C = B # label(fact_right__minus__eq) # label(axiom). [clausify(752)].
% 7.26/7.46 1565 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | C != B # label(fact_right__minus__eq) # label(axiom). [clausify(752)].
% 7.26/7.46 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),B) = A. [resolve(1559,a,1560,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),B) = A. [resolve(1559,a,1561,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1559,a,1562,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1559,a,1563,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | B = A. [resolve(1559,a,1564,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | B != A. [resolve(1559,a,1565,a)].
% 7.26/7.46 1566 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom). [assumption].
% 7.26/7.46 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),B) = A. [resolve(1566,a,1560,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),B) = A. [resolve(1566,a,1561,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(1566,a,1562,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1566,a,1563,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | B = A. [resolve(1566,a,1564,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | B != A. [resolve(1566,a,1565,a)].
% 7.26/7.46 1567 class_Groups_Ogroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ogroup__add) # label(axiom). [assumption].
% 7.26/7.46 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)),B) = A. [resolve(1567,a,1560,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),B) = A. [resolve(1567,a,1561,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1567,a,1562,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1567,a,1563,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = A. [resolve(1567,a,1564,a)].
% 7.26/7.46 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | B != A. [resolve(1567,a,1565,a)].
% 7.26/7.46 1568 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom). [clausify(1011)].
% 7.26/7.46 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),C) = B. [resolve(1568,b,1560,a)].
% 7.26/7.46 Derived: -class_Groups_Oab__group__add(A) | 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(1568,b,1561,a)].
% 7.26/7.46 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1568,b,1562,a)].
% 7.39/7.59 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1568,b,1563,a)].
% 7.39/7.59 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = B. [resolve(1568,b,1564,a)].
% 7.39/7.59 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C != B. [resolve(1568,b,1565,a)].
% 7.39/7.59 1569 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 7.39/7.59 1570 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(732)].
% 7.39/7.59 1571 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(732)].
% 7.39/7.59 1572 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(748)].
% 7.39/7.59 1573 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(748)].
% 7.39/7.59 1574 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(786)].
% 7.39/7.59 1575 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(786)].
% 7.39/7.59 1576 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(787)].
% 7.39/7.59 1577 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(787)].
% 7.39/7.59 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)). [resolve(1569,a,1570,a)].
% 7.39/7.59 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)). [resolve(1569,a,1571,a)].
% 7.39/7.59 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)). [resolve(1569,a,1572,a)].
% 7.39/7.59 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)). [resolve(1569,a,1573,a)].
% 7.39/7.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1569,a,1574,a)].
% 7.39/7.60 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1569,a,1575,a)].
% 7.39/7.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1569,a,1576,a)].
% 7.39/7.60 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1569,a,1577,a)].
% 7.39/7.60 1578 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 7.39/7.60 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)). [resolve(1578,a,1570,a)].
% 7.39/7.60 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)). [resolve(1578,a,1571,a)].
% 7.39/7.60 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)). [resolve(1578,a,1572,a)].
% 7.39/7.60 Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)). [resolve(1578,a,1573,a)].
% 7.39/7.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1578,a,1574,a)].
% 7.39/7.60 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1578,a,1575,a)].
% 7.39/7.60 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1578,a,1576,a)].
% 7.39/7.60 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). [resolve(1578,a,1577,a)].
% 7.39/7.60 1579 -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(986)].
% 7.39/7.60 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)). [resolve(1579,b,1570,a)].
% 7.39/7.60 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)). [resolve(1579,b,1571,a)].
% 7.56/7.74 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)). [resolve(1579,b,1572,a)].
% 7.56/7.74 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D),E)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)). [resolve(1579,b,1573,a)].
% 7.56/7.74 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1579,b,1574,a)].
% 7.56/7.74 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1579,b,1575,a)].
% 7.56/7.74 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1579,b,1576,a)].
% 7.56/7.74 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1579,b,1577,a)].
% 7.56/7.74 1580 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption].
% 7.56/7.74 1581 -class_Rings_Oring(A) | 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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),E)) # label(fact_mult__diff__mult) # label(axiom). [clausify(782)].
% 7.56/7.74 1582 -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),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F) = D # label(fact_eq__add__iff1) # label(axiom). [clausify(783)].
