TSTP Solution File: SWW249+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW249+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 01:15:59 EDT 2022
% Result : Timeout 300.06s 300.37s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWW249+1 : TPTP v8.1.0. Released v5.2.0.
% 0.05/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.30 % Computer : n017.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sun Jun 5 13:13:30 EDT 2022
% 0.10/0.31 % CPUTime :
% 2.22/2.57 ============================== Prover9 ===============================
% 2.22/2.57 Prover9 (32) version 2009-11A, November 2009.
% 2.22/2.57 Process 27889 was started by sandbox2 on n017.cluster.edu,
% 2.22/2.57 Sun Jun 5 13:13:32 2022
% 2.22/2.57 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27736_n017.cluster.edu".
% 2.22/2.57 ============================== end of head ===========================
% 2.22/2.57
% 2.22/2.57 ============================== INPUT =================================
% 2.22/2.57
% 2.22/2.57 % Reading from file /tmp/Prover9_27736_n017.cluster.edu
% 2.22/2.57
% 2.22/2.57 set(prolog_style_variables).
% 2.22/2.57 set(auto2).
% 2.22/2.57 % set(auto2) -> set(auto).
% 2.22/2.57 % set(auto) -> set(auto_inference).
% 2.22/2.57 % set(auto) -> set(auto_setup).
% 2.22/2.57 % set(auto_setup) -> set(predicate_elim).
% 2.22/2.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.22/2.57 % set(auto) -> set(auto_limits).
% 2.22/2.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.22/2.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.22/2.57 % set(auto) -> set(auto_denials).
% 2.22/2.57 % set(auto) -> set(auto_process).
% 2.22/2.57 % set(auto2) -> assign(new_constants, 1).
% 2.22/2.57 % set(auto2) -> assign(fold_denial_max, 3).
% 2.22/2.57 % set(auto2) -> assign(max_weight, "200.000").
% 2.22/2.57 % set(auto2) -> assign(max_hours, 1).
% 2.22/2.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.22/2.57 % set(auto2) -> assign(max_seconds, 0).
% 2.22/2.57 % set(auto2) -> assign(max_minutes, 5).
% 2.22/2.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.22/2.57 % set(auto2) -> set(sort_initial_sos).
% 2.22/2.57 % set(auto2) -> assign(sos_limit, -1).
% 2.22/2.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.22/2.57 % set(auto2) -> assign(max_megs, 400).
% 2.22/2.57 % set(auto2) -> assign(stats, some).
% 2.22/2.57 % set(auto2) -> clear(echo_input).
% 2.22/2.57 % set(auto2) -> set(quiet).
% 2.22/2.57 % set(auto2) -> clear(print_initial_clauses).
% 2.22/2.57 % set(auto2) -> clear(print_given).
% 2.22/2.57 assign(lrs_ticks,-1).
% 2.22/2.57 assign(sos_limit,10000).
% 2.22/2.57 assign(order,kbo).
% 2.22/2.57 set(lex_order_vars).
% 2.22/2.57 clear(print_given).
% 2.22/2.57
% 2.22/2.57 % formulas(sos). % not echoed (1215 formulas)
% 2.22/2.57
% 2.22/2.57 ============================== end of input ==========================
% 2.22/2.57
% 2.22/2.57 % From the command line: assign(max_seconds, 300).
% 2.22/2.57
% 2.22/2.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.22/2.57
% 2.22/2.57 % Formulas that are not ordinary clauses:
% 2.22/2.57 1 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 2 class_Rings_Oidom(t_a) -> -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)) # label(fact_assms) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 3 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n)))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 4 class_Rings_Oidom(t_a) -> -(all B_z (B_z != c_Groups_Ozero__class_Ozero(t_a) -> hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z) = c_Groups_Ozero__class_Ozero(t_a))) # label(fact_th) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 5 class_Rings_Oidom(t_a) -> -(all B_z (B_z != c_Groups_Ozero__class_Ozero(t_a) -> hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z) = c_Groups_Ozero__class_Ozero(t_a))) # label(fact__096ALL_Az_O_Az_A_126_061_A_I0_058_058_Ha_J_A_N_N_062_Apoly_Acs_Az_A_061_A_I0_058_058_Ha_J_A_061_061_062_AFalse_096) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 6 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_n)))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 7 (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,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 8 (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].
% 2.22/2.57 9 (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].
% 2.22/2.57 10 (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].
% 2.22/2.57 11 (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),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))))))) # label(fact_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 12 (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].
% 2.22/2.57 13 (all V_x all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))))) # label(fact_poly__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 14 (all V_y_2 all V_x_2 all V_b_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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].
% 2.22/2.57 15 (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].
% 2.22/2.57 16 (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].
% 2.22/2.57 17 (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].
% 2.22/2.57 18 (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].
% 2.22/2.57 19 (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].
% 2.22/2.57 20 (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].
% 2.22/2.57 21 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(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].
% 2.22/2.57 22 (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].
% 2.22/2.57 23 (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].
% 2.22/2.57 24 (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].
% 2.22/2.57 25 (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].
% 2.22/2.57 26 (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].
% 2.22/2.57 27 (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].
% 2.22/2.57 28 (all V_pa_2 all T_b (class_Int_Oring__char__0(T_b) & class_Rings_Oidom(T_b) -> (c_Polynomial_Opoly(T_b,V_pa_2) = c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))) # label(fact_poly__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 29 (all V_f_2 all T_c all T_b (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2) <-> (all B_x all B_y hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)))) # label(fact_constant__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 30 (all V_m_2 all V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(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 = hAPP(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].
% 2.22/2.57 31 (all V_n hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_power__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.57 32 (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].
% 2.22/2.58 33 (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].
% 2.22/2.58 34 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 35 (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].
% 2.22/2.58 36 (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].
% 2.22/2.58 37 (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].
% 2.22/2.58 38 (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].
% 2.22/2.58 39 (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].
% 2.22/2.58 40 (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),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(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].
% 2.22/2.58 41 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(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].
% 2.22/2.58 42 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(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].
% 2.22/2.58 43 (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].
% 2.22/2.58 44 (all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_one__poly__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 45 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(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].
% 2.22/2.58 46 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(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].
% 2.22/2.58 47 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(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].
% 2.22/2.58 48 (all V_pa_2 all T_b (class_Groups_Ozero(T_b) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))) # label(fact_psize__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 49 (all V_y all V_x (hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 50 (all V_nat_H_2 all V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 51 (all V_n hAPP(c_Nat_OSuc,V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 52 (all V_n V_n != hAPP(c_Nat_OSuc,V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 53 (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].
% 2.22/2.58 54 (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].
% 2.22/2.58 55 (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].
% 2.22/2.58 56 (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].
% 2.22/2.58 57 (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].
% 2.22/2.58 58 (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].
% 2.22/2.58 59 (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].
% 2.22/2.58 60 (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].
% 2.22/2.58 61 (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].
% 2.22/2.58 62 (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].
% 2.22/2.58 63 (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].
% 2.22/2.58 64 (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].
% 2.22/2.58 65 (all V_q_2 all V_b_2 all V_pa_2 all V_a_2 all T_b (class_Groups_Ozero(T_b) -> (hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2) = hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2) <-> V_a_2 = V_b_2 & V_pa_2 = V_q_2))) # label(fact_pCons__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 66 (all V_q_2 all V_pa_2 all T_b (class_Int_Oring__char__0(T_b) & class_Rings_Oidom(T_b) -> (c_Polynomial_Opoly(T_b,V_pa_2) = c_Polynomial_Opoly(T_b,V_q_2) <-> V_pa_2 = V_q_2))) # label(fact_poly__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 67 (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].
% 2.22/2.58 68 (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].
% 2.22/2.58 69 (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].
% 2.22/2.58 70 (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].
% 2.22/2.58 71 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 72 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 73 (all V_nat_H_1 hAPP(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].
% 2.22/2.58 74 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 75 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 76 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 77 (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].
% 2.22/2.58 78 (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].
% 2.22/2.58 79 (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].
% 2.22/2.58 80 (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].
% 2.22/2.58 81 (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].
% 2.22/2.58 82 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(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].
% 2.22/2.58 83 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(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].
% 2.22/2.58 84 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(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].
% 2.22/2.58 85 (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,hAPP(c_Nat_OSuc,V_i)),V_k))))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 86 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> (hAPP(c_Nat_OSuc,V_m) != V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 87 (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),hAPP(c_Nat_OSuc,V_n))))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 88 (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),hAPP(c_Nat_OSuc,V_m))) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 89 (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),hAPP(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].
% 2.22/2.58 90 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(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].
% 2.22/2.58 91 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(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].
% 2.22/2.58 92 (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),hAPP(c_Nat_OSuc,V_m_2))))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 93 (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].
% 2.22/2.58 94 (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].
% 2.22/2.58 95 (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].
% 2.22/2.58 96 (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].
% 2.22/2.58 97 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 98 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(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].
% 2.22/2.58 99 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(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].
% 2.22/2.58 100 (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].
% 2.22/2.58 101 (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].
% 2.22/2.58 102 (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].
% 2.22/2.58 103 (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].
% 2.22/2.58 104 (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].
% 2.22/2.58 105 (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].
% 2.22/2.58 106 (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].
% 2.22/2.58 107 (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].
% 2.22/2.58 108 (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].
% 2.22/2.58 109 (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].
% 2.22/2.58 110 (all V_pa_2 all V_a_2 all T_b (class_Groups_Ozero(T_b) -> (hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))) # label(fact_pCons__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 111 (all T_a (class_Groups_Ozero(T_a) -> hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_pCons__0__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 112 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)))) # label(fact_add__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 113 (all V_x all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_poly__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 114 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 115 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 116 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a))) # label(fact_poly__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 117 (all V_x all V_n all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n))) # label(fact_poly__power) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 118 (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].
% 2.22/2.58 119 (all V_n_2 all V_a_2 all T_b (class_Power_Opower(T_b) & class_Rings_Omult__zero(T_b) & class_Rings_Ono__zero__divisors(T_b) & class_Rings_Ozero__neq__one(T_b) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 120 (all V_n_2 all V_m_2 all V_a_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_a_2)) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) <-> V_m_2 = V_n_2)))) # label(fact_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 121 (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)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_power__0__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 122 (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),hAPP(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].
% 2.22/2.58 123 (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),hAPP(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].
% 2.22/2.58 124 (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].
% 2.22/2.58 125 (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].
% 2.22/2.58 126 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = hAPP(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].
% 2.22/2.58 127 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(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].
% 2.22/2.58 128 (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 = hAPP(c_Nat_OSuc,B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 129 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(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 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 130 (all V_n_2 all V_m_2 (hAPP(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 = hAPP(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 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 131 (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].
% 2.22/2.58 132 (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 = hAPP(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].
% 2.22/2.58 133 (all V_m all V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(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].
% 2.22/2.58 134 (all V_m all V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(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].
% 2.22/2.58 135 (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].
% 2.22/2.58 136 (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].
% 2.22/2.58 137 (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].
% 2.22/2.58 138 (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),hAPP(c_Nat_OSuc,V_n))))))) # label(fact_power__gt1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 139 (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].
% 2.22/2.58 140 (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].
% 2.22/2.58 141 (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].
% 2.22/2.58 142 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_b) | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 143 (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].
% 2.22/2.58 144 class_Rings_Oidom(t_a) -> -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))) # label(fact_pCons_Oprems) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 145 (all V_n hAPP(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].
% 2.22/2.58 146 (all V_n hAPP(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].
% 2.22/2.58 147 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x = hAPP(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].
% 2.22/2.58 148 (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].
% 2.22/2.58 149 (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].
% 2.22/2.58 150 (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),hAPP(c_Nat_OSuc,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 151 (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),hAPP(c_Nat_OSuc,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 152 (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),hAPP(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].
% 2.22/2.58 153 (all V_q all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_mult__poly__0__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 154 (all V_q all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = V_q)) # label(fact_add__poly__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 155 (all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_mult__poly__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 156 (all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p)) # label(fact_add__poly__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 157 (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].
% 2.22/2.58 158 (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].
% 2.22/2.58 159 (all V_r all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)))) # label(fact_mult__poly__add__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.58 160 (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].
% 2.22/2.58 161 (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].
% 2.22/2.58 162 (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].
% 2.22/2.58 163 (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].
% 2.22/2.58 164 (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].
% 2.22/2.58 165 (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].
% 2.22/2.58 166 (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].
% 2.22/2.58 167 (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].
% 2.22/2.58 168 (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].
% 2.22/2.58 169 (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].
% 2.22/2.58 170 (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].
% 2.22/2.59 171 (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].
% 2.22/2.59 172 (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].
% 2.22/2.59 173 (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].
% 2.22/2.59 174 (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].
% 2.22/2.59 175 (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].
% 2.22/2.59 176 (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].
% 2.22/2.59 177 (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].
% 2.22/2.59 178 (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].
% 2.22/2.59 179 (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].
% 2.22/2.59 180 (all V_b_2 all V_a_2 all T_b (class_Rings_Oring__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) | V_b_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 181 (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].
% 2.22/2.59 182 (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].
% 2.22/2.59 183 (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].
% 2.22/2.59 184 (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].
% 2.22/2.59 185 (all V_a_2 all V_b_2 all T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) -> (V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 186 (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].
% 2.22/2.59 187 (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].
% 2.22/2.59 188 (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].
% 2.22/2.59 189 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) -> (V_a_2 != V_b_2 & V_ca_2 != V_d_2 <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 190 (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].
% 2.22/2.59 191 (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].
% 2.22/2.59 192 (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].
% 2.22/2.59 193 (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].
% 2.22/2.59 194 (all V_z_2 all V_x_2 all V_y_2 all V_w_2 all T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),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].
% 2.22/2.59 195 (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].
% 2.22/2.59 196 (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].
% 2.22/2.59 197 (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].
% 2.22/2.59 198 (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].
% 2.22/2.59 199 (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].
% 2.22/2.59 200 (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].
% 2.22/2.59 201 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2))))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 202 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2))))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 203 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 204 (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].
% 2.22/2.59 205 (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].
% 2.22/2.59 206 (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].
% 2.22/2.59 207 (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].
% 2.22/2.59 208 (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].
% 2.22/2.59 209 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 210 (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].
% 2.22/2.59 211 (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].
% 2.22/2.59 212 (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].
% 2.22/2.59 213 (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].
% 2.22/2.59 214 (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].
% 2.22/2.59 215 (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].
% 2.22/2.59 216 (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].
% 2.22/2.59 217 (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].
% 2.22/2.59 218 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 219 (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].
% 2.22/2.59 220 (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].
% 2.22/2.59 221 (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].
% 2.22/2.59 222 (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].
% 2.22/2.59 223 (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].
% 2.22/2.59 224 (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].
% 2.22/2.59 225 (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].
% 2.22/2.59 226 (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].
% 2.22/2.59 227 class_Rings_Oidom(t_a) -> (-c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____)) -> (exists B_k exists B_a (B_a != c_Groups_Ozero__class_Ozero(t_a) & B_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & (exists B_q (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____) & (all B_z hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z))))))))) # label(fact_pCons_Ohyps) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 228 (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].
% 2.22/2.59 229 (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].
% 2.22/2.59 230 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Opcompose(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_q) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))))) # label(fact_pcompose__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 231 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 232 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 233 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 234 (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].
% 2.22/2.59 235 (all V_q all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_pcompose__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 236 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__pcompose) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 237 (all V_x_2 all T_b (class_Groups_Ozero(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = V_x_2 <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 238 (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].
% 2.22/2.59 239 (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].
% 2.22/2.59 240 (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].
% 2.22/2.59 241 (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].
% 2.22/2.59 242 (all V_ca_2 all V_a_2 all V_b_2 all T_b (class_Groups_Ocancel__semigroup__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2) <-> V_b_2 = V_ca_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 243 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Ocancel__semigroup__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2) <-> V_b_2 = V_ca_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 244 (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].
% 2.22/2.59 245 (all V_x_2 all T_b (class_Groups_Oone(T_b) -> (c_Groups_Oone__class_Oone(T_b) = V_x_2 <-> V_x_2 = c_Groups_Oone__class_Oone(T_b)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 246 (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].
% 2.22/2.59 247 (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].
% 2.22/2.59 248 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 249 (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].
% 2.22/2.59 250 (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].
% 2.22/2.59 251 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 252 (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].
% 2.22/2.59 253 (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].
% 2.22/2.59 254 (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].
% 2.22/2.59 255 (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].
% 2.22/2.59 256 (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].
% 2.22/2.59 257 (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].
% 2.22/2.59 258 (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].
% 2.22/2.59 259 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 260 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 261 (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].
% 2.22/2.59 262 (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].
% 2.22/2.59 263 (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].
% 2.22/2.59 264 (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].
% 2.22/2.59 265 (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].
% 2.22/2.59 266 (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].
% 2.22/2.59 267 (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].
% 2.22/2.59 268 (all V_q_2 all V_pa_2 all T_b (class_Rings_Ocomm__semiring__0(T_b) -> c_Polynomial_Opcompose(T_b,V_pa_2,V_q_2) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2))),V_pa_2))) # label(fact_pcompose__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 269 (all V_a_2 all V_pa_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) | c_Polynomial_Oorder(T_b,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_order__root) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 270 (all T_b (class_Power_Opower(T_b) -> c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)))) # label(fact_power__power__power) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 271 class_Rings_Oidom(t_a) -> (exists B_k exists B_a (B_a != c_Groups_Ozero__class_Ozero(t_a) & (exists B_q (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____) & (all B_z hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z))))))) # label(fact__096EX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_Ipsize_Aq_A_L_Ak_J_A_061_Apsize_Acs_A_G_A_IALL_Az_O_Apoly_Acs_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 272 (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].
% 2.22/2.59 273 (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].
% 2.22/2.59 274 (all V_pa_2 all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)) <-> c_Polynomial_Opos__poly(T_b,V_pa_2) | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_pos__poly__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 275 (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].
% 2.22/2.59 276 (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].
% 2.22/2.59 277 (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].
% 2.22/2.59 278 (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].
% 2.22/2.59 279 (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].
% 2.22/2.59 280 (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].
% 2.22/2.59 281 (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].
% 2.22/2.59 282 (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].
% 2.22/2.59 283 (all T_a (class_Rings_Olinordered__idom(T_a) -> -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_not__pos__poly__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 284 (all V_q all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_p) -> (c_Polynomial_Opos__poly(T_a,V_q) -> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)))))) # label(fact_pos__poly__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 285 (all V_q all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_p) -> (c_Polynomial_Opos__poly(T_a,V_q) -> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))))) # label(fact_pos__poly__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 286 (all V_a_2 all V_times_2 all V_one_2 all T_b hAPP(hAPP(c_Power_Opower_Opower(T_b,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].
% 2.22/2.59 287 (all V_n_2 all V_a_2 all V_times_2 all V_one_2 all T_b hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2))) # label(fact_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 288 (all T_b all V_z_2 all V_f_2 all T_c (class_Groups_Ozero(T_c) -> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2) = V_z_2 -> c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))) = V_z_2))) # label(fact_poly__rec__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 289 (all V_pa_2 all V_a_2 all V_f_2 all V_z_2 all T_b all T_c (class_Groups_Ozero(T_c) -> c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(c_Polynomial_OpCons(T_c),V_a_2),V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_b,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2,c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2))))) # label(fact_poly__rec_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 290 (all V_pa_2 all V_a_2 all T_b all V_z_2 all V_f_2 all T_c (class_Groups_Ozero(T_c) -> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2) = V_z_2 -> c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(c_Polynomial_OpCons(T_c),V_a_2),V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2))))) # label(fact_poly__rec__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 291 (all V_q_2 all V_pa_2 all T_b (class_Rings_Ocomm__semiring__0(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b)),V_q_2)))),hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ozero__class_Ozero(T_b)))),V_pa_2))) # label(fact_times__poly__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.59 292 (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].
% 2.22/2.60 293 (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].
% 2.22/2.60 294 (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].
% 2.22/2.60 295 (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].
% 2.22/2.60 296 (all V_x all V_p all V_n all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))) # label(fact_poly__replicate__append) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 297 (all V_n all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n))) # label(fact_smult__monom) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 298 (all V_b_2 all V_n_2 all V_a_2 all T_b (class_Groups_Ozero(T_b) -> (c_Polynomial_Omonom(T_b,V_a_2,V_n_2) = c_Polynomial_Omonom(T_b,V_b_2,V_n_2) <-> V_a_2 = V_b_2))) # label(fact_monom__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 299 (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].
% 2.22/2.60 300 (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].
% 2.22/2.60 301 (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].
% 2.22/2.60 302 (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].
% 2.22/2.60 303 (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].
% 2.22/2.60 304 (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].
% 2.22/2.60 305 (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].
% 2.22/2.60 306 (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].
% 2.22/2.60 307 (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].
% 2.22/2.60 308 (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].
% 2.22/2.60 309 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)) = hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_p))) # label(fact_smult__smult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 310 (all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Oone__class_Oone(T_a)),V_p) = V_p)) # label(fact_smult__1__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 311 (all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_smult__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 312 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))) # label(fact_smult__add__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 313 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q) = hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))) # label(fact_mult__smult__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 314 (all V_q all V_a all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)) = hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))) # label(fact_mult__smult__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 315 (all V_pa_2 all V_a_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))) # label(fact_smult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 316 (all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_smult__0__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 317 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_p)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)))) # label(fact_smult__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 318 (all V_x all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))) # label(fact_poly__smult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 319 (all V_a all V_p all V_c all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p) = hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p) -> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_synthetic__div__unique__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 320 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_p) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)))) # label(fact_smult__add__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 321 (all V_n_2 all V_a_2 all T_b (class_Groups_Ozero(T_b) -> (c_Polynomial_Omonom(T_b,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_monom__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 322 (all V_n all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_monom__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 323 (all V_b all V_n all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_n))) # label(fact_add__monom) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 324 (all V_a all V_p all V_c all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_offset__poly__eq__0__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 325 (all V_n all V_a all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Omonom(T_a,V_a,hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)))) # label(fact_monom__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 326 (all V_x all V_n all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))) # label(fact_poly__monom) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 327 (all V_a all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_monom__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 328 (all V_n all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)))) # label(fact_mult__monom) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 329 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_q) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))))) # label(fact_mult__pCons__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 330 (all V_q all V_a all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_q)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))))) # label(fact_mult__pCons__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 331 (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].
% 2.22/2.60 332 (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].
% 2.22/2.60 333 (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].
% 2.22/2.60 334 (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].
% 2.22/2.60 335 (all V_h_2 all V_pa_2 all T_b (class_Rings_Ocomm__semiring__0(T_b) -> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),hAPP(c_COMBS(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_Polynomial_Osmult(T_b),V_h_2)))),c_Polynomial_OpCons(T_b))),V_pa_2))) # label(fact_offset__poly__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 336 (all V_r all V_q all V_c all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),V_r),V_q) -> V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c) & V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))) # label(fact_synthetic__div__unique) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 337 (all V_c all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))) # label(fact_synthetic__div__correct) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 338 (all V_h all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_h) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_h),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))))) # label(fact_offset__poly__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 339 (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].
% 2.22/2.60 340 (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].
% 2.22/2.60 341 (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].
% 2.22/2.60 342 (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].
% 2.22/2.60 343 (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].
% 2.22/2.60 344 (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].
% 2.22/2.60 345 (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].
% 2.22/2.60 346 (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].
% 2.22/2.60 347 (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].
% 2.22/2.60 348 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),V_b_2))))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 349 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),V_b_2))))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 350 (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].
% 2.22/2.60 351 (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].
% 2.22/2.60 352 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n))) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 353 (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,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 354 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(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 = hAPP(c_Nat_OSuc,V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 355 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),hAPP(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].
% 2.22/2.60 356 (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),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 357 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> V_m = hAPP(c_Nat_OSuc,V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 358 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(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].
% 2.22/2.60 359 (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].
% 2.22/2.60 360 (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].
% 2.22/2.60 361 (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].
% 2.22/2.60 362 (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].
% 2.22/2.60 363 (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].
% 2.22/2.60 364 (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].
% 2.22/2.60 365 (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].
% 2.22/2.60 366 (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].
% 2.22/2.60 367 (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].
% 2.22/2.60 368 (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].
% 2.22/2.60 369 (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].
% 2.22/2.60 370 (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].
% 2.22/2.60 371 (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].
% 2.22/2.60 372 (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].
% 2.22/2.60 373 (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].
% 2.22/2.60 374 (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].
% 2.22/2.60 375 (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].
% 2.22/2.60 376 (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].
% 2.22/2.60 377 (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].
% 2.22/2.60 378 (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].
% 2.22/2.60 379 (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].
% 2.22/2.60 380 (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].
% 2.22/2.60 381 (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].
% 2.22/2.60 382 (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].
% 2.22/2.60 383 (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].
% 2.22/2.60 384 (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].
% 2.22/2.60 385 (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].
% 2.22/2.60 386 (all V_y_2 all V_x_2 all V_b_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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].
% 2.22/2.60 387 (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].
% 2.22/2.60 388 (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].
% 2.22/2.60 389 (all V_b_2 all V_a_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 390 (all V_b_2 all V_a_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2))))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 391 (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].
% 2.22/2.60 392 (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].
% 2.22/2.60 393 (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].
% 2.22/2.60 394 (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].
% 2.22/2.60 395 (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].
% 2.22/2.60 396 (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].
% 2.22/2.60 397 (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].
% 2.22/2.60 398 (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].
% 2.22/2.60 399 (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].
% 2.22/2.60 400 (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].
% 2.22/2.60 401 (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].
% 2.22/2.60 402 (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].
% 2.22/2.60 403 (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].
% 2.22/2.60 404 (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].
% 2.22/2.60 405 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 406 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 407 (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].
% 2.22/2.60 408 (all V_y_2 all V_x_2 all T_b (class_Groups_Oordered__comm__monoid__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 409 (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].
% 2.22/2.60 410 (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].
% 2.22/2.60 411 (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].
% 2.22/2.60 412 (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].
% 2.22/2.60 413 (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].
% 2.22/2.60 414 (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].
% 2.22/2.60 415 (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].
% 2.22/2.60 416 (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].
% 2.22/2.60 417 (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].
% 2.22/2.60 418 (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].
% 2.22/2.60 419 (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,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 420 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(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].
% 2.22/2.60 421 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(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].
% 2.22/2.60 422 (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),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 423 (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,hAPP(c_Nat_OSuc,V_m)),V_n)))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 424 (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),hAPP(c_Nat_OSuc,V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 425 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(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].
% 2.22/2.60 426 (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),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(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].
% 2.22/2.60 427 (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].
% 2.22/2.60 428 (all V_c all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_synthetic__div__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.60 429 (all V_h_2 all V_pa_2 all T_b (class_Rings_Ocomm__semiring__0(T_b) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))) # label(fact_offset__poly__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 430 (all V_h all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_offset__poly__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 431 (all V_n_2 c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2))) # label(fact_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 432 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),V_b_2)))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 433 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_b_2),V_a_2)))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 434 (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].
% 2.22/2.61 435 (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].
% 2.22/2.61 436 (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].
% 2.22/2.61 437 (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].
% 2.22/2.61 438 (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].
% 2.22/2.61 439 (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].
% 2.22/2.61 440 (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].
% 2.22/2.61 441 (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].
% 2.22/2.61 442 (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].
% 2.22/2.61 443 (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].
% 2.22/2.61 444 (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].
% 2.22/2.61 445 (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].
% 2.22/2.61 446 (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].
% 2.22/2.61 447 (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].
% 2.22/2.61 448 (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].
% 2.22/2.61 449 (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].
% 2.22/2.61 450 (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].
% 2.22/2.61 451 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 452 (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].
% 2.22/2.61 453 (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].
% 2.22/2.61 454 (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].
% 2.22/2.61 455 (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),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(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].
% 2.22/2.61 456 (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),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(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].
% 2.22/2.61 457 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(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,hAPP(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,hAPP(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].
% 2.22/2.61 458 (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].
% 2.22/2.61 459 (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].
% 2.22/2.61 460 (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].
% 2.22/2.61 461 (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].
% 2.22/2.61 462 (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].
% 2.22/2.61 463 (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].
% 2.22/2.61 464 (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].
% 2.22/2.61 465 (all V_n all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(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].
% 2.22/2.61 466 (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].
% 2.22/2.61 467 (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].
% 2.22/2.61 468 (all V_x all V_h all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_h),V_x)))) # label(fact_poly__offset__poly) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 469 (all V_c all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osynthetic__div(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_c) = hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))) # label(fact_synthetic__div__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 470 (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].
% 2.22/2.61 471 (all V_h all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_offset__poly__single) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 472 (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].
% 2.22/2.61 473 (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].
% 2.22/2.61 474 (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),hAPP(c_Nat_OSuc,V_n))),V_r)))))) # label(fact_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 475 (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].
% 2.22/2.61 476 (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].
% 2.22/2.61 477 (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].
% 2.22/2.61 478 (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].
% 2.22/2.61 479 (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].
% 2.22/2.61 480 (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].
% 2.22/2.61 481 (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].
% 2.22/2.61 482 (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].
% 2.22/2.61 483 (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].
% 2.22/2.61 484 (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].
% 2.22/2.61 485 (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].
% 2.22/2.61 486 (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].
% 2.22/2.61 487 (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].
% 2.22/2.61 488 (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].
% 2.22/2.61 489 (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].
% 2.22/2.61 490 (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].
% 2.22/2.61 491 (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].
% 2.22/2.61 492 (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].
% 2.22/2.61 493 (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].
% 2.22/2.61 494 (all V_p all V_c all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_c)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p)) # label(fact_synthetic__div__correct_H) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 495 (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].
% 2.22/2.61 496 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_y_2),V_x_2))))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 497 (all V_p all V_a all T_b (class_Groups_Oab__group__add(T_b) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a),V_p)) = hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)))) # label(fact_minus__poly__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 498 (all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)))) # label(fact_minus__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 499 (all V_x all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))) # label(fact_poly__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 500 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_b,V_b_2) <-> V_a_2 = V_b_2))) # label(fact_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 501 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2) = V_b_2 <-> c_Groups_Ouminus__class_Ouminus(T_b,V_b_2) = V_a_2))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 502 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (V_a_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_b_2) <-> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 503 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a)) # label(fact_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 504 (all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n))) # label(fact_minus__monom) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 505 (all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)))) # label(fact_smult__minus__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 506 (all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)))) # label(fact_smult__minus__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 507 (all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_minus__poly__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 508 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w))) # label(fact_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 509 (all V_w all V_z c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) # label(fact_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 510 (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_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b)) # label(fact_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 511 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)) = V_b)) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 512 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(T_a,V_b)),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_minus__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 513 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 514 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(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),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 515 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(T_a,V_a)),V_b))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 516 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 517 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) # label(fact_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 518 (all V_b_2 all V_a_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) <-> V_a_2 = V_b_2 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 519 (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_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))) # label(fact_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 520 (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_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)))) # label(fact_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 521 (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),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))) # label(fact_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 522 (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_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)))) # label(fact_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 523 (all V_a_2 all V_b_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))))) # label(fact_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 524 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2))))) # label(fact_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 525 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))))) # label(fact_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 526 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))))) # label(fact_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 527 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2))))) # label(fact_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 528 (all V_a_2 all V_b_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),V_b_2))))) # label(fact_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 529 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__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,c_Groups_Ouminus__class_Ouminus(T_a,V_b)),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))))) # label(fact_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 530 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2) = V_a_2 <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 531 (all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 532 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (V_a_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 533 (all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = c_Groups_Ouminus__class_Ouminus(T_b,V_a_2) <-> c_Groups_Ozero__class_Ozero(T_b) = V_a_2))) # label(fact_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 534 (all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_minus__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 535 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 536 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 537 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 538 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 539 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 540 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 541 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 542 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 543 (all V_y_2 all V_x_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)))) # label(fact_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 544 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b))) # label(fact_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 545 (all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 546 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 547 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (V_a_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_b_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 548 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_right__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 549 (all V_x_2 all T_b (class_Rings_Oring__1__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) <-> V_x_2 = c_Groups_Oone__class_Oone(T_b) | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b))))) # label(fact_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 550 (all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 551 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.61 552 (all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Polynomial_Opos__poly(T_a,V_p) | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)))) # label(fact_pos__poly__total) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 553 (all V_n all V_a all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 554 (all V_y_2 all V_x_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_x_2 = V_y_2 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))) # label(fact_realpow__two__disj) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 555 (all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c),V_f_2),V_g_2)) <-> (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_c,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 556 (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].