% 7.56/7.74 1583 -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),c_Groups_Ominus__class_Ominus(A,E,B)),C)),F) != D # label(fact_eq__add__iff1) # label(axiom). [clausify(783)].
% 7.56/7.74 1584 -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),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D) = F # label(fact_eq__add__iff2) # label(axiom). [clausify(784)].
% 7.56/7.74 1585 -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),c_Groups_Ominus__class_Ominus(A,B,E)),C)),D) != F # label(fact_eq__add__iff2) # label(axiom). [clausify(784)].
% 7.56/7.75 Derived: 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),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C)),D)). [resolve(1580,a,1581,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B)),E) = C. [resolve(1580,a,1582,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B)),E) != C. [resolve(1580,a,1583,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B)),C) = E. [resolve(1580,a,1584,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B)),C) != E. [resolve(1580,a,1585,a)].
% 7.56/7.75 1586 class_Rings_Oring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring) # label(axiom). [assumption].
% 7.56/7.75 Derived: 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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),D)). [resolve(1586,a,1581,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B)),E) = C. [resolve(1586,a,1582,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B)),E) != C. [resolve(1586,a,1583,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B)),C) = E. [resolve(1586,a,1584,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B)),C) != E. [resolve(1586,a,1585,a)].
% 7.56/7.75 1587 class_Rings_Oring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring) # label(axiom). [assumption].
% 7.56/7.75 Derived: 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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),D)). [resolve(1587,a,1581,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,D,A)),B)),E) = C. [resolve(1587,a,1582,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,D,A)),B)),E) != C. [resolve(1587,a,1583,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D)),B)),C) = E. [resolve(1587,a,1584,a)].
% 7.56/7.75 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),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D)),B)),C) != E. [resolve(1587,a,1585,a)].
% 7.56/7.75 1588 -class_Rings_Ocomm__ring(A) | class_Rings_Oring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom). [clausify(1020)].
% 7.56/7.75 Derived: -class_Rings_Ocomm__ring(A) | 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)),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),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,D)),E)). [resolve(1588,b,1581,a)].
% 7.68/7.89 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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C)),F) = D. [resolve(1588,b,1582,a)].
% 7.68/7.89 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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C)),F) != D. [resolve(1588,b,1583,a)].
% 7.68/7.89 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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C)),D) = F. [resolve(1588,b,1584,a)].
% 7.68/7.89 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)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C)),D) != F. [resolve(1588,b,1585,a)].
% 7.68/7.89 1589 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 7.68/7.89 1590 -class_Rings_Oring__1(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Oone__class_Oone(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(792)].
% 7.68/7.89 Derived: 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)) = 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))),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1589,a,1590,a)].
% 7.68/7.89 1591 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom). [assumption].
% 7.68/7.89 Derived: 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)) = 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))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). [resolve(1591,a,1590,a)].
% 7.68/7.89 1592 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom). [assumption].
% 7.68/7.89 Derived: 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)) = 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))),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))). [resolve(1592,a,1590,a)].
% 7.83/8.03 1593 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom). [clausify(1017)].
% 7.83/8.03 Derived: -class_Rings_Ocomm__ring__1(A) | 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))) = 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)))),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1593,b,1590,a)].
% 7.83/8.03 1594 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 7.83/8.03 1595 -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(851)].
% 7.83/8.03 1596 -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(851)].
% 7.83/8.03 1597 -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(852)].
% 7.83/8.03 1598 -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(853)].
% 7.83/8.03 1599 -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(854)].
% 7.83/8.03 1600 -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(855)].
% 7.83/8.03 1601 -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(856)].
% 7.83/8.03 1602 -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(858)].
% 7.83/8.03 1603 -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(859)].
% 7.83/8.03 1604 -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(860)].
% 7.83/8.03 1605 -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(879)].
% 7.83/8.03 1606 -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(880)].
% 7.83/8.03 1607 -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(881)].
% 7.83/8.03 1608 -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(882)].
% 7.83/8.03 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(1594,a,1595,a)].
% 7.83/8.03 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(1594,a,1596,a)].
% 7.83/8.03 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(1594,a,1597,a)].
% 7.83/8.03 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(1594,a,1598,a)].
% 7.83/8.03 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(1594,a,1599,a)].
% 7.83/8.03 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(1594,a,1601,a)].
% 7.83/8.03 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(1594,a,1602,a)].
% 7.83/8.03 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(1594,a,1603,a)].