% 2.22/2.62 557 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_y_2),V_x_2))))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 558 (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].
% 2.22/2.62 559 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c),V_f_2),V_g_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_c,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 560 (all V_x_2 all V_y_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_y_2),V_x_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 561 (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].
% 2.22/2.62 562 (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].
% 2.22/2.62 563 (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].
% 2.22/2.62 564 (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].
% 2.22/2.62 565 (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].
% 2.22/2.62 566 (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].
% 2.22/2.62 567 (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].
% 2.22/2.62 568 (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].
% 2.22/2.62 569 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c),V_f_2),V_g_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_c,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 570 (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].
% 2.22/2.62 571 (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].
% 2.22/2.62 572 (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].
% 2.22/2.62 573 (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].
% 2.22/2.62 574 (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].
% 2.22/2.62 575 (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].
% 2.22/2.62 576 (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].
% 2.22/2.62 577 (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].
% 2.22/2.62 578 (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].
% 2.22/2.62 579 (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].
% 2.22/2.62 580 (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].
% 2.22/2.62 581 (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].
% 2.22/2.62 582 (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].
% 2.22/2.62 583 (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].
% 2.22/2.62 584 (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].
% 2.22/2.62 585 (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].
% 2.22/2.62 586 (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].
% 2.22/2.62 587 (all V_x_2 all V_y_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 588 (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].
% 2.22/2.62 589 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,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].
% 2.22/2.62 590 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (V_x_2 != V_y_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 591 (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].
% 2.22/2.62 592 (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].
% 2.22/2.62 593 (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].
% 2.22/2.62 594 (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].
% 2.22/2.62 595 (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].
% 2.22/2.62 596 (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].
% 2.22/2.62 597 (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].
% 2.22/2.62 598 (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].
% 2.22/2.62 599 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 600 (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].
% 2.22/2.62 601 (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].
% 2.22/2.62 602 (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].
% 2.22/2.62 603 (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].
% 2.22/2.62 604 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 605 (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].
% 2.22/2.62 606 (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].
% 2.22/2.62 607 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 608 (all V_y_2 all V_x_2 all T_b (class_Orderings_Opreorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_y_2),V_x_2))))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 609 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 610 (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].
% 2.22/2.62 611 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_x_2),V_y_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 612 (all V_a all V_p all T_a (class_Rings_Oidom(T_a) -> (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p))))) # label(fact_order) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 613 (all V_a all V_p all T_a (class_Rings_Oidom(T_a) -> (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p))))) # label(fact_order__2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 614 (all V_y_2 all V_x_2 all T_b (class_Lattices_Oboolean__algebra(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_y_2),V_x_2))))) # label(fact_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 615 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(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,c_Groups_Ouminus__class_Ouminus(T_a,V_y)),c_Groups_Ouminus__class_Ouminus(T_a,V_x)))))) # label(fact_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 616 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_dvd__0__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 617 (all V_y_2 all V_x_2 all T_b (class_Rings_Ocomm__ring__1(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))))) # label(fact_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 618 (all V_y_2 all V_x_2 all T_b (class_Rings_Ocomm__ring__1(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))))) # label(fact_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 619 (all V_z c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z) # label(fact_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 620 (all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c),V_f_2),V_g_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c),V_f_2),V_g_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c),V_g_2),V_f_2))))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 621 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))))) # label(fact_smult__dvd__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 622 (all V_a all V_q all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))))) # label(fact_dvd__smult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 623 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)))) # label(fact_dvd__refl) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 624 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)))))) # label(fact_dvd__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 625 (all V_n all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))))) # label(fact_dvd__power__same) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 626 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)))) # label(fact_one__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 627 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))))) # label(fact_dvd__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 628 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))))) # label(fact_dvd__mult__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 629 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))))) # label(fact_dvd__mult__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 630 (all V_k all V_b all V_a all T_a (class_Rings_Odvd(T_a) -> (V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a))))) # label(fact_dvdI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 631 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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__dvd__mono) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 632 (all V_b all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 633 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_dvd__mult2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 634 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))))) # label(fact_dvd__triv__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 635 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))) # label(fact_dvd__triv__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 636 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__0__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 637 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Rings_Oidom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) <-> V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))))) # label(fact_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 638 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Oidom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))))) # label(fact_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 639 (all V_a all V_n all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_le__imp__power__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 640 (all V_m all V_n all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))))))) # label(fact_dvd__power__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 641 (all V_m all V_b all V_n all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)))))) # label(fact_power__le__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 642 (all V_q_2 all V_pa_2 all V_a_2 all T_b (class_Fields_Ofield(T_b) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)))))) # label(fact_dvd__smult__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 643 (all V_a all V_q all V_p all T_a (class_Fields_Ofield(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)))))) # label(fact_smult__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 644 (all V_q all V_a all V_p all T_a (class_Fields_Ofield(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)))))) # label(fact_dvd__smult__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 645 (all V_q_2 all V_pa_2 all V_a_2 all T_b (class_Fields_Ofield(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2)) <-> (V_a_2 = c_Groups_Ozero__class_Ozero(T_b) -> V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) & (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)))))) # label(fact_smult__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 646 (all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a)) # label(fact_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 647 (all V_x all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x)) # label(fact_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 648 (all V_b all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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))) # label(fact_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 649 (all V_y_2 all V_x_2 all T_b (class_Lattices_Oboolean__algebra(T_b) -> (c_Groups_Ouminus__class_Ouminus(T_b,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_b,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 650 (all V_x_2 all V_A_2 all T_c all T_b (class_Groups_Ouminus(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_b,hAPP(V_A_2,V_x_2)))) # label(fact_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 651 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x)) # label(fact_double__compl) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 652 (all V_x all V_n all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) | V_x = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))))) # label(fact_dvd__power) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 653 (all V_x_2 all V_A_2 all T_c all T_b (class_Groups_Ouminus(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_b,hAPP(V_A_2,V_x_2)))) # label(fact_fun__Compl__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 654 (all V_ca_2 all V_pa_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_b) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2))))) # label(fact_poly__eq__0__iff__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 655 (all V_pa_2 all V_ca_2 all T_b (class_Rings_Oidom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2)) <-> hAPP(c_Polynomial_Opoly(T_b,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_dvd__iff__poly__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 656 (all V_p all V_a all T_a (class_Rings_Oidom(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)))) # label(fact_order__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 657 (all V_l_2 all V_P_2 all T_b (class_Rings_Odvd(T_b) & class_Rings_Osemiring__0(T_b) -> ((exists B_x hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) & hBOOL(hAPP(V_P_2,B_x))))))) # label(fact_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 658 (all V_pa_2 all V_a_2 all T_b (class_Rings_Oidom(T_b) -> c_Polynomial_Oorder(T_b,V_a_2,V_pa_2) = c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),c_Nat_OSuc))),V_pa_2))))) # label(fact_order__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 659 (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].
% 2.22/2.62 660 (all V_k hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k))) # label(fact_dvd__1__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 661 (all V_t_2 all V_d_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))))) # label(fact_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 662 (all V_t_2 all V_d_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2)))) # label(fact_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 663 (all V_n_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)))) # label(fact_dvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 664 (all V_m_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 665 (all V_t_2 all V_m_2 all V_k_2 (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)))))) # label(fact_zdvd__mono) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 666 (all V_P_2 all T_b (class_Orderings_Owellorder(T_b) -> ((exists B_x1 hBOOL(hAPP(V_P_2,B_x1))) -> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))))) # label(fact_LeastI__ex) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 667 (all V_k_2 all V_P_2 all T_b (class_Orderings_Owellorder(T_b) -> (hBOOL(hAPP(V_P_2,V_k_2)) -> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))))) # label(fact_LeastI) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 668 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) -> V_m = V_n))))) # label(fact_zdvd__antisym__nonneg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 669 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m),V_n)) -> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))))) # label(fact_zdvd__not__zless) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 670 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))) -> (V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))))) # label(fact_zdvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 671 (all V_ca_2 all V_t_2 all V_x_2 all V_d_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2))),V_t_2)))))) # label(fact_zdvd__period) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 672 (all V_m_2 all V_n_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)))) # label(fact_zdvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 673 (all V_m_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 674 (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(tc_Nat_Onat,V_m),V_n)) -> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))))) # label(fact_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 675 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 676 (all V_k_2 all V_P_2 all T_b (class_Orderings_Owellorder(T_b) -> (hBOOL(hAPP(V_P_2,V_k_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2))))) # label(fact_Least__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 677 (all V_P_2 all V_k_2 all T_b (class_Orderings_Owellorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2))) -> -hBOOL(hAPP(V_P_2,V_k_2))))) # label(fact_not__less__Least) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 678 (all V_n all V_z (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_n))))) # label(fact_zdvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 679 (all V_n all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),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_k),V_n))))) # label(fact_dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 680 (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(hAPP(c_Rings_Odvd__class_Odvd(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(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 681 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))))) # label(fact_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 682 (all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,V_n_2)) -> (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc)))))) # label(fact_Least__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 683 (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)),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2)) <-> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_dvd__mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 684 (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)),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2)) <-> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_dvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 685 (all V_n all V_m all V_i (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))))) # label(fact_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 686 (all V_b_2 all V_a_2 all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))))) # label(fact_pow__divides__eq__nat) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 687 (all V_b all V_n all V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))))) # label(fact_pow__divides__pow__nat) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 688 (all V_b all V_n all V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))))) # label(fact_pow__divides__pow__int) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 689 (all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x))) # label(fact_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 690 (all V_y_2 all V_x_2 (V_x_2 = V_y_2 <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)))) # label(fact_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 691 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) | V_x_2 = V_y_2)) # label(fact_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 692 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) & V_x_2 != V_y_2)) # label(fact_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 693 (all V_b all V_a (V_a != V_b -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))))) # label(fact_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 694 (all V_y all V_x (V_x = V_y -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))) # label(fact_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 695 (all V_x_2 all V_y_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) <-> V_x_2 = V_y_2))) # label(fact_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 696 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) | V_x = V_y)) # label(fact_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 697 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))))) # label(fact_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.62 698 (all V_c all V_b all V_a (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))))) # label(fact_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 699 (all V_c all V_b all V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))))) # label(fact_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 700 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) -> V_m = V_n))) # label(fact_dvd__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 701 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> V_x = V_y))) # label(fact_dvd_Oantisym) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 702 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))))) # label(fact_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 703 (all V_c all V_b all V_a (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))))) # label(fact_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 704 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))))) # label(fact_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 705 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> V_x != V_y)) # label(fact_dvd_Oless__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 706 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))))) # label(fact_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 707 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))) # label(fact_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 708 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))))) # label(fact_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 709 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> V_x != V_y)) # label(fact_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 710 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> V_y != V_x)) # label(fact_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 711 (all V_c all V_b all V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))))) # label(fact_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 712 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))))) # label(fact_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 713 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) -> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))))) # label(fact_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 714 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))))) # label(fact_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 715 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))))) # label(fact_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 716 (all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 717 (all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x))) # label(fact_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 718 (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(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))))) # label(fact_dvd__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 719 (all V_b_2 all V_a_2 all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2))))) # label(fact_pow__divides__eq__int) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 720 (all V_y_2 all V_x_2 all V_f_2 all T_b (class_Orderings_Oorder(T_b) -> (c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))))))) # label(fact_dvd_Ostrict__monoD) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 721 (all V_k_2 all V_P_2 all V_d_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) -> ((all B_x (hBOOL(hAPP(V_P_2,B_x)) -> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_x (hBOOL(hAPP(V_P_2,B_x)) -> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))))))))) # label(fact_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 722 (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].
% 2.22/2.63 723 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)))))) # label(fact_dvd__diffD1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 724 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)))))) # label(fact_dvd__diffD) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 725 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))))) # label(fact_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 726 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))))))) # label(fact_dvd__diff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 727 (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].
% 2.22/2.63 728 (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].
% 2.22/2.63 729 (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)),hAPP(c_Nat_OSuc,V_m)))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 730 (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].
% 2.22/2.63 731 (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].
% 2.22/2.63 732 (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].
% 2.22/2.63 733 (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,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(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].
% 2.22/2.63 734 (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].
% 2.22/2.63 735 (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].
% 2.22/2.63 736 (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].
% 2.22/2.63 737 (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].
% 2.22/2.63 738 (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].
% 2.22/2.63 739 (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].
% 2.22/2.63 740 (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].
% 2.22/2.63 741 (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].
% 2.22/2.63 742 (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].
% 2.22/2.63 743 (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].
% 2.22/2.63 744 (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].
% 2.22/2.63 745 (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].
% 2.22/2.63 746 (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].
% 2.22/2.63 747 (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].
% 2.22/2.63 748 (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].
% 2.22/2.63 749 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(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].
% 2.22/2.63 750 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(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].
% 2.22/2.63 751 (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].
% 2.22/2.63 752 (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].
% 2.22/2.63 753 (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].
% 2.22/2.63 754 (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].
% 2.22/2.63 755 (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].
% 2.22/2.63 756 (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].
% 2.22/2.63 757 (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].
% 2.22/2.63 758 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ca_2),V_d_2)))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 759 (all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (class_Groups_Ominus(T_b) -> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_b,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 760 (all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (class_Groups_Ominus(T_b) -> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_b,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)))) # label(fact_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 761 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q)) = hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)))) # label(fact_diff__pCons) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 762 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__diff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 763 (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].
% 2.22/2.63 764 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Oab__group__add(T_b) -> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2) -> (V_a_2 = V_b_2 <-> V_ca_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 765 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)))) # label(fact_smult__diff__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 766 (all V_b all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n))) # label(fact_diff__monom) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 767 (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].
% 2.22/2.63 768 (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].
% 2.22/2.63 769 (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].
% 2.22/2.63 770 (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].
% 2.22/2.63 771 (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].
% 2.22/2.63 772 (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].
% 2.22/2.63 773 (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].
% 2.22/2.63 774 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(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].
% 2.22/2.63 775 (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,hAPP(c_Nat_OSuc,V_m),V_n),hAPP(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].
% 2.22/2.63 776 (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].
% 2.22/2.63 777 (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].
% 2.22/2.63 778 (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].
% 2.22/2.63 779 (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].
% 2.22/2.63 780 (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].
% 2.22/2.63 781 (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].
% 2.22/2.63 782 (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].
% 2.22/2.63 783 (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].
% 2.22/2.63 784 (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].
% 2.22/2.63 785 (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].
% 2.22/2.63 786 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 787 (all V_b_2 all V_a_2 all T_b (class_Groups_Oab__group__add(T_b) -> (V_a_2 = V_b_2 <-> c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 788 (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].
% 2.22/2.63 789 (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].
% 2.22/2.63 790 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Ouminus__class_Ouminus(T_a,V_y)))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 791 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) # label(fact_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 792 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 793 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_diff__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 794 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a))) # label(fact_diff__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 795 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oring(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) <-> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2)),V_d_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 796 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oring(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2)),V_ca_2) = V_d_2))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 797 (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].
% 2.22/2.63 798 (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].
% 2.22/2.63 799 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 800 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 801 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),V_d_2)))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 802 (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].
% 2.22/2.63 803 (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].
% 2.22/2.63 804 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) # label(fact_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 805 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2)),V_d_2)))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 806 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2)),V_ca_2)),V_d_2))))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 807 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2)),V_ca_2)),V_d_2))))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 808 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2)),V_d_2)))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 809 (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].
% 2.22/2.63 810 (all V_t_2 all V_D_2 all V_d_2 all T_b (class_Rings_Ocomm__ring(T_b) & class_Rings_Odvd(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) -> (all B_x all B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))))))) # label(fact_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 811 (all V_t_2 all V_D_2 all V_d_2 all T_b (class_Rings_Ocomm__ring(T_b) & class_Rings_Odvd(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) -> (all B_x all B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))))))) # label(fact_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 812 (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,hAPP(c_Nat_OSuc,V_i))),V_n)))) # label(fact_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 813 (all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n)) # label(fact_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 814 (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].
% 2.22/2.63 815 (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].
% 2.22/2.63 816 (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,hAPP(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,hAPP(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].
% 2.22/2.63 817 (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,hAPP(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),hAPP(c_Nat_OSuc,V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.63 818 (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].
% 2.22/2.64 819 (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].
% 2.22/2.64 820 (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].
% 2.22/2.64 821 (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].
% 2.22/2.64 822 (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].
% 2.22/2.64 823 (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].
% 2.22/2.64 824 (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 = hAPP(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].
% 2.22/2.64 825 (all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hAPP(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].
% 2.22/2.64 826 (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) = hAPP(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].
% 2.22/2.64 827 (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].
% 2.22/2.64 828 (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].
% 2.22/2.64 829 (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].
% 2.22/2.64 830 (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].
% 2.22/2.64 831 (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),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Nat_OSuc,hAPP(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].
% 2.22/2.64 832 (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].
% 2.22/2.64 833 (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,hAPP(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].
% 2.22/2.64 834 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))))) # label(fact_zdvd__zdiffD) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 835 (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].
% 2.22/2.64 836 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_b),V_x_2),V_y_2)) <-> V_x_2 = V_y_2 | c_Polynomial_Opos__poly(T_b,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b),V_y_2,V_x_2))))) # label(fact_less__eq__poly__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 837 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))) # label(fact_smult__diff__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 838 (all V_p all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p)) # label(fact_diff__poly__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 839 (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].
% 2.22/2.64 840 (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].
% 2.22/2.64 841 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2),V_y_2)) <-> c_Polynomial_Opos__poly(T_b,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b),V_y_2,V_x_2))))) # label(fact_less__poly__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 842 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)) # label(fact_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 843 (all V_w all V_z c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) # label(fact_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 844 (all V_q all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q))) # label(fact_diff__poly__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 845 (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].
% 2.22/2.64 846 (all V_f_2 all T_b (class_Orderings_Oorder(T_b) -> (c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) -> c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)))) # label(fact_dvd_Ostrict__mono__mono) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 847 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) # label(fact_Limits_Ominus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 848 (all V_y_2 all V_x_2 all V_f_2 all T_b (class_Orderings_Oorder(T_b) -> (c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))))))) # label(fact_dvd_OmonoD) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 849 (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].
% 2.22/2.64 850 (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,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_int__power__div__base) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 851 (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].
% 2.22/2.64 852 (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].
% 2.22/2.64 853 (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].
% 2.22/2.64 854 (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].
% 2.22/2.64 855 (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].
% 2.22/2.64 856 (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].
% 2.22/2.64 857 (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].
% 2.22/2.64 858 (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].
% 2.22/2.64 859 (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].
% 2.22/2.64 860 (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].
% 2.22/2.64 861 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b))) # label(fact_dvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 862 (all V_a all V_b all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)))) # label(fact_div__mult__swap) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 863 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b))) # label(fact_dvd__div__mult__self) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 864 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a)))) # label(fact_dvd__div__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 865 (all V_w all V_z all V_x all V_y all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_div__mult__div__if__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 866 (all V_y all V_x all V_z all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y)) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_z)),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)))))) # label(fact_div__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 867 (all V_x all V_y all T_a (class_Divides_Oring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y))))) # label(fact_dvd__div__neg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 868 (all V_x all V_y all T_a (class_Divides_Oring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y))))) # label(fact_dvd__neg__div) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 869 (all V_n all V_x all V_y all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))))) # label(fact_div__power) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 870 (all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) # label(fact_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 871 (all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)) # label(fact_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 872 (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].
% 2.22/2.64 873 (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].
% 2.22/2.64 874 (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].
% 2.22/2.64 875 (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].
% 2.22/2.64 876 (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].
% 2.22/2.64 877 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2))))))) # label(fact_div__dvd__div) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 878 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m)) # label(fact_zdvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 879 (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].
% 2.22/2.64 880 (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].
% 2.22/2.64 881 (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].
% 2.22/2.64 882 (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].
% 2.22/2.64 883 (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].
% 2.22/2.64 884 (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].
% 2.22/2.64 885 (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].
% 2.22/2.64 886 (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].
% 2.22/2.64 887 (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].
% 2.22/2.64 888 (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].
% 2.22/2.64 889 (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].
% 2.22/2.64 890 (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].
% 2.22/2.64 891 (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].
% 2.22/2.64 892 (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].
% 2.22/2.64 893 (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].
% 2.22/2.64 894 (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].
% 2.22/2.64 895 (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].
% 2.22/2.64 896 (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].
% 2.22/2.64 897 (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].
% 2.22/2.64 898 (all V_d_2 all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2)) -> (c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2) = c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)))))))) # label(fact_dvd__div__div__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 899 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) -> (c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2) = V_ca_2 <-> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)))))) # label(fact_dvd__div__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 900 (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].
% 2.22/2.64 901 (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].
% 2.22/2.64 902 (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].
% 2.22/2.64 903 (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].
% 2.22/2.64 904 (all V_k all V_l ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_SMT_Oz3div(V_k,V_l) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l)) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_SMT_Oz3div(V_k,V_l) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)))))) # label(fact_z3div__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 905 (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].
% 2.22/2.64 906 (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].
% 2.22/2.64 907 (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].
% 2.22/2.64 908 (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].
% 2.22/2.64 909 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_poly__div__minus__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 910 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_poly__div__minus__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 911 (all V_m c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m) # label(fact_div__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 912 (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].
% 2.22/2.64 913 (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].
% 2.22/2.64 914 (all V_y all V_x all V_a all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y) = hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_div__smult__left) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 915 (all V_z all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z))) # label(fact_poly__div__mult__right) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.64 916 (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].
% 2.22/2.64 917 (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].
% 2.22/2.65 918 (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].
% 2.22/2.65 919 (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].
% 2.22/2.65 920 (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].
% 2.22/2.65 921 (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) = hAPP(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].
% 2.22/2.65 922 (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) = hAPP(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].
% 2.22/2.65 923 (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].
% 2.22/2.65 924 (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),hAPP(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].
% 2.22/2.65 925 (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),hAPP(c_Nat_OSuc,B_q)))) & hBOOL(hAPP(V_P_2,B_q)))))) # label(fact_split__div_H) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 926 (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) = hAPP(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].
% 2.22/2.65 927 (all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) & (V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)) -> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)) -> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))))))) # label(fact_sgn__poly__def) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 928 (all V_k_2 all V_P_2 all V_d_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) -> ((all B_x (hBOOL(hAPP(V_P_2,B_x)) -> hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2))))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_x (hBOOL(hAPP(V_P_2,B_x)) -> hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))))))))) # label(fact_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 929 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_sgn__greater) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 930 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_sgn__less) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 931 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)))) # label(fact_sgn__minus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 932 (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].
% 2.22/2.65 933 (all V_x_2 all T_b (class_RealVector_Oreal__normed__vector(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_x_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 934 (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].
% 2.22/2.65 935 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sgn__0__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 936 (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].
% 2.22/2.65 937 (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].
% 2.22/2.65 938 (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].
% 2.22/2.65 939 (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].
% 2.22/2.65 940 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_sgn__1__pos) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 941 (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].
% 2.22/2.65 942 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_sgn__1__neg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 943 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 944 (all V_x all T_a (class_Groups_Osgn__if(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)) & (V_x != c_Groups_Ozero__class_Ozero(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))))) # label(fact_sgn__if) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 945 (all V_n_2 all V_P_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(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all 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(hAPP(V_P_2,B_i),B_j))))))) # label(fact_split__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 946 (all V_n_2 all V_P_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all 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(hAPP(V_P_2,B_i),B_j))))))) # label(fact_split__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 947 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))) # label(fact_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 948 (all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 949 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 950 (all V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a)) # label(fact_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 951 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a)) # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 952 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 953 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 954 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> 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),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) # label(fact_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 955 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> 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_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) # label(fact_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 956 (all V_k all V_b all V_a hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)) # label(fact_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 957 (all V_k all V_a all V_b hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)) # label(fact_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 958 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))) # label(fact_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 959 (all V_b all V_a V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) # label(fact_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 960 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) # label(fact_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 961 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)),V_n))) # label(fact_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 962 (all V_m_2 all V_n_2 all V_k_2 all T_b (class_Divides_Osemiring__div(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)))))) # label(fact_dvd__mod__iff) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 963 (all V_a all V_b all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c)))) # label(fact_mod__mod__cancel) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 964 (all V_n all V_m all V_f (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))))) # label(fact_zdvd__zmod) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 965 (all V_n all V_m all V_k all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))))))) # label(fact_dvd__mod) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 966 (all V_n all V_m all V_k all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)))))) # label(fact_dvd__mod__imp__dvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 967 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))))) # label(fact_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 968 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 969 (all V_b_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) <-> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 970 (all V_l all V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 971 (all V_l all V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 972 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 973 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 974 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 975 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,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) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 976 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,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) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 977 (all V_b c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 978 (all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__self) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 979 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 980 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 981 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__self) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 982 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 983 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 984 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 985 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c))) # label(fact_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 986 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 987 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 988 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 989 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c))))) # label(fact_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 990 (all T (class_Rings_Oidom(T) -> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T))) # label(clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 991 (all T (class_Rings_Oidom(T) -> class_Groups_Ocancel__ab__semigroup__add(T))) # label(clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 992 (all T (class_Rings_Oidom(T) -> class_Rings_Oring__1__no__zero__divisors(T))) # label(clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 993 (all T (class_Rings_Oidom(T) -> class_Rings_Oring__no__zero__divisors(T))) # label(clrel_Rings_Oidom__Rings_Oring__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 994 (all T (class_Rings_Oidom(T) -> class_Groups_Ocancel__semigroup__add(T))) # label(clrel_Rings_Oidom__Groups_Ocancel__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 995 (all T (class_Rings_Oidom(T) -> class_Groups_Oab__semigroup__mult(T))) # label(clrel_Rings_Oidom__Groups_Oab__semigroup__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 996 (all T (class_Rings_Oidom(T) -> class_Groups_Ocomm__monoid__mult(T))) # label(clrel_Rings_Oidom__Groups_Ocomm__monoid__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 997 (all T (class_Rings_Oidom(T) -> class_Groups_Oab__semigroup__add(T))) # label(clrel_Rings_Oidom__Groups_Oab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 998 (all T (class_Rings_Oidom(T) -> class_Rings_Ono__zero__divisors(T))) # label(clrel_Rings_Oidom__Rings_Ono__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 999 (all T (class_Rings_Oidom(T) -> class_Groups_Ocomm__monoid__add(T))) # label(clrel_Rings_Oidom__Groups_Ocomm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1000 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__semiring__1(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__semiring__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1001 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__semiring__0(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__semiring__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1002 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__semiring(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__semiring) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1003 (all T (class_Rings_Oidom(T) -> class_Groups_Oab__group__add(T))) # label(clrel_Rings_Oidom__Groups_Oab__group__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1004 (all T (class_Rings_Oidom(T) -> class_Rings_Ozero__neq__one(T))) # label(clrel_Rings_Oidom__Rings_Ozero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1005 (all T (class_Rings_Oidom(T) -> class_Groups_Omonoid__mult(T))) # label(clrel_Rings_Oidom__Groups_Omonoid__mult) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1006 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__ring__1(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__ring__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1007 (all T (class_Rings_Oidom(T) -> class_Groups_Omonoid__add(T))) # label(clrel_Rings_Oidom__Groups_Omonoid__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1008 (all T (class_Rings_Oidom(T) -> class_Rings_Osemiring__0(T))) # label(clrel_Rings_Oidom__Rings_Osemiring__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1009 (all T (class_Rings_Oidom(T) -> class_Groups_Ogroup__add(T))) # label(clrel_Rings_Oidom__Groups_Ogroup__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1010 (all T (class_Rings_Oidom(T) -> class_Rings_Omult__zero(T))) # label(clrel_Rings_Oidom__Rings_Omult__zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1011 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__ring(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__ring) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1012 (all T (class_Rings_Oidom(T) -> class_Rings_Osemiring(T))) # label(clrel_Rings_Oidom__Rings_Osemiring) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1013 (all T (class_Rings_Oidom(T) -> class_Groups_Ouminus(T))) # label(clrel_Rings_Oidom__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1014 (all T (class_Rings_Oidom(T) -> class_Rings_Oring__1(T))) # label(clrel_Rings_Oidom__Rings_Oring__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1015 (all T (class_Rings_Oidom(T) -> class_Groups_Ominus(T))) # label(clrel_Rings_Oidom__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1016 (all T (class_Rings_Oidom(T) -> class_Power_Opower(T))) # label(clrel_Rings_Oidom__Power_Opower) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1017 (all T (class_Rings_Oidom(T) -> class_Groups_Ozero(T))) # label(clrel_Rings_Oidom__Groups_Ozero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1018 (all T (class_Rings_Oidom(T) -> class_Rings_Oring(T))) # label(clrel_Rings_Oidom__Rings_Oring) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1019 (all T (class_Rings_Oidom(T) -> class_Groups_Oone(T))) # label(clrel_Rings_Oidom__Groups_Oone) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1020 (all T (class_Rings_Oidom(T) -> class_Rings_Odvd(T))) # label(clrel_Rings_Oidom__Rings_Odvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1021 (all T (class_Rings_Oidom(T) -> class_Groups_Ocancel__comm__monoid__add(T))) # label(clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1022 (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].
% 2.22/2.65 1023 (all T_2 all T_1 (class_Lattices_Oboolean__algebra(T_1) -> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1024 (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].
% 2.22/2.65 1025 (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].
% 2.22/2.65 1026 (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].
% 2.22/2.65 1027 (all T_2 all T_1 (class_Groups_Ouminus(T_1) -> class_Groups_Ouminus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1028 (all T_2 all T_1 (class_Groups_Ominus(T_1) -> class_Groups_Ominus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1029 (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].
% 2.22/2.65 1030 (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].
% 2.22/2.65 1031 (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].
% 2.22/2.65 1032 (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].
% 2.22/2.65 1033 (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].
% 2.22/2.65 1034 (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].
% 2.22/2.65 1035 (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].
% 2.22/2.65 1036 (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].
% 2.22/2.65 1037 (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].
% 2.22/2.65 1038 (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].
% 2.22/2.65 1039 (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].
% 2.22/2.65 1040 (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].
% 2.22/2.65 1041 (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].
% 2.22/2.65 1042 (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].
% 2.22/2.65 1043 (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].
% 2.22/2.65 1044 (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].
% 2.22/2.65 1045 (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].
% 2.22/2.65 1046 (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].
% 2.22/2.65 1047 (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].
% 2.22/2.65 1048 (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].
% 2.22/2.65 1049 (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].
% 2.22/2.65 1050 (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].
% 2.22/2.65 1051 (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].
% 2.22/2.65 1052 (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].
% 2.22/2.65 1053 (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].
% 2.22/2.65 1054 (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].
% 2.22/2.65 1055 (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].
% 2.22/2.65 1056 (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].
% 2.22/2.65 1057 (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].
% 2.22/2.65 1058 (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].
% 2.22/2.65 1059 (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].
% 2.22/2.65 1060 (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].
% 2.22/2.65 1061 (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].
% 2.22/2.65 1062 (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].
% 2.22/2.65 1063 (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].
% 2.22/2.65 1064 (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].
% 2.22/2.65 1065 (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].
% 2.22/2.65 1066 (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].
% 2.22/2.65 1067 (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].
% 2.22/2.65 1068 (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].
% 2.22/2.65 1069 (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].
% 2.22/2.65 1070 (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].
% 2.22/2.65 1071 (all T_1 (class_Fields_Ofield(T_1) -> class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Divides_Oring__div) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1072 (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].
% 2.22/2.65 1073 (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].
% 2.22/2.65 1074 (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].
% 2.22/2.65 1075 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1076 (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].
% 2.22/2.65 1077 (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].
% 2.22/2.65 1078 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1079 (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].
% 2.22/2.65 1080 (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].
% 2.22/2.65 1081 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ominus(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1082 (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].
% 2.22/2.65 1083 (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].
% 2.22/2.65 1084 (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].
% 2.22/2.65 1085 (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].
% 2.22/2.65 1086 (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].
% 2.22/2.65 1087 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Odvd(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Odvd) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1088 (all V_Q all V_P all T_b all T_a hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1089 (all V_R_2 all V_Q_2 all V_P_2 all T_d all T_b all T_c hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),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].
% 2.22/2.65 1090 (all V_R_2 all V_Q_2 all V_P_2 all T_b all T_d all T_c hAPP(hAPP(c_COMBC(T_c,T_d,T_b,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].
% 2.22/2.65 1091 (all V_R_2 all V_Q_2 all V_P_2 all T_b all T_d all T_c hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),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].