% 7.83/8.03 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1594,a,1604,a)].
% 7.83/8.03 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(1594,a,1605,a)].
% 7.83/8.03 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(1594,a,1606,a)].
% 7.83/8.03 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(1594,a,1607,a)].
% 7.83/8.03 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(1594,a,1608,a)].
% 7.83/8.03 1609 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption].
% 7.83/8.04 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(1609,a,1595,a)].
% 7.83/8.04 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(1609,a,1596,a)].
% 7.83/8.04 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(1609,a,1597,a)].
% 7.83/8.04 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(1609,a,1598,a)].
% 7.83/8.04 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(1609,a,1599,a)].
% 7.83/8.04 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(1609,a,1601,a)].
% 7.83/8.04 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(1609,a,1602,a)].
% 7.83/8.04 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(1609,a,1603,a)].
% 7.83/8.04 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1609,a,1604,a)].
% 7.83/8.04 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(1609,a,1605,a)].
% 7.83/8.04 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(1609,a,1606,a)].
% 7.83/8.04 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(1609,a,1607,a)].
% 7.83/8.04 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(1609,a,1608,a)].
% 7.83/8.04 1610 -class_Fields_Ofield(A) | class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [clausify(1000)].
% 7.83/8.04 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1610,b,1595,a)].
% 7.83/8.04 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,D). [resolve(1610,b,1596,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),B) = C. [resolve(1610,b,1597,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),B) = C. [resolve(1610,b,1598,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,D). [resolve(1610,b,1599,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,B) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(1610,b,1601,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1610,b,1602,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1610,b,1603,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1610,b,1604,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)). [resolve(1610,b,1605,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)). [resolve(1610,b,1606,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),B),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1610,b,1607,a)].
% 7.96/8.18 Derived: -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1610,b,1608,a)].
% 7.96/8.18 1611 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 7.96/8.18 1612 -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(927)].
% 7.96/8.18 1613 -class_Fields_Ofield__inverse__zero(A) | -class_RealVector_Oreal__normed__field(A) | 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),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)) # label(fact_norm__divide) # label(axiom). [clausify(932)].
% 8.13/8.33 1614 -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(939)].
% 8.13/8.33 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(1611,a,1612,a)].
% 8.13/8.33 Derived: -class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) | 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),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)). [resolve(1611,a,1613,a)].
% 8.13/8.33 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(1611,a,1614,a)].
% 8.13/8.33 1615 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 8.13/8.33 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(1615,a,1612,a)].
% 8.13/8.33 Derived: -class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) | 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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)). [resolve(1615,a,1613,a)].
% 8.13/8.33 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(1615,a,1614,a)].
% 8.13/8.33 1616 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom). [assumption].
% 8.13/8.33 1617 -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(928)].
% 8.13/8.33 1618 -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(930)].
% 8.13/8.33 1619 -class_Rings_Odivision__ring(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),C),D)) # label(fact_times__divide__eq__right) # label(axiom). [clausify(933)].
% 8.13/8.33 1620 -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(936)].
% 8.13/8.33 1621 -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) | B = C # label(fact_right__inverse__eq) # label(axiom). [clausify(941)].
% 8.13/8.33 1622 -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) | B != C # label(fact_right__inverse__eq) # label(axiom). [clausify(941)].
% 8.13/8.33 1623 -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(942)].
% 8.13/8.33 1624 -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(944)].
% 8.13/8.33 1625 -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(945)].
% 8.13/8.33 1626 -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(946)].
% 8.13/8.33 1627 -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(946)].
% 8.13/8.33 1628 -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(947)].
% 8.13/8.33 1629 -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(947)].
% 8.13/8.33 1630 -class_Rings_Odivision__ring(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),C),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),D),C)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),c_Groups_Ominus__class_Ominus(A,B,D)),C) # label(fact_diff__divide__distrib) # label(axiom). [clausify(951)].
% 8.13/8.33 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(1616,a,1617,a)].
% 8.13/8.33 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(1616,a,1618,a)].
% 8.13/8.33 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),C)). [resolve(1616,a,1619,a)].
% 8.13/8.33 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(1616,a,1620,a)].
% 8.13/8.33 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) | A = B. [resolve(1616,a,1621,a)].
% 8.13/8.33 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) | A != B. [resolve(1616,a,1622,a)].
% 8.26/8.47 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(1616,a,1623,a)].
% 8.26/8.47 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A) != C | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),C),A) = B. [resolve(1616,a,1624,a)].
% 8.26/8.47 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),B),A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A) = B. [resolve(1616,a,1626,a)].
% 8.26/8.47 Derived: c_Groups_Ominus__class_Ominus(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),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),B). [resolve(1616,a,1630,a)].
% 8.26/8.47 1631 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom). [assumption].
% 8.26/8.47 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1631,a,1617,a)].
% 8.26/8.47 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(1631,a,1618,a)].
% 8.26/8.47 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(1631,a,1619,a)].
% 8.26/8.47 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(1631,a,1620,a)].
% 8.26/8.47 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) | A = B. [resolve(1631,a,1621,a)].
% 8.26/8.47 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) | A != B. [resolve(1631,a,1622,a)].
% 8.26/8.47 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(1631,a,1623,a)].
% 8.26/8.47 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A) != C | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),A) = B. [resolve(1631,a,1624,a)].
% 8.26/8.47 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A) = B. [resolve(1631,a,1626,a)].
% 8.26/8.47 Derived: c_Groups_Ominus__class_Ominus(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),B)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),B). [resolve(1631,a,1630,a)].
% 8.26/8.47 1632 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 8.26/8.47 1633 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__zero) # label(axiom). [clausify(935)].
% 8.26/8.47 1634 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),B),B) # label(fact_divide__self__if) # label(axiom). [clausify(943)].
% 8.47/8.71 1635 -class_Rings_Odivision__ring__inverse__zero(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__if) # label(axiom). [clausify(943)].
% 8.47/8.71 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(1632,a,1633,a)].
% 8.47/8.71 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),A),A). [resolve(1632,a,1634,a)].
% 8.47/8.71 1636 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 8.47/8.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(1636,a,1633,a)].
% 8.47/8.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A). [resolve(1636,a,1634,a)].
% 8.47/8.71 1637 class_Fields_Ofield(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield) # label(axiom). [assumption].
% 8.47/8.71 1638 -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(940)].
% 8.47/8.71 1639 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,D,C)) # label(fact_power__diff) # label(axiom). [clausify(955)].
% 8.47/8.71 Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B)). [resolve(1637,a,1639,a)].
% 8.47/8.71 1640 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom). [assumption].
% 8.47/8.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | -hBOOL(hAPP(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B)). [resolve(1640,a,1639,a)].
% 8.47/8.71 1641 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1610,b,1595,a)].
% 8.47/8.71 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(1641,a,1637,a)].
% 8.47/8.71 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(1641,a,1640,a)].
% 8.47/8.71 1642 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,D). [resolve(1610,b,1596,a)].
% 8.47/8.71 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(1642,a,1637,a)].
% 8.47/8.71 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(1642,a,1640,a)].
% 8.47/8.71 1643 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),B) = C. [resolve(1610,b,1597,a)].
% 8.47/8.71 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(1643,a,1637,a)].
% 8.47/8.71 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(1643,a,1640,a)].
% 8.47/8.71 1644 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),B) = C. [resolve(1610,b,1598,a)].
% 8.47/8.71 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(1644,a,1637,a)].
% 8.47/8.71 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(1644,a,1640,a)].
% 8.47/8.71 1645 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,D). [resolve(1610,b,1599,a)].
% 8.47/8.71 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(1645,a,1637,a)].
% 8.47/8.71 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(1645,a,1640,a)].
% 8.47/8.71 1646 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,B) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(1610,b,1601,a)].
% 8.47/8.71 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(1646,a,1637,a)].
% 8.47/8.71 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(1646,a,1640,a)].
% 8.47/8.71 1647 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1610,b,1602,a)].
% 8.47/8.71 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(1647,a,1637,a)].
% 8.47/8.71 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(1647,a,1640,a)].
% 8.47/8.71 1648 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1610,b,1603,a)].
% 8.47/8.71 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(1648,a,1637,a)].
% 8.47/8.71 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(1648,a,1640,a)].
% 8.47/8.71 1649 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1610,b,1604,a)].
% 8.47/8.71 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(1649,a,1637,a)].
% 8.47/8.71 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(1649,a,1640,a)].
% 8.47/8.71 1650 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)). [resolve(1610,b,1605,a)].