% 2.22/2.65 1092 (all V_y_2 all V_x_2 (-hBOOL(c_fequal(V_x_2,V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1093 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(c_fequal(V_x_2,V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1094 (all V_P_2 (-hBOOL(hAPP(c_fNot,V_P_2)) | -hBOOL(V_P_2))) # label(help_c__fNot__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1095 (all V_P_2 (--hBOOL(V_P_2) | hBOOL(hAPP(c_fNot,V_P_2)))) # label(help_c__fNot__2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1096 (all V_Q_2 all V_P_2 (-hBOOL(V_P_2) | -hBOOL(V_Q_2) | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)))) # label(help_c__fconj__1) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1097 (all V_Q_2 all V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) | hBOOL(V_P_2))) # label(help_c__fconj__2) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.65 1098 (all V_Q_2 all V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) | hBOOL(V_Q_2))) # label(help_c__fconj__3) # label(axiom) # label(non_clause). [assumption].
% 2.51/2.77 1099 (all B_z hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),v_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,v_q),B_z))))) # label(conj_2) # label(hypothesis) # label(non_clause). [assumption].
% 2.51/2.77 1100 -(exists B_a (B_a != c_Groups_Ozero__class_Ozero(t_a) & 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_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) & (exists B_q (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)) & (all B_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),v_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,v_q),B_z))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,B_q),B_z))))))))) # label(conj_3) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.51/2.77
% 2.51/2.77 ============================== end of process non-clausal formulas ===
% 2.51/2.77
% 2.51/2.77 ============================== PROCESS INITIAL CLAUSES ===============
% 2.51/2.77
% 2.51/2.77 ============================== PREDICATE ELIMINATION =================
% 2.51/2.77 1101 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.51/2.77 1102 -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(9)].
% 2.51/2.77 1103 -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(10)].
% 2.51/2.77 1104 -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),hAPP(c_Nat_OSuc,C))),c_Groups_Oone__class_Oone(A))) # label(fact_power__Suc__less__one) # label(axiom). [clausify(11)].
% 2.51/2.77 1105 -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(12)].
% 2.51/2.77 1106 -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(14)].
% 2.51/2.77 1107 -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(14)].
% 2.51/2.77 1108 -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(118)].
% 2.51/2.77 1109 -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(120)].
% 2.51/2.77 1110 -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(120)].
% 2.51/2.77 1111 -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(135)].
% 2.51/2.77 1112 -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(136)].
% 2.51/2.77 1113 -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),hAPP(c_Nat_OSuc,C)))) # label(fact_power__gt1) # label(axiom). [clausify(138)].
% 2.51/2.77 1114 -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(139)].
% 2.51/2.77 1115 -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(140)].
% 2.51/2.77 1116 -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(141)].
% 2.51/2.77 1117 -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(217)].
% 2.51/2.77 1118 -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(220)].
% 2.51/2.77 1119 -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(221)].
% 2.51/2.77 1120 -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(222)].
% 2.51/2.77 1121 -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(223)].
% 2.51/2.77 1122 -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(339)].
% 2.51/2.77 1123 -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(342)].
% 2.51/2.77 1124 -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(385)].
% 2.51/2.77 1125 -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(386)].
% 2.51/2.77 1126 -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(386)].
% 2.51/2.77 1127 -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(387)].
% 2.51/2.77 1128 -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(414)].
% 2.51/2.77 1129 -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(415)].
% 2.51/2.77 1130 -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(416)].
% 2.51/2.77 1131 -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(417)].
% 2.51/2.77 1132 -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(418)].
% 2.51/2.77 1133 -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(454)].
% 2.51/2.77 1134 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(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(455)].
% 2.51/2.77 1135 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(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(456)].
% 2.51/2.77 1136 -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(467)].
% 2.51/2.77 1137 -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),hAPP(c_Nat_OSuc,C))),B)) # label(fact_realpow__Suc__le__self) # label(axiom). [clausify(474)].
% 2.51/2.77 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(1101,a,1102,a)].
% 2.51/2.77 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(1101,a,1103,a)].
% 2.51/2.77 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),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1101,a,1104,a)].
% 2.51/2.77 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(1101,a,1105,a)].
% 2.51/2.77 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(1101,a,1106,a)].
% 2.51/2.77 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(1101,a,1107,a)].
% 2.51/2.77 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(1101,a,1108,a)].
% 2.51/2.77 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(1101,a,1109,a)].
% 2.51/2.77 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(1101,a,1110,a)].
% 2.51/2.77 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(1101,a,1111,a)].
% 2.51/2.77 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(1101,a,1112,a)].
% 2.51/2.77 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),hAPP(c_Nat_OSuc,B)))). [resolve(1101,a,1113,a)].
% 2.51/2.77 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(1101,a,1116,a)].
% 2.51/2.77 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(1101,a,1117,a)].
% 2.51/2.77 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(1101,a,1118,a)].
% 2.51/2.78 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(1101,a,1119,a)].
% 2.51/2.78 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(1101,a,1120,a)].
% 2.51/2.78 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(1101,a,1121,a)].
% 2.51/2.78 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(1101,a,1122,a)].
% 2.51/2.78 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(1101,a,1123,a)].
% 2.51/2.78 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(1101,a,1124,a)].
% 2.51/2.78 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(1101,a,1125,a)].
% 2.51/2.78 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(1101,a,1126,a)].
% 2.51/2.78 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(1101,a,1128,a)].
% 2.51/2.78 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(1101,a,1129,a)].
% 2.51/2.78 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(1101,a,1130,a)].
% 2.51/2.78 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(1101,a,1131,a)].
% 2.51/2.78 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(1101,a,1132,a)].
% 2.51/2.78 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(1101,a,1133,a)].
% 2.51/2.78 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(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(1101,a,1134,a)].
% 2.51/2.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(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(1101,a,1135,a)].
% 2.51/2.78 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(1101,a,1136,a)].
% 2.51/2.78 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),hAPP(c_Nat_OSuc,B))),A)). [resolve(1101,a,1137,a)].
% 2.51/2.78 1138 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.51/2.78 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(1138,a,1102,a)].
% 2.51/2.78 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(1138,a,1103,a)].
% 2.51/2.78 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),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1138,a,1104,a)].
% 2.51/2.78 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(1138,a,1105,a)].
% 2.51/2.78 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(1138,a,1106,a)].
% 2.51/2.78 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(1138,a,1107,a)].
% 2.51/2.78 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(1138,a,1108,a)].
% 2.51/2.78 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(1138,a,1109,a)].
% 2.51/2.78 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(1138,a,1110,a)].
% 2.51/2.78 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(1138,a,1111,a)].
% 2.51/2.78 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(1138,a,1112,a)].
% 2.51/2.78 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),hAPP(c_Nat_OSuc,B)))). [resolve(1138,a,1113,a)].
% 2.51/2.78 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(1138,a,1116,a)].
% 2.51/2.78 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(1138,a,1117,a)].
% 2.51/2.78 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(1138,a,1118,a)].
% 2.51/2.78 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(1138,a,1119,a)].
% 2.51/2.78 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(1138,a,1120,a)].
% 2.51/2.78 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(1138,a,1121,a)].
% 2.51/2.78 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(1138,a,1122,a)].
% 2.51/2.78 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(1138,a,1123,a)].
% 2.51/2.78 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(1138,a,1124,a)].
% 2.51/2.78 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(1138,a,1125,a)].
% 2.51/2.78 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(1138,a,1126,a)].
% 2.51/2.78 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(1138,a,1128,a)].
% 2.51/2.78 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(1138,a,1129,a)].
% 2.51/2.78 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(1138,a,1130,a)].
% 2.51/2.78 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(1138,a,1131,a)].
% 2.51/2.78 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(1138,a,1132,a)].
% 2.51/2.78 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(1138,a,1133,a)].
% 2.51/2.78 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(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(1138,a,1134,a)].
% 2.51/2.79 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(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(1138,a,1135,a)].
% 2.51/2.79 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(1138,a,1136,a)].
% 2.51/2.79 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),hAPP(c_Nat_OSuc,B))),A)). [resolve(1138,a,1137,a)].
% 2.51/2.79 1139 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(1048)].
% 2.51/2.79 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(1139,b,1102,a)].
% 2.51/2.79 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(1139,b,1103,a)].
% 2.51/2.79 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),hAPP(c_Nat_OSuc,C))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1139,b,1104,a)].
% 2.51/2.79 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(1139,b,1105,a)].
% 2.51/2.79 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(1139,b,1106,a)].
% 2.51/2.79 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(1139,b,1107,a)].
% 2.51/2.79 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(1139,b,1108,a)].
% 2.51/2.79 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(1139,b,1109,a)].
% 2.51/2.79 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(1139,b,1110,a)].
% 2.51/2.79 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(1139,b,1111,a)].
% 2.51/2.79 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(1139,b,1112,a)].
% 2.51/2.79 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),hAPP(c_Nat_OSuc,C)))). [resolve(1139,b,1113,a)].
% 2.51/2.79 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(1139,b,1116,a)].
% 2.51/2.79 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(1139,b,1117,a)].
% 2.51/2.79 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(1139,b,1118,a)].
% 2.51/2.79 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(1139,b,1119,a)].
% 2.51/2.79 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(1139,b,1120,a)].
% 2.51/2.79 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(1139,b,1121,a)].
% 2.51/2.79 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(1139,b,1122,a)].
% 2.51/2.79 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(1139,b,1123,a)].
% 2.51/2.79 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(1139,b,1124,a)].
% 2.51/2.79 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(1139,b,1125,a)].
% 2.51/2.79 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(1139,b,1126,a)].
% 2.51/2.79 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(1139,b,1128,a)].
% 2.51/2.79 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(1139,b,1129,a)].
% 2.65/2.92 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(1139,b,1130,a)].
% 2.65/2.92 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(1139,b,1131,a)].
% 2.65/2.92 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(1139,b,1132,a)].
% 2.65/2.92 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(1139,b,1133,a)].
% 2.65/2.92 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),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),hAPP(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(1139,b,1134,a)].
% 2.65/2.92 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),hAPP(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(1139,b,1135,a)].
% 2.65/2.92 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(1139,b,1136,a)].
% 2.65/2.92 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),hAPP(c_Nat_OSuc,C))),B)). [resolve(1139,b,1137,a)].
% 2.65/2.92 1140 -class_Rings_Oidom(A) | class_Groups_Omonoid__mult(A) # label(clrel_Rings_Oidom__Groups_Omonoid__mult) # label(axiom). [clausify(1005)].
% 2.65/2.92 1141 -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(20)].
% 2.65/2.92 1142 -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(69)].
% 2.65/2.92 1143 -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(70)].
% 2.65/2.92 1144 -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(109)].
% 2.65/2.92 1145 -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_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) # label(fact_power__Suc2) # label(axiom). [clausify(122)].
% 2.65/2.92 1146 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) # label(fact_power__add) # label(axiom). [clausify(125)].
% 2.65/2.92 1147 -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(262)].
% 2.65/2.92 1148 -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(264)].
% 2.65/2.92 1149 -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_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) = hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B) # label(fact_realpow__minus__mult) # label(axiom). [clausify(722)].
% 2.65/2.92 1150 -class_Groups_Omonoid__mult(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | 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) = hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,C),B)) # label(fact_lemma__realpow__diff) # label(axiom). [clausify(833)].
% 2.65/2.92 Derived: -class_Rings_Oidom(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)). [resolve(1140,b,1141,a)].
% 2.65/2.92 Derived: -class_Rings_Oidom(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)). [resolve(1140,b,1142,a)].
% 2.65/2.92 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B). [resolve(1140,b,1143,a)].
% 2.65/2.92 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B. [resolve(1140,b,1144,a)].
% 2.65/2.92 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)). [resolve(1140,b,1145,a)].
% 2.65/2.92 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)). [resolve(1140,b,1146,a)].
% 2.65/2.92 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B. [resolve(1140,b,1147,a)].
% 2.65/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B. [resolve(1140,b,1148,a)].
% 2.65/2.93 Derived: -class_Rings_Oidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B). [resolve(1140,b,1149,a)].
% 2.65/2.93 Derived: -class_Rings_Oidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | 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) = hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,C),B)). [resolve(1140,b,1150,a)].
% 2.65/2.93 1151 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.65/2.93 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(1151,a,1141,a)].
% 2.65/2.93 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(1151,a,1142,a)].
% 2.65/2.93 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(1151,a,1143,a)].
% 2.65/2.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1151,a,1144,a)].
% 2.65/2.93 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_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)). [resolve(1151,a,1145,a)].
% 2.65/2.93 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1151,a,1146,a)].
% 2.65/2.93 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1151,a,1147,a)].
% 2.65/2.93 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(1151,a,1148,a)].
% 2.65/2.93 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A). [resolve(1151,a,1149,a)].
% 2.65/2.93 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | 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) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),A)). [resolve(1151,a,1150,a)].
% 2.65/2.93 1152 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.65/2.93 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(1152,a,1141,a)].
% 2.65/2.93 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(1152,a,1142,a)].
% 2.69/2.94 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(1152,a,1143,a)].
% 2.69/2.94 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1152,a,1144,a)].
% 2.69/2.94 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_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)). [resolve(1152,a,1145,a)].
% 2.69/2.94 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(1152,a,1146,a)].
% 2.69/2.94 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1152,a,1147,a)].
% 2.69/2.94 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(1152,a,1148,a)].
% 2.69/2.94 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A). [resolve(1152,a,1149,a)].
% 2.69/2.94 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | 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) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),A)). [resolve(1152,a,1150,a)].
% 2.69/2.94 1153 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1066)].
% 2.69/2.94 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(1153,b,1141,a)].
% 2.69/2.94 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(1153,b,1142,a)].
% 2.69/2.94 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(1153,b,1143,a)].
% 2.69/2.94 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(1153,b,1144,a)].
% 2.69/2.94 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_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C)). [resolve(1153,b,1145,a)].
% 2.69/2.94 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)). [resolve(1153,b,1146,a)].
% 2.69/2.94 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(1153,b,1147,a)].
% 2.81/3.11 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(1153,b,1148,a)].
% 2.81/3.11 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_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) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),B). [resolve(1153,b,1149,a)].
% 2.81/3.11 Derived: -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | 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) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,C),B)). [resolve(1153,b,1150,a)].
% 2.81/3.11 1154 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 2.81/3.11 1155 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) != c_Polynomial_Opoly(A,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B # label(fact_poly__zero) # label(axiom). [clausify(28)].
% 2.81/3.11 1156 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Polynomial_Opoly(A,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B # label(fact_poly__zero) # label(axiom). [clausify(28)].
% 2.81/3.11 1157 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,B) != c_Polynomial_Opoly(A,C) | B = C # label(fact_poly__eq__iff) # label(axiom). [clausify(66)].
% 2.81/3.11 1158 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,B) = c_Polynomial_Opoly(A,C) | B != C # label(fact_poly__eq__iff) # label(axiom). [clausify(66)].
% 2.81/3.11 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) != c_Polynomial_Opoly(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) = A. [resolve(1154,a,1155,a)].
% 2.81/3.11 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) = c_Polynomial_Opoly(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)) != A. [resolve(1154,a,1156,a)].
% 2.81/3.11 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) != c_Polynomial_Opoly(tc_Int_Oint,B) | A = B. [resolve(1154,a,1157,a)].
% 2.81/3.11 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) = c_Polynomial_Opoly(tc_Int_Oint,B) | A != B. [resolve(1154,a,1158,a)].
% 2.81/3.11 1159 -class_Rings_Olinordered__idom(A) | class_Int_Oring__char__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom). [clausify(1075)].
% 2.81/3.11 Derived: -class_Rings_Olinordered__idom(A) | -class_Rings_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(A)))) != c_Polynomial_Opoly(tc_Polynomial_Opoly(A),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(A))) = B. [resolve(1159,b,1155,a)].
% 2.81/3.11 Derived: -class_Rings_Olinordered__idom(A) | -class_Rings_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(A)))) = c_Polynomial_Opoly(tc_Polynomial_Opoly(A),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(A))) != B. [resolve(1159,b,1156,a)].
% 2.81/3.11 Derived: -class_Rings_Olinordered__idom(A) | -class_Rings_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(tc_Polynomial_Opoly(A),B) != c_Polynomial_Opoly(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1159,b,1157,a)].
% 2.99/3.25 Derived: -class_Rings_Olinordered__idom(A) | -class_Rings_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(tc_Polynomial_Opoly(A),B) = c_Polynomial_Opoly(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1159,b,1158,a)].