% 8.47/8.71 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(1650,a,1637,a)].
% 8.47/8.71 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(1650,a,1640,a)].
% 8.47/8.71 1651 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)). [resolve(1610,b,1606,a)].
% 8.47/8.71 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(1651,a,1637,a)].
% 8.47/8.71 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(1651,a,1640,a)].
% 8.47/8.71 1652 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),B),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1610,b,1607,a)].
% 8.47/8.71 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(1652,a,1637,a)].
% 8.47/8.71 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(1652,a,1640,a)].
% 8.47/8.71 1653 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),C,B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1610,b,1608,a)].
% 8.47/8.71 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(1653,a,1637,a)].
% 8.70/8.92 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(1653,a,1640,a)].
% 8.70/8.92 1654 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption].
% 8.70/8.92 1655 -class_RealVector_Oreal__field(A) | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),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),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),c_Groups_Ominus__class_Ominus(A,B,D)),F)),E)) # label(fact_DERIV__mult__lemma) # label(axiom). [clausify(952)].
% 8.70/8.92 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),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),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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),E)),D)). [resolve(1654,a,1655,a)].
% 8.70/8.92 1656 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 8.70/8.92 Derived: hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),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),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),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),E)),D)). [resolve(1656,a,1655,a)].
% 8.70/8.92 1657 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 8.70/8.92 1658 -class_Fields_Olinordered__field__inverse__zero(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,D),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(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(959)].
% 8.70/8.92 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(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))) | hBOOL(hAPP(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(1657,a,1658,a)].
% 9.94/10.16 1659 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom). [assumption].
% 9.94/10.16 1660 -class_Fields_Olinordered__field(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))) | hBOOL(hAPP(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(960)].
% 9.94/10.16 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C)) | -hBOOL(hAPP(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))) | hBOOL(hAPP(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(1659,a,1660,a)].
% 9.94/10.16
% 9.94/10.16 ============================== end predicate elimination =============
% 9.94/10.16
% 9.94/10.16 Auto_denials: (non-Horn, no changes).
% 9.94/10.16
% 9.94/10.16 Term ordering decisions:
% 9.94/10.16 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Nat_Onat=1. tc_Int_Oint=1. tc_Complex_Ocomplex=1. c_Complex_OIm=1. c_Complex_ORe=1. v_f____=1. c_Complex_Oii=1. v_s=1. v_ga____=1. v_r=1. tc_HOL_Obool=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. hAPP=1. c_Orderings_Oord__class_Oless=1. c_Orderings_Oord__class_Oless__eq=1. c_RealVector_Onorm__class_Onorm=1. c_Groups_Oabs__class_Oabs=1. c_RealDef_Oreal=1. c_Complex_Ocomplex_OComplex=1. c_Groups_Osgn__class_Osgn=1. tc_fun=1. c_Complex_Orcis=1. c_Nat__Transfer_Otsub=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Nat_Osize__class_Osize=1. f1=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f14=1. f15=1. f16=1. f17=1. f20=1. f23=1. f25=1. f26=1. f27=1. f28=1. f30=1. f31=1. f33=1. f34=1. f37=1. f38=1. f40=1. f41=1. f43=1. f44=1. f45=1. f47=1. f49=1. f52=1. f53=1. f54=1. f56=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_Oone__class_Oone=1. c_Power_Opower__class_Opower=1. c_Nat_OSuc=1. c_Rings_Oinverse__class_Odivide=1. c_Transcendental_Oln=1. c_RComplete_Onatfloor=1. c_Transcendental_Ocos=1. c_Transcendental_Osin=1. c_RComplete_Onatceiling=1. c_Complex_Ocis=1. c_Complex_Oexpi=1. c_Complex_Oarg=1. c_Complex_Ocomplex_Ocomplex__size=1. c_Transcendental_Oarccos=1. f3=1. f4=1. f21=1. f22=1. f24=1. f29=1. f42=1. f46=1. f51=1. f55=1. f59=1. f69=1. c_Groups_Ominus__class_Ominus=1. c_Divides_Odiv__class_Odiv=1. c_Power_Opower_Opower=1. c_COMBK=1. c_Complex_Ocomplex_Ocomplex__case=1. c_Complex_Ocomplex_Ocomplex__rec=1. f13=1. f18=1. f32=1. f35=1. f36=1. f39=1. f48=1. f50=1. f57=1. f58=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f2=1. f19=1. f60=1. c_COMBB=1. c_COMBC=1. c_COMBS=1.