% 2.99/3.25 1160 -class_Rings_Oidom(A) | class_Rings_Oring__1__no__zero__divisors(A) # label(clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors) # label(axiom). [clausify(992)].
% 2.99/3.25 1161 -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(67)].
% 2.99/3.25 1162 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Oone__class_Oone(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B # label(fact_square__eq__1__iff) # label(axiom). [clausify(549)].
% 2.99/3.25 1163 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Oone__class_Oone(A) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(549)].
% 2.99/3.25 1164 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(549)].
% 2.99/3.25 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C). [resolve(1160,b,1161,a)].
% 2.99/3.25 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Oone__class_Oone(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B. [resolve(1160,b,1162,a)].
% 2.99/3.25 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Oone__class_Oone(A) != B. [resolve(1160,b,1163,a)].
% 2.99/3.25 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B. [resolve(1160,b,1164,a)].
% 2.99/3.25 1165 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.99/3.25 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(1165,a,1161,a)].
% 2.99/3.25 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | c_Groups_Oone__class_Oone(tc_Int_Oint) = A | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1165,a,1162,a)].
% 2.99/3.25 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | c_Groups_Oone__class_Oone(tc_Int_Oint) != A. [resolve(1165,a,1163,a)].
% 2.99/3.25 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) != A. [resolve(1165,a,1164,a)].
% 2.99/3.25 1166 -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(1039)].
% 2.99/3.25 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(1166,b,1161,a)].
% 2.99/3.25 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(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)) = B | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1166,b,1162,a)].
% 3.22/3.54 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(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)) != B. [resolve(1166,b,1163,a)].
% 3.22/3.54 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) != B. [resolve(1166,b,1164,a)].
% 3.22/3.54 1167 -class_Rings_Oidom(A) | class_Groups_Ocomm__monoid__mult(A) # label(clrel_Rings_Oidom__Groups_Ocomm__monoid__mult) # label(axiom). [clausify(996)].
% 3.22/3.54 1168 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C) # label(fact_power__mult__distrib) # label(axiom). [clausify(68)].
% 3.22/3.54 1169 -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(261)].
% 3.22/3.54 1170 -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(263)].
% 3.22/3.54 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C). [resolve(1167,b,1168,a)].
% 3.22/3.54 1171 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.22/3.54 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(1171,a,1168,a)].
% 3.22/3.54 1172 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.22/3.54 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),B). [resolve(1172,a,1168,a)].
% 3.22/3.54 1173 -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(1050)].
% 3.22/3.54 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),C). [resolve(1173,b,1168,a)].
% 3.22/3.54 1174 -class_Rings_Oidom(A) | class_Power_Opower(A) # label(clrel_Rings_Oidom__Power_Opower) # label(axiom). [clausify(1016)].
% 3.22/3.54 1175 -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(119)].
% 3.22/3.54 1176 -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(119)].
% 3.22/3.55 1177 -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(119)].
% 3.22/3.55 1178 -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)),hAPP(c_Nat_OSuc,B)) # label(fact_power__0__Suc) # label(axiom). [clausify(121)].
% 3.22/3.55 1179 -class_Power_Opower(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),hAPP(c_Nat_OSuc,C)) # label(fact_power__Suc) # label(axiom). [clausify(123)].
% 3.22/3.55 1180 -class_Power_Opower(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_power__0) # label(axiom). [clausify(124)].
% 3.22/3.55 1181 -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(137)].
% 3.22/3.55 1182 -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(137)].
% 3.22/3.55 1183 -class_Power_Opower(A) | c_Power_Opower_Opower(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A)) = c_Power_Opower__class_Opower(A) # label(fact_power__power__power) # label(axiom). [clausify(270)].
% 3.22/3.55 1184 -class_Power_Opower(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),B) # label(fact_realpow__num__eq__if) # label(axiom). [clausify(832)].
% 3.22/3.55 1185 -class_Power_Opower(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B) # label(fact_realpow__num__eq__if) # label(axiom). [clausify(832)].
% 3.22/3.55 Derived: -class_Rings_Oidom(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. [resolve(1174,b,1176,a)].
% 3.22/3.55 Derived: -class_Rings_Oidom(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. [resolve(1174,b,1177,a)].
% 3.22/3.55 Derived: -class_Rings_Oidom(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)),hAPP(c_Nat_OSuc,B)). [resolve(1174,b,1178,a)].
% 3.22/3.55 Derived: -class_Rings_Oidom(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),hAPP(c_Nat_OSuc,C)). [resolve(1174,b,1179,a)].
% 3.22/3.55 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1174,b,1180,a)].
% 3.22/3.55 Derived: -class_Rings_Oidom(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). [resolve(1174,b,1181,a)].
% 3.22/3.55 Derived: -class_Rings_Oidom(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). [resolve(1174,b,1182,a)].
% 3.31/3.55 Derived: -class_Rings_Oidom(A) | c_Power_Opower_Opower(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A)) = c_Power_Opower__class_Opower(A). [resolve(1174,b,1183,a)].
% 3.31/3.55 Derived: -class_Rings_Oidom(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),B). [resolve(1174,b,1184,a)].
% 3.31/3.55 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B). [resolve(1174,b,1185,a)].
% 3.31/3.55 1186 class_Power_Opower(tc_Int_Oint) # label(arity_Int__Oint__Power_Opower) # label(axiom). [assumption].
% 3.31/3.55 Derived: -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(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(1186,a,1176,a)].
% 3.31/3.55 Derived: -class_Rings_Omult__zero(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(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(1186,a,1177,a)].
% 3.31/3.55 Derived: -class_Rings_Osemiring__0(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)),hAPP(c_Nat_OSuc,A)). [resolve(1186,a,1178,a)].
% 3.31/3.55 Derived: 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),hAPP(c_Nat_OSuc,B)). [resolve(1186,a,1179,a)].
% 3.31/3.55 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1186,a,1180,a)].
% 3.31/3.55 Derived: -class_Rings_Osemiring__0(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(1186,a,1181,a)].
% 3.31/3.55 Derived: -class_Rings_Osemiring__0(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(1186,a,1182,a)].
% 3.31/3.55 Derived: c_Power_Opower_Opower(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)) = c_Power_Opower__class_Opower(tc_Int_Oint). [resolve(1186,a,1183,a)].
% 3.31/3.55 Derived: 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),B),A). [resolve(1186,a,1184,a)].
% 3.31/3.55 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A). [resolve(1186,a,1185,a)].
% 3.31/3.55 1187 class_Power_Opower(tc_Nat_Onat) # label(arity_Nat__Onat__Power_Opower) # label(axiom). [assumption].
% 3.31/3.55 Derived: -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(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(1187,a,1175,a)].
% 3.31/3.55 Derived: -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(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(1187,a,1176,a)].
% 3.31/3.56 Derived: -class_Rings_Omult__zero(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(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(1187,a,1177,a)].
% 3.31/3.56 Derived: -class_Rings_Osemiring__0(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)),hAPP(c_Nat_OSuc,A)). [resolve(1187,a,1178,a)].
% 3.31/3.56 Derived: 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),hAPP(c_Nat_OSuc,B)). [resolve(1187,a,1179,a)].
% 3.31/3.56 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1187,a,1180,a)].
% 3.31/3.56 Derived: -class_Rings_Osemiring__0(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(1187,a,1181,a)].
% 3.31/3.56 Derived: -class_Rings_Osemiring__0(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(1187,a,1182,a)].
% 3.31/3.56 Derived: c_Power_Opower_Opower(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)) = c_Power_Opower__class_Opower(tc_Nat_Onat). [resolve(1187,a,1183,a)].
% 3.31/3.56 Derived: 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),B),A). [resolve(1187,a,1184,a)].
% 3.31/3.56 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A). [resolve(1187,a,1185,a)].
% 3.31/3.56 1188 -class_Rings_Ocomm__semiring__1(A) | class_Power_Opower(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Power_Opower) # label(axiom). [clausify(1082)].
% 3.31/3.56 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(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(1188,b,1175,a)].
% 3.31/3.56 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(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(1188,b,1176,a)].
% 3.31/3.56 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(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(1188,b,1177,a)].
% 3.31/3.56 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(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))),hAPP(c_Nat_OSuc,B)). [resolve(1188,b,1178,a)].
% 3.46/3.72 Derived: -class_Rings_Ocomm__semiring__1(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),hAPP(c_Nat_OSuc,C)). [resolve(1188,b,1179,a)].
% 3.46/3.72 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)),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1188,b,1180,a)].
% 3.46/3.72 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(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(1188,b,1181,a)].
% 3.46/3.72 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(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(1188,b,1182,a)].
% 3.46/3.72 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Power_Opower_Opower(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A))) = c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)). [resolve(1188,b,1183,a)].
% 3.46/3.72 Derived: -class_Rings_Ocomm__semiring__1(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),B). [resolve(1188,b,1184,a)].
% 3.46/3.72 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),B). [resolve(1188,b,1185,a)].
% 3.46/3.72 1189 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 3.46/3.72 1190 -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(142)].
% 3.46/3.72 1191 -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(142)].
% 3.46/3.72 1192 -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(142)].
% 3.46/3.72 1193 -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(201)].
% 3.46/3.72 1194 -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(201)].
% 3.46/3.72 1195 -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(201)].
% 3.46/3.72 1196 -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(201)].
% 3.46/3.72 1197 -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(201)].
% 3.46/3.72 1198 -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(201)].
% 3.46/3.72 1199 -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(202)].
% 3.46/3.72 1200 -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(202)].
% 3.46/3.72 1201 -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(202)].
% 3.46/3.72 1202 -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(202)].
% 3.46/3.72 1203 -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(202)].
% 3.46/3.72 1204 -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(202)].
% 3.46/3.72 1205 -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(203)].
% 3.46/3.72 1206 -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(203)].
% 3.46/3.72 1207 -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(209)].
% 3.46/3.72 1208 -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(209)].
% 3.46/3.72 1209 -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(211)].
% 3.46/3.72 1210 -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(215)].
% 3.46/3.72 1211 -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(216)].
% 3.46/3.72 1212 -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(218)].
% 3.46/3.72 1213 -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(218)].
% 3.46/3.72 1214 -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(218)].
% 3.46/3.72 1215 -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(389)].
% 3.46/3.72 1216 -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(389)].
% 3.46/3.72 1217 -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(389)].
% 3.46/3.72 1218 -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(389)].
% 3.46/3.72 1219 -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(389)].
% 3.46/3.72 1220 -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(389)].
% 3.46/3.72 1221 -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(390)].
% 3.46/3.72 1222 -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(390)].
% 3.46/3.72 1223 -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(390)].
% 3.46/3.72 1224 -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(390)].
% 3.46/3.72 1225 -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(390)].
% 3.46/3.72 1226 -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(390)].
% 3.46/3.72 1227 -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(432)].
% 3.46/3.72 1228 -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(432)].
% 3.46/3.72 1229 -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(433)].
% 3.46/3.72 1230 -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(433)].
% 3.46/3.72 1231 -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(451)].
% 3.46/3.72 1232 -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(451)].
% 3.46/3.72 1233 -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(451)].
% 3.46/3.72 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(1189,a,1190,a)].
% 3.46/3.72 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(1189,a,1191,a)].
% 3.46/3.72 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(1189,a,1192,a)].
% 3.46/3.72 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(1189,a,1193,a)].
% 3.46/3.72 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(1189,a,1194,a)].
% 3.46/3.72 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(1189,a,1195,a)].
% 3.46/3.72 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(1189,a,1196,a)].
% 3.46/3.72 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(1189,a,1197,a)].
% 3.46/3.72 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(1189,a,1198,a)].
% 3.46/3.72 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(1189,a,1199,a)].
% 3.46/3.72 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(1189,a,1200,a)].
% 3.46/3.72 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(1189,a,1201,a)].
% 3.46/3.72 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(1189,a,1202,a)].
% 3.46/3.72 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(1189,a,1203,a)].
% 3.46/3.72 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(1189,a,1204,a)].
% 3.46/3.72 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(1189,a,1205,a)].
% 3.46/3.72 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(1189,a,1207,a)].
% 3.46/3.72 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(1189,a,1209,a)].
% 3.46/3.72 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(1189,a,1212,a)].
% 3.46/3.72 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(1189,a,1213,a)].
% 3.46/3.72 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(1189,a,1214,a)].
% 3.46/3.72 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,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1189,a,1215,a)].
% 3.46/3.72 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(1189,a,1216,a)].
% 3.46/3.73 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(1189,a,1217,a)].
% 3.46/3.73 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,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1189,a,1218,a)].
% 3.46/3.73 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(1189,a,1219,a)].
% 3.46/3.73 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(1189,a,1220,a)].
% 3.46/3.73 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,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1189,a,1221,a)].
% 3.46/3.73 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(1189,a,1222,a)].
% 3.46/3.73 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(1189,a,1223,a)].
% 3.46/3.73 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,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(1189,a,1224,a)].
% 3.46/3.73 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(1189,a,1225,a)].
% 3.46/3.73 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(1189,a,1226,a)].
% 3.46/3.74 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(1189,a,1227,a)].
% 3.46/3.74 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(1189,a,1228,a)].
% 3.46/3.74 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(1189,a,1229,a)].
% 3.46/3.74 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(1189,a,1230,a)].
% 3.46/3.74 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(1189,a,1231,a)].
% 3.46/3.74 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(1189,a,1232,a)].
% 3.46/3.74 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(1189,a,1233,a)].
% 3.46/3.74 1234 -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(1041)].
% 3.46/3.74 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(1234,b,1190,a)].
% 3.46/3.74 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(1234,b,1191,a)].
% 3.46/3.74 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(1234,b,1192,a)].
% 3.46/3.74 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(1234,b,1193,a)].
% 3.46/3.74 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(1234,b,1194,a)].
% 3.46/3.74 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(1234,b,1195,a)].
% 3.46/3.74 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(1234,b,1196,a)].
% 3.46/3.74 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(1234,b,1197,a)].
% 3.46/3.74 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(1234,b,1198,a)].
% 3.46/3.74 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(1234,b,1199,a)].
% 3.46/3.74 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(1234,b,1200,a)].
% 3.46/3.74 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(1234,b,1201,a)].
% 3.46/3.74 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(1234,b,1202,a)].
% 3.46/3.74 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(1234,b,1203,a)].
% 3.46/3.74 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(1234,b,1204,a)].
% 3.46/3.74 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(1234,b,1205,a)].
% 3.46/3.74 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(1234,b,1207,a)].
% 3.46/3.74 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(1234,b,1209,a)].
% 3.46/3.74 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(1234,b,1212,a)].
% 3.46/3.74 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(1234,b,1213,a)].
% 3.46/3.74 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(1234,b,1214,a)].
% 3.46/3.74 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),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1234,b,1215,a)].
% 3.46/3.74 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(1234,b,1216,a)].
% 3.46/3.74 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(1234,b,1217,a)].
% 3.46/3.74 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),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1234,b,1218,a)].
% 3.46/3.74 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(1234,b,1219,a)].
% 3.46/3.74 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(1234,b,1220,a)].
% 3.46/3.74 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),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1234,b,1221,a)].
% 3.46/3.74 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(1234,b,1222,a)].
% 3.46/3.74 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(1234,b,1223,a)].
% 3.46/3.74 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),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)). [resolve(1234,b,1224,a)].
% 3.46/3.74 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(1234,b,1225,a)].
% 3.46/3.74 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(1234,b,1226,a)].
% 3.46/3.74 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(1234,b,1227,a)].
% 3.46/3.74 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(1234,b,1228,a)].
% 3.46/3.74 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(1234,b,1229,a)].
% 3.63/3.89 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(1234,b,1230,a)].
% 3.63/3.89 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(1234,b,1231,a)].
% 3.63/3.89 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(1234,b,1232,a)].
% 3.63/3.89 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(1234,b,1233,a)].
% 3.63/3.89 1235 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 3.63/3.89 1236 -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(143)].
% 3.63/3.89 1237 -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(200)].
% 3.63/3.89 1238 -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(388)].
% 3.63/3.89 1239 -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(450)].
% 3.63/3.89 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(1235,a,1236,a)].
% 3.63/3.89 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(1235,a,1237,a)].
% 3.63/3.89 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(1235,a,1238,a)].
% 3.63/3.89 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(1235,a,1239,a)].
% 3.78/4.06 1240 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom). [clausify(1055)].
% 3.78/4.06 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(1240,b,1236,a)].
% 3.78/4.06 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(1240,b,1237,a)].