% 9.94/10.16
% 9.94/10.16 ============================== end of process initial clauses ========
% 9.94/10.16
% 9.94/10.16 ============================== CLAUSES FOR SEARCH ====================
% 9.94/10.16
% 9.94/10.16 ============================== end of clauses for search =============
% 9.94/10.16
% 9.94/10.16 ============================== SEARCH ================================
% 9.94/10.16
% 9.94/10.16 % Starting search at 7.81 seconds.
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=42.000, iters=3345
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=41.000, iters=3503
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=39.000, iters=3438
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=38.000, iters=3344
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=37.000, iters=3397
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=36.000, iters=3351
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=35.000, iters=3344
% 9.94/10.16
% 9.94/10.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 96 (0.00 of 8.22 sec).
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=34.000, iters=3337
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=33.000, iters=3348
% 9.94/10.16
% 9.94/10.16 Low Water (keep): wt=32.000, iters=3354
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=31.000, iters=3362
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=30.000, iters=3364
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=29.000, iters=3343
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=27.000, iters=3371
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=26.000, iters=3391
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=25.000, iters=3333
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=24.000, iters=3333
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=23.000, iters=3342
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=22.000, iters=3366
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=21.000, iters=3353
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=20.000, iters=3339
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=19.000, iters=3333
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=18.000, iters=3339
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=17.000, iters=3333
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=16.000, iters=3335
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=15.000, iters=3335
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=14.000, iters=3344
% 28.86/29.06
% 28.86/29.06 Low Water (displace): id=17110, wt=13.000
% 28.86/29.06
% 28.86/29.06 Low Water (displace): id=17165, wt=12.000
% 28.86/29.06
% 28.86/29.06 Low Water (displace): id=18687, wt=11.000
% 28.86/29.06
% 28.86/29.06 Low Water (displace): id=18881, wt=10.000
% 28.86/29.06
% 28.86/29.06 Low Water (keep): wt=13.000, iters=3337
% 28.86/29.06
% 28.86/29.06 ============================== PROOF =================================
% 28.86/29.06 % SZS status Theorem
% 28.86/29.06 % SZS output start Refutation
% 28.86/29.06
% 28.86/29.06 % Proof 1 at 26.79 (+ 0.45) seconds.
% 28.86/29.06 % Length of proof is 48.
% 28.86/29.06 % Level of proof is 7.
% 28.86/29.06 % Maximum clause weight is 24.000.
% 28.86/29.06 % Given clauses 9395.
% 28.86/29.06
% 28.86/29.06 10 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) & V_x_2 != V_y_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 28.86/29.06 70 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 28.86/29.06 88 (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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].
% 28.86/29.06 99 (all V_r c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)) # label(fact_real__norm__def) # label(axiom) # label(non_clause). [assumption].
% 28.86/29.06 207 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(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].
% 28.86/29.06 268 (all V_x (hBOOL(hAPP(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].
% 28.86/29.06 406 (all V_x (hBOOL(hAPP(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].
% 28.86/29.06 562 (all V_a all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) -> hBOOL(hAPP(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].
% 28.86/29.06 651 (all V_n c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 28.86/29.06 773 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 28.86/29.06 776 (all V_n all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m)))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 28.86/29.06 819 (all V_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r)) & hBOOL(hAPP(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].
% 28.86/29.06 1026 -(exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) & (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 28.86/29.06 1080 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_not__leE) # label(axiom). [clausify(70)].
% 28.86/29.06 1088 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 28.86/29.06 1662 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) # label(fact_rp) # label(axiom). [assumption].
% 28.86/29.06 1665 -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) # label(fact_real__less__def) # label(axiom). [clausify(10)].
% 28.86/29.06 1709 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,A)))),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). [clausify(88)].
% 28.86/29.06 1715 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) # label(fact_real__norm__def) # label(axiom). [clausify(99)].
% 28.86/29.06 1716 c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A). [copy(1715),flip(a)].
% 28.86/29.06 1727 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) # label(fact_real__zero__not__eq__one) # label(axiom). [assumption].
% 28.86/29.06 1728 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [copy(1727),flip(a)].