% 3.78/4.06 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(1240,b,1238,a)].
% 3.78/4.06 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(1240,b,1239,a)].
% 3.78/4.06 1241 -class_Rings_Oidom(A) | class_Rings_Oring__no__zero__divisors(A) # label(clrel_Rings_Oidom__Rings_Oring__no__zero__divisors) # label(axiom). [clausify(993)].
% 3.78/4.06 1242 -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(180)].
% 3.78/4.06 1243 -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(180)].
% 3.78/4.06 1244 -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(180)].
% 3.78/4.06 Derived: -class_Rings_Oidom(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. [resolve(1241,b,1242,a)].
% 3.78/4.06 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B. [resolve(1241,b,1243,a)].
% 3.78/4.06 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != C. [resolve(1241,b,1244,a)].
% 3.78/4.06 1245 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 3.78/4.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1245,a,1242,a)].
% 3.78/4.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1245,a,1243,a)].
% 3.78/4.06 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1245,a,1244,a)].
% 3.78/4.06 1246 -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(1042)].
% 3.78/4.06 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(1246,b,1242,a)].
% 3.92/4.20 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(1246,b,1243,a)].
% 3.92/4.20 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(1246,b,1244,a)].
% 3.92/4.20 1247 -class_Rings_Oidom(A) | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) # label(clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [clausify(990)].
% 3.92/4.20 1248 -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(185)].
% 3.92/4.20 1249 -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(185)].
% 3.92/4.20 1250 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(189)].
% 3.92/4.20 1251 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(189)].
% 3.92/4.20 1252 -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(189)].
% 3.92/4.20 1253 -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(194)].
% 3.92/4.20 1254 -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(194)].
% 3.92/4.20 1255 -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(194)].
% 3.92/4.21 1256 -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(219)].
% 3.92/4.21 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != B | c_Groups_Ozero__class_Ozero(A) = C. [resolve(1247,b,1248,a)].
% 3.92/4.21 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = B | c_Groups_Ozero__class_Ozero(A) != C. [resolve(1247,b,1249,a)].
% 3.92/4.21 Derived: -class_Rings_Oidom(A) | B = C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). [resolve(1247,b,1250,a)].
% 3.92/4.21 Derived: -class_Rings_Oidom(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). [resolve(1247,b,1251,a)].
% 3.92/4.21 Derived: -class_Rings_Oidom(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)). [resolve(1247,b,1252,a)].
% 3.92/4.21 Derived: -class_Rings_Oidom(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)). [resolve(1247,b,1256,a)].
% 3.92/4.21 1257 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].
% 3.92/4.21 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1257,a,1248,a)].
% 3.92/4.21 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1257,a,1249,a)].
% 3.92/4.21 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),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),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),B),C)). [resolve(1257,a,1250,a)].
% 3.92/4.21 Derived: A != B | 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),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),B),C)). [resolve(1257,a,1251,a)].
% 3.92/4.21 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(1257,a,1252,a)].
% 3.92/4.21 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(1257,a,1256,a)].
% 3.92/4.22 1258 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].
% 3.92/4.22 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1258,a,1248,a)].
% 3.92/4.22 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1258,a,1249,a)].
% 3.92/4.22 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),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),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),B),C)). [resolve(1258,a,1250,a)].
% 3.92/4.22 Derived: A != B | 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),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),B),C)). [resolve(1258,a,1251,a)].
% 3.92/4.22 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(1258,a,1252,a)].
% 3.92/4.22 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(1258,a,1256,a)].
% 3.92/4.22 1259 -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(1029)].
% 3.92/4.22 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(1259,b,1248,a)].
% 3.92/4.22 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(1259,b,1249,a)].
% 3.92/4.22 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)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),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)),C),D)). [resolve(1259,b,1250,a)].
% 3.92/4.22 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)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),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)),C),D)). [resolve(1259,b,1251,a)].
% 3.92/4.22 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(1259,b,1252,a)].
% 4.29/4.54 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(1259,b,1256,a)].
% 4.29/4.54 1260 -class_Rings_Oidom(A) | class_Rings_Ocomm__semiring(A) # label(clrel_Rings_Oidom__Rings_Ocomm__semiring) # label(axiom). [clausify(1002)].
% 4.29/4.54 1261 -class_Rings_Ocomm__semiring(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),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(190)].
% 4.29/4.54 Derived: -class_Rings_Oidom(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),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C). [resolve(1260,b,1261,a)].
% 4.29/4.54 1262 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 4.29/4.54 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),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(1262,a,1261,a)].
% 4.29/4.54 1263 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 4.29/4.54 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),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B). [resolve(1263,a,1261,a)].
% 4.29/4.54 1264 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1060)].
% 4.29/4.54 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)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),C). [resolve(1264,b,1261,a)].
% 4.29/4.54 1265 -class_Rings_Oidom(A) | class_Rings_Osemiring(A) # label(clrel_Rings_Oidom__Rings_Osemiring) # label(axiom). [clausify(1012)].
% 4.29/4.54 1266 -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(193)].
% 4.29/4.54 Derived: -class_Rings_Oidom(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)). [resolve(1265,b,1266,a)].
% 4.29/4.54 1267 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 4.29/4.54 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(1267,a,1266,a)].
% 4.40/4.70 1268 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 4.40/4.70 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(1268,a,1266,a)].
% 4.40/4.70 1269 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom). [clausify(1076)].
% 4.40/4.70 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(1269,b,1266,a)].
% 4.40/4.70 1270 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 4.40/4.70 1271 -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(204)].
% 4.40/4.70 1272 -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(205)].
% 4.40/4.70 1273 -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(206)].
% 4.40/4.70 1274 -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(207)].
% 4.40/4.70 1275 -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(208)].
% 4.40/4.70 1276 -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(210)].
% 4.40/4.70 1277 -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(212)].
% 4.40/4.70 1278 -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(213)].
% 4.40/4.70 1279 -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(434)].
% 4.40/4.70 1280 -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(435)].
% 4.40/4.70 1281 -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(436)].
% 4.40/4.70 1282 -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(437)].
% 4.40/4.70 1283 -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(439)].
% 4.40/4.70 1284 -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(441)].
% 4.40/4.70 1285 -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(442)].
% 4.40/4.70 1286 -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(443)].
% 4.40/4.70 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(1270,a,1271,a)].
% 4.40/4.70 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(1270,a,1272,a)].
% 4.40/4.70 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(1270,a,1273,a)].
% 4.40/4.70 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(1270,a,1274,a)].
% 4.40/4.70 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(1270,a,1275,a)].
% 4.40/4.70 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(1270,a,1279,a)].
% 4.40/4.70 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(1270,a,1280,a)].
% 4.40/4.70 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(1270,a,1281,a)].
% 4.40/4.70 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(1270,a,1282,a)].
% 4.40/4.70 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(1270,a,1283,a)].
% 4.40/4.70 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(1270,a,1284,a)].
% 4.40/4.70 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(1270,a,1285,a)].
% 4.40/4.70 1287 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 4.40/4.70 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(1287,a,1271,a)].
% 4.40/4.70 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(1287,a,1272,a)].
% 4.40/4.70 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(1287,a,1273,a)].
% 4.40/4.70 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(1287,a,1274,a)].
% 4.40/4.70 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(1287,a,1275,a)].
% 4.40/4.70 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(1287,a,1277,a)].
% 4.40/4.71 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_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(1287,a,1278,a)].
% 4.40/4.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),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(1287,a,1279,a)].
% 4.40/4.71 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),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(1287,a,1280,a)].
% 4.40/4.71 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),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(1287,a,1281,a)].
% 4.40/4.71 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(1287,a,1282,a)].
% 4.40/4.71 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(1287,a,1283,a)].
% 4.40/4.71 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(1287,a,1284,a)].
% 4.40/4.71 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(1287,a,1285,a)].
% 4.40/4.71 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(1287,a,1286,a)].
% 4.40/4.71 1288 -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(1034)].
% 4.40/4.71 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(1288,b,1271,a)].
% 4.40/4.71 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(1288,b,1272,a)].
% 4.40/4.71 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(1288,b,1273,a)].
% 4.40/4.71 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(1288,b,1274,a)].
% 4.40/4.71 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(1288,b,1275,a)].
% 4.40/4.71 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(1288,b,1279,a)].
% 4.40/4.71 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(1288,b,1280,a)].
% 4.80/5.04 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(1288,b,1281,a)].
% 4.80/5.04 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(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(1288,b,1282,a)].
% 4.80/5.04 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(1288,b,1283,a)].
% 4.80/5.04 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(1288,b,1284,a)].
% 4.80/5.04 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(1288,b,1285,a)].
% 4.80/5.04 1289 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 4.80/5.04 1290 -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(214)].
% 4.80/5.04 1291 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 4.80/5.04 1292 -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(1032)].
% 4.80/5.04 1293 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 4.80/5.04 1294 -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(231)].
% 4.80/5.05 1295 -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(231)].
% 4.80/5.05 1296 -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(233)].
% 4.80/5.05 1297 -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(233)].
% 4.80/5.05 1298 -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(248)].
% 4.80/5.05 1299 -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(248)].
% 4.80/5.05 1300 -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(251)].
% 4.80/5.05 1301 -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(251)].
% 4.80/5.05 1302 -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(405)].
% 4.80/5.05 1303 -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(405)].
% 4.80/5.05 1304 -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(406)].
% 4.80/5.05 1305 -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(406)].
% 4.80/5.05 1306 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__zero) # label(axiom). [clausify(530)].
% 4.80/5.05 1307 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__zero) # label(axiom). [clausify(530)].
% 4.80/5.05 1308 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_equal__neg__zero) # label(axiom). [clausify(532)].
% 4.80/5.05 1309 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_equal__neg__zero) # label(axiom). [clausify(532)].
% 4.80/5.05 1310 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ouminus__class_Ouminus(A,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__minus__self__iff) # label(axiom). [clausify(536)].
% 4.80/5.05 1311 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ouminus__class_Ouminus(A,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__minus__self__iff) # label(axiom). [clausify(536)].
% 4.80/5.05 1312 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_minus__le__self__iff) # label(axiom). [clausify(538)].
% 4.80/5.05 1313 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_minus__le__self__iff) # label(axiom). [clausify(538)].
% 4.80/5.05 1314 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__nonneg) # label(axiom). [clausify(539)].
% 4.80/5.05 1315 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__nonneg) # label(axiom). [clausify(539)].
% 4.80/5.05 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(1293,a,1294,a)].
% 4.80/5.05 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(1293,a,1296,a)].
% 4.80/5.05 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(1293,a,1297,a)].
% 4.80/5.05 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(1293,a,1298,a)].
% 4.80/5.05 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(1293,a,1299,a)].
% 4.80/5.05 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(1293,a,1302,a)].
% 4.80/5.05 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(1293,a,1303,a)].
% 4.80/5.06 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(1293,a,1304,a)].
% 4.80/5.06 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(1293,a,1305,a)].
% 4.80/5.06 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1293,a,1306,a)].
% 4.80/5.06 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1293,a,1307,a)].
% 4.80/5.06 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1293,a,1310,a)].
% 4.80/5.06 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1293,a,1311,a)].
% 4.80/5.06 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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(1293,a,1312,a)].
% 4.80/5.06 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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(1293,a,1313,a)].
% 4.80/5.06 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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(1293,a,1314,a)].
% 4.80/5.06 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(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(1293,a,1315,a)].
% 4.80/5.06 1316 -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(1037)].
% 4.80/5.06 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(1316,b,1294,a)].
% 4.80/5.06 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(1316,b,1296,a)].
% 4.80/5.06 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(1316,b,1297,a)].
% 4.80/5.06 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(1316,b,1298,a)].
% 4.80/5.06 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(1316,b,1299,a)].
% 4.80/5.06 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(1316,b,1302,a)].
% 4.80/5.06 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(1316,b,1303,a)].
% 4.80/5.06 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(1316,b,1304,a)].
% 4.80/5.06 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(1316,b,1305,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1316,b,1306,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1316,b,1307,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1316,b,1310,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1316,b,1311,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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(1316,b,1312,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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(1316,b,1313,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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(1316,b,1314,a)].
% 4.80/5.06 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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(1316,b,1315,a)].
% 4.97/5.22 1317 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.97/5.22 1318 -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(234)].
% 4.97/5.22 1319 -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(267)].
% 4.97/5.22 1320 -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(407)].
% 4.97/5.22 1321 -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(408)].
% 4.97/5.22 1322 -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(408)].
% 4.97/5.22 1323 -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(408)].
% 4.97/5.22 1324 -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(409)].
% 4.97/5.22 1325 -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(410)].
% 4.97/5.22 1326 -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(411)].
% 4.97/5.22 1327 -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(444)].
% 4.97/5.22 1328 -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(445)].
% 4.97/5.22 1329 -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(446)].
% 4.97/5.22 1330 -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(447)].
% 4.97/5.22 1331 -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(448)].
% 4.97/5.22 1332 -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(449)].
% 4.97/5.22 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(1317,a,1319,a)].
% 4.97/5.22 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(1317,a,1320,a)].
% 4.97/5.22 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(1317,a,1321,a)].
% 4.97/5.22 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(1317,a,1322,a)].
% 4.97/5.22 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(1317,a,1323,a)].
% 4.97/5.23 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(1317,a,1324,a)].
% 4.97/5.23 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(1317,a,1325,a)].
% 4.97/5.23 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(1317,a,1326,a)].
% 4.97/5.23 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(1317,a,1327,a)].
% 4.97/5.23 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(1317,a,1328,a)].
% 4.97/5.23 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(1317,a,1329,a)].
% 4.97/5.23 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(1317,a,1330,a)].
% 4.97/5.23 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(1317,a,1331,a)].
% 4.97/5.23 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(1317,a,1332,a)].
% 4.97/5.23 1333 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.97/5.23 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(1333,a,1319,a)].
% 4.97/5.23 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(1333,a,1320,a)].
% 4.97/5.23 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(1333,a,1321,a)].
% 4.97/5.23 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(1333,a,1322,a)].
% 4.97/5.23 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(1333,a,1323,a)].
% 4.97/5.23 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(1333,a,1324,a)].
% 4.97/5.23 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(1333,a,1325,a)].
% 4.97/5.23 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(1333,a,1326,a)].
% 4.97/5.23 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(1333,a,1327,a)].
% 4.97/5.23 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(1333,a,1328,a)].
% 4.97/5.23 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(1333,a,1329,a)].
% 4.97/5.23 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(1333,a,1330,a)].
% 4.97/5.23 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(1333,a,1331,a)].
% 4.97/5.23 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(1333,a,1332,a)].
% 4.97/5.23 1334 -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(1036)].
% 4.97/5.23 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(1334,b,1319,a)].
% 4.97/5.23 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(1334,b,1320,a)].
% 4.97/5.23 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(1334,b,1321,a)].
% 4.97/5.23 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(1334,b,1322,a)].
% 4.97/5.23 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(1334,b,1323,a)].
% 4.97/5.23 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(1334,b,1324,a)].
% 4.97/5.23 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(1334,b,1325,a)].
% 5.14/5.39 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(1334,b,1326,a)].
% 5.14/5.39 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(1334,b,1327,a)].
% 5.14/5.39 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(1334,b,1328,a)].
% 5.14/5.39 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(1334,b,1329,a)].
% 5.14/5.39 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(1334,b,1330,a)].
% 5.14/5.39 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(1334,b,1331,a)].
% 5.14/5.39 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(1334,b,1332,a)].
% 5.14/5.39 1335 -class_Rings_Oidom(A) | class_Groups_Oab__semigroup__mult(A) # label(clrel_Rings_Oidom__Groups_Oab__semigroup__mult) # label(axiom). [clausify(995)].
% 5.14/5.39 1336 -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(238)].
% 5.14/5.39 Derived: -class_Rings_Oidom(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)). [resolve(1335,b,1336,a)].
% 5.31/5.57 1337 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 5.31/5.57 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(1337,a,1336,a)].
% 5.31/5.57 1338 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 5.31/5.57 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(1338,a,1336,a)].
% 5.31/5.57 1339 -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(1049)].
% 5.31/5.57 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(1339,b,1336,a)].
% 5.31/5.57 1340 -class_Rings_Oidom(A) | class_Groups_Ocancel__semigroup__add(A) # label(clrel_Rings_Oidom__Groups_Ocancel__semigroup__add) # label(axiom). [clausify(994)].