% 28.86/29.06 1794 -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | A != B # label(fact_nat__less__le) # label(axiom). [clausify(207)].
% 28.86/29.06 1834 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) # label(fact_natceiling__add__one) # label(axiom). [clausify(268)].
% 28.86/29.06 1954 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | c_RComplete_Onatceiling(A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) # label(fact_natceiling__neg) # label(axiom). [clausify(406)].
% 28.86/29.06 2105 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(A)),B)) # label(fact_natceiling__le) # label(axiom). [clausify(562)].
% 28.86/29.06 2229 c_Nat_OSuc(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) # label(fact_Suc__eq__plus1) # label(axiom). [clausify(651)].
% 28.86/29.06 2387 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) # label(fact_diff__is__0__eq_H) # label(axiom). [clausify(773)].
% 28.86/29.06 2390 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)),c_Nat_OSuc(A))) # label(fact_diff__less__Suc) # label(axiom). [clausify(776)].
% 28.86/29.06 2391 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). [copy(2390),rewrite([2229(5)])].
% 28.86/29.06 2446 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,f59(A)))) # label(fact_reals__Archimedean6) # label(axiom). [clausify(819)].
% 28.86/29.06 2781 -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,f69(A))))))),A)) # label(conj_0) # label(negated_conjecture). [clausify(1026)].
% 28.86/29.06 2782 -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,f69(A))))))),A)). [copy(2781),rewrite([1716(18)])].
% 28.86/29.06 2911 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),A)). [resolve(1088,a,1080,a)].
% 28.86/29.06 4112 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,A)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). [back_rewrite(1709),rewrite([1716(7)])].
% 28.86/29.06 4116 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_0. [new_symbol(1728)].
% 28.86/29.06 4402 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,A)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_0))). [back_rewrite(4112),rewrite([4116(14)])].
% 28.86/29.06 4518 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_0)). [back_rewrite(1834),rewrite([4116(11)]),flip(b)].
% 28.86/29.06 6327 c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(2391,a,1794,a)].
% 28.86/29.06 6818 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_RealDef_Oreal(tc_Nat_Onat,f59(v_r)))). [resolve(2446,a,1662,a)].
% 28.86/29.06 9408 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A)) | c_RComplete_Onatceiling(A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(2911,a,1954,a)].
% 28.86/29.06 11307 -hBOOL(hAPP(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),v_r),c_0))). [resolve(4402,a,2782,b)].
% 28.86/29.06 11847 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(v_r)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_0)). [resolve(4518,a,1662,a)].
% 28.86/29.06 15887 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_RealDef_Oreal(tc_Nat_Onat,f59(v_r)))). [resolve(6818,a,1665,a)].
% 28.86/29.06 17691 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(v_r)),f59(v_r))). [resolve(15887,a,2105,a)].
% 28.86/29.06 17693 c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(v_r),f59(v_r)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(17691,a,2387,a)].
% 28.86/29.06 18613 c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_0)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [para(17693(a,1),6327(a,1)),rewrite([11847(10)]),flip(a)].
% 28.86/29.06 34225 $F. [resolve(9408,a,11307,a),unit_del(a,18613)].
% 28.86/29.06
% 28.86/29.06 % SZS output end Refutation
% 28.86/29.06 ============================== end of proof ==========================
% 28.86/29.06
% 28.86/29.06 ============================== STATISTICS ============================
% 28.86/29.06
% 28.86/29.06 Given=9395. Generated=710949. Kept=32056. proofs=1.
% 28.86/29.06 Usable=9237. Sos=9997. Demods=2248. Limbo=3, Disabled=15687. Hints=0.
% 28.86/29.06 Megabytes=61.17.
% 28.86/29.06 User_CPU=26.79, System_CPU=0.45, Wall_clock=27.
% 28.86/29.06
% 28.86/29.06 ============================== end of statistics =====================
% 28.86/29.06
% 28.86/29.06 ============================== end of search =========================
% 28.86/29.06
% 28.86/29.06 THEOREM PROVED
% 28.86/29.06 % SZS status Theorem
% 28.86/29.06
% 28.86/29.06 Exiting with 1 proof.
% 28.86/29.06
% 28.86/29.06 Process 876 exit (max_proofs) Sun Jun 5 07:33:02 2022
% 28.86/29.06 Prover9 interrupted
%------------------------------------------------------------------------------