% 5.31/5.57 1341 -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(239)].
% 5.31/5.57 1342 -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(241)].
% 5.31/5.57 1343 -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(242)].
% 5.31/5.57 1344 -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(242)].
% 5.31/5.57 1345 -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(243)].
% 5.31/5.57 1346 -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(243)].
% 5.31/5.57 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D. [resolve(1340,b,1341,a)].
% 5.31/5.57 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D. [resolve(1340,b,1342,a)].
% 5.31/5.57 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B != D. [resolve(1340,b,1344,a)].
% 5.31/5.57 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C != D. [resolve(1340,b,1346,a)].
% 5.31/5.57 1347 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.31/5.57 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(1347,a,1341,a)].
% 5.31/5.57 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(1347,a,1342,a)].
% 5.65/5.92 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(1347,a,1344,a)].
% 5.65/5.92 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(1347,a,1346,a)].
% 5.65/5.92 1348 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.65/5.92 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(1348,a,1341,a)].
% 5.65/5.92 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(1348,a,1342,a)].
% 5.65/5.92 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(1348,a,1344,a)].
% 5.65/5.92 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(1348,a,1346,a)].
% 5.65/5.92 1349 -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(1046)].
% 5.65/5.92 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(1349,b,1341,a)].
% 5.65/5.92 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(1349,b,1342,a)].
% 5.65/5.92 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(1349,b,1344,a)].
% 5.65/5.92 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(1349,b,1346,a)].
% 5.65/5.92 1350 -class_Rings_Oidom(A) | class_Groups_Ocancel__ab__semigroup__add(A) # label(clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add) # label(axiom). [clausify(991)].
% 5.65/5.92 1351 -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(240)].
% 5.65/5.92 1352 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.65/5.92 1353 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.65/5.92 1354 -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(1038)].
% 5.65/5.92 1355 -class_Rings_Oidom(A) | class_Groups_Oab__semigroup__add(A) # label(clrel_Rings_Oidom__Groups_Oab__semigroup__add) # label(axiom). [clausify(997)].
% 5.65/5.92 1356 -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(244)].
% 5.65/5.92 Derived: -class_Rings_Oidom(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)). [resolve(1355,b,1356,a)].
% 5.65/5.92 1357 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 6.01/6.26 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(1357,a,1356,a)].
% 6.01/6.26 1358 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 6.01/6.26 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(1358,a,1356,a)].
% 6.01/6.26 1359 -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(1051)].
% 6.01/6.26 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(1359,b,1356,a)].
% 6.01/6.26 1360 -class_Rings_Oidom(A) | class_Groups_Omonoid__add(A) # label(clrel_Rings_Oidom__Groups_Omonoid__add) # label(axiom). [clausify(1007)].
% 6.01/6.26 1361 -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(250)].
% 6.01/6.26 1362 -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(253)].
% 6.01/6.26 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B. [resolve(1360,b,1361,a)].
% 6.01/6.26 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B. [resolve(1360,b,1362,a)].
% 6.01/6.26 1363 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 6.01/6.26 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1363,a,1361,a)].
% 6.01/6.26 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(1363,a,1362,a)].
% 6.01/6.26 1364 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 6.01/6.26 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1364,a,1361,a)].
% 6.01/6.26 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A. [resolve(1364,a,1362,a)].
% 6.01/6.26 1365 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom). [clausify(1068)].
% 6.01/6.26 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(1365,b,1361,a)].
% 6.01/6.26 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(1365,b,1362,a)].
% 6.01/6.26 1366 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].
% 6.01/6.26 1367 -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(254)].
% 6.01/6.26 1368 -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(255)].
% 6.01/6.26 1369 -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(259)].
% 6.01/6.26 1370 -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(259)].
% 6.01/6.26 1371 -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(260)].
% 6.01/6.26 1372 -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(260)].
% 6.01/6.26 1373 -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(343)].
% 6.01/6.26 1374 -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(344)].
% 6.01/6.26 1375 -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(348)].
% 6.01/6.26 1376 -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(348)].
% 6.01/6.26 1377 -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(349)].
% 6.01/6.26 1378 -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(349)].
% 6.01/6.26 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(1366,a,1367,a)].
% 6.01/6.26 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(1366,a,1368,a)].
% 6.01/6.26 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(1366,a,1370,a)].
% 6.01/6.27 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(1366,a,1372,a)].
% 6.01/6.27 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(1366,a,1373,a)].
% 6.01/6.27 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(1366,a,1374,a)].
% 6.01/6.27 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(1366,a,1376,a)].
% 6.01/6.27 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(1366,a,1378,a)].
% 6.01/6.27 1379 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].
% 6.01/6.27 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(1379,a,1367,a)].
% 6.01/6.27 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(1379,a,1368,a)].
% 6.01/6.27 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(1379,a,1370,a)].
% 6.01/6.27 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(1379,a,1372,a)].
% 6.01/6.27 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(1379,a,1373,a)].
% 6.01/6.27 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(1379,a,1374,a)].
% 6.01/6.27 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(1379,a,1376,a)].
% 6.01/6.27 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(1379,a,1378,a)].
% 6.01/6.27 1380 -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(1031)].
% 6.20/6.44 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(1380,b,1367,a)].
% 6.20/6.44 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(1380,b,1368,a)].
% 6.20/6.44 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(1380,b,1370,a)].
% 6.20/6.44 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(1380,b,1372,a)].
% 6.20/6.44 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(1380,b,1373,a)].
% 6.20/6.44 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(1380,b,1374,a)].
% 6.20/6.44 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(1380,b,1376,a)].
% 6.20/6.44 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(1380,b,1378,a)].
% 6.20/6.44 1381 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 6.20/6.44 1382 -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(256)].
% 6.20/6.44 1383 -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(257)].
% 6.20/6.44 1384 -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(258)].
% 6.20/6.44 1385 -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(412)].
% 6.20/6.45 1386 -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(413)].
% 6.20/6.45 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(1381,a,1382,a)].
% 6.20/6.45 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(1381,a,1385,a)].
% 6.20/6.45 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(1381,a,1386,a)].
% 6.20/6.45 1387 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 6.20/6.45 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(1387,a,1382,a)].
% 6.20/6.45 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(1387,a,1385,a)].
% 6.20/6.45 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(1387,a,1386,a)].
% 6.20/6.45 1388 -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(1030)].
% 6.20/6.45 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(1388,b,1382,a)].
% 6.20/6.45 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(1388,b,1385,a)].
% 6.20/6.45 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(1388,b,1386,a)].
% 6.71/6.96 1389 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 6.71/6.96 1390 -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(340)].
% 6.71/6.96 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(1389,a,1390,a)].
% 6.71/6.96 1391 -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(1033)].
% 6.71/6.96 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(1391,b,1390,a)].
% 6.71/6.96 1392 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 6.71/6.96 1393 -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(345)].
% 6.71/6.96 1394 -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(346)].
% 6.71/6.96 1395 -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(347)].
% 6.71/6.96 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(1392,a,1393,a)].
% 6.87/7.14 1396 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 6.87/7.14 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(1396,a,1393,a)].
% 6.87/7.14 1397 -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(1035)].
% 6.87/7.14 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(1397,b,1393,a)].
% 6.87/7.14 1398 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.87/7.14 1399 -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(391)].
% 6.87/7.14 1400 -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(392)].
% 6.87/7.14 1401 -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(393)].
% 6.87/7.14 1402 -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(394)].
% 6.87/7.14 1403 -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(404)].
% 6.87/7.14 1404 -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(404)].
% 7.04/7.31 1405 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 7.04/7.31 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(1405,a,1399,a)].
% 7.04/7.31 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(1405,a,1400,a)].
% 7.04/7.31 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(1405,a,1401,a)].
% 7.04/7.31 1406 -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(1040)].
% 7.04/7.31 1407 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 7.04/7.31 1408 -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(395)].
% 7.04/7.31 1409 -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(399)].
% 7.04/7.31 1410 -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(400)].
% 7.04/7.31 1411 -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(403)].
% 7.04/7.31 1412 -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(403)].
% 7.04/7.31 1413 -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(805)].
% 7.04/7.31 1414 -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(805)].
% 7.04/7.31 1415 -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(806)].
% 7.04/7.31 1416 -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(806)].
% 7.04/7.31 1417 -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(807)].
% 7.04/7.31 1418 -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(807)].
% 7.04/7.31 1419 -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(808)].
% 7.04/7.31 1420 -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(808)].
% 7.04/7.31 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(1407,a,1409,a)].
% 7.04/7.32 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(1407,a,1410,a)].
% 7.04/7.32 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(1407,a,1413,a)].
% 7.04/7.32 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(1407,a,1414,a)].
% 7.04/7.32 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(1407,a,1415,a)].
% 7.04/7.32 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(1407,a,1416,a)].
% 7.04/7.32 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(1407,a,1417,a)].
% 7.04/7.32 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(1407,a,1418,a)].
% 7.04/7.32 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(1407,a,1419,a)].
% 7.04/7.32 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(1407,a,1420,a)].
% 7.04/7.32 1421 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom). [clausify(1063)].
% 7.04/7.32 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(1421,b,1409,a)].
% 7.04/7.32 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(1421,b,1410,a)].
% 7.04/7.32 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(1421,b,1413,a)].
% 7.04/7.32 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(1421,b,1414,a)].
% 7.04/7.32 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(1421,b,1415,a)].
% 7.04/7.32 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(1421,b,1416,a)].
% 7.23/7.48 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(1421,b,1417,a)].
% 7.23/7.48 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(1421,b,1418,a)].
% 7.23/7.48 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(1421,b,1419,a)].
% 7.23/7.48 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(1421,b,1420,a)].
% 7.23/7.48 1422 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 7.23/7.48 1423 -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(396)].
% 7.23/7.48 1424 -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(397)].
% 7.23/7.49 1425 -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(401)].
% 7.23/7.49 1426 -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(402)].
% 7.23/7.49 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(1422,a,1423,a)].
% 7.23/7.49 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(1422,a,1424,a)].
% 7.23/7.49 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(1422,a,1425,a)].
% 7.23/7.49 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(1422,a,1426,a)].
% 7.23/7.49 1427 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 7.23/7.49 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(1427,a,1423,a)].
% 7.23/7.49 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(1427,a,1424,a)].
% 7.23/7.49 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(1427,a,1425,a)].
% 7.42/7.66 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(1427,a,1426,a)].
% 7.42/7.66 1428 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom). [clausify(1052)].
% 7.42/7.66 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(1428,b,1423,a)].
% 7.42/7.66 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(1428,b,1424,a)].
% 7.42/7.66 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(1428,b,1425,a)].
% 7.42/7.66 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(1428,b,1426,a)].
% 7.42/7.66 1429 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 7.42/7.66 1430 -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(398)].
% 7.74/8.01 1431 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 7.74/8.01 1432 -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(1043)].
% 7.74/8.01 1433 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 7.74/8.01 1434 -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(438)].
% 7.74/8.01 1435 -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(440)].
% 7.74/8.01 1436 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 7.74/8.01 1437 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom). [clausify(1047)].
% 7.74/8.01 1438 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 7.74/8.01 1439 -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(466)].
% 7.74/8.01 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(1438,a,1439,a)].
% 7.74/8.01 1440 -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(1044)].
% 7.74/8.01 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(1440,b,1439,a)].
% 7.93/8.17 1441 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 7.93/8.17 1442 -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(496)].
% 7.93/8.17 1443 -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(496)].
% 7.93/8.17 1444 -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(556)].
% 7.93/8.17 1445 -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(570)].
% 7.93/8.17 1446 -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(571)].
% 7.93/8.17 1447 -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(586)].
% 7.93/8.17 1448 -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(587)].
% 7.93/8.17 1449 -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(587)].
% 7.93/8.17 1450 -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(588)].
% 7.93/8.17 1451 -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(589)].
% 7.93/8.17 1452 -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(589)].
% 7.93/8.17 1453 -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(589)].
% 7.93/8.17 1454 -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(590)].
% 7.93/8.17 1455 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(590)].
% 7.93/8.17 1456 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(590)].
% 7.93/8.17 1457 -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(599)].
% 7.93/8.17 1458 -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(599)].
% 7.93/8.17 1459 -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(601)].
% 7.93/8.17 1460 -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(604)].
% 7.93/8.18 1461 -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(604)].
% 7.93/8.18 1462 -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(605)].
% 7.93/8.18 1463 -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(606)].
% 7.93/8.18 1464 -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(610)].
% 7.93/8.18 1465 -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(611)].
% 7.93/8.18 1466 -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(611)].
% 7.93/8.18 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1441,a,1442,a)].
% 7.93/8.18 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1441,a,1443,a)].
% 7.93/8.18 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(1441,a,1444,a)].
% 7.93/8.18 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(1441,a,1446,a)].
% 7.93/8.18 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(1441,a,1449,a)].
% 7.93/8.18 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(1441,a,1452,a)].
% 7.93/8.18 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | A != B. [resolve(1441,a,1453,a)].
% 7.93/8.18 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1441,a,1456,a)].
% 7.93/8.18 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(1441,a,1457,a)].
% 7.93/8.18 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(1441,a,1461,a)].
% 7.93/8.18 1467 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 7.93/8.18 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A)). [resolve(1467,a,1442,a)].
% 7.93/8.18 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A)). [resolve(1467,a,1443,a)].
% 7.93/8.18 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(1467,a,1444,a)].
% 7.93/8.18 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(1467,a,1446,a)].
% 7.93/8.18 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(1467,a,1449,a)].
% 7.93/8.18 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(1467,a,1452,a)].
% 7.93/8.18 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | A != B. [resolve(1467,a,1453,a)].
% 8.12/8.36 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1467,a,1456,a)].
% 8.12/8.36 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(1467,a,1457,a)].
% 8.12/8.36 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(1467,a,1461,a)].
% 8.12/8.36 1468 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1065)].
% 8.12/8.36 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),B)). [resolve(1468,b,1442,a)].
% 8.12/8.36 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),B)). [resolve(1468,b,1443,a)].
% 8.12/8.36 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(1468,b,1444,a)].
% 8.12/8.36 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(1468,b,1446,a)].
% 8.12/8.36 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(1468,b,1449,a)].
% 8.12/8.36 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(1468,b,1452,a)].
% 8.12/8.36 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | B != C. [resolve(1468,b,1453,a)].
% 8.12/8.36 Derived: -class_Rings_Olinordered__idom(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1468,b,1456,a)].
% 8.12/8.36 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(1468,b,1457,a)].
% 8.12/8.36 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(1468,b,1461,a)].
% 8.12/8.36 1469 -class_Rings_Oidom(A) | class_Groups_Ogroup__add(A) # label(clrel_Rings_Oidom__Groups_Ogroup__add) # label(axiom). [clausify(1009)].
% 8.12/8.36 1470 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ouminus__class_Ouminus(A,C) | B = C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(500)].
% 8.12/8.36 1471 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ouminus__class_Ouminus(A,C) | B != C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(500)].
% 8.12/8.36 1472 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_minus__equation__iff) # label(axiom). [clausify(501)].
% 8.12/8.36 1473 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_minus__equation__iff) # label(axiom). [clausify(501)].
% 8.12/8.36 1474 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_equation__minus__iff) # label(axiom). [clausify(502)].
% 8.12/8.36 1475 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_equation__minus__iff) # label(axiom). [clausify(502)].
% 8.12/8.36 1476 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B)) = B # label(fact_minus__minus) # label(axiom). [clausify(503)].
% 8.12/8.36 1477 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = C # label(fact_minus__add__cancel) # label(axiom). [clausify(510)].
% 8.12/8.36 1478 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)) = C # label(fact_add__minus__cancel) # label(axiom). [clausify(511)].
% 8.12/8.36 1479 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_minus__add) # label(axiom). [clausify(512)].
% 8.12/8.36 1480 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(531)].
% 8.12/8.36 1481 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(531)].
% 8.12/8.36 1482 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(533)].
% 8.12/8.36 1483 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(533)].
% 8.12/8.36 1484 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_minus__zero) # label(axiom). [clausify(534)].
% 8.12/8.36 1485 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ouminus__class_Ouminus(A,B) = C # label(fact_add__eq__0__iff) # label(axiom). [clausify(543)].
% 8.12/8.36 1486 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ouminus__class_Ouminus(A,B) != C # label(fact_add__eq__0__iff) # label(axiom). [clausify(543)].
% 8.12/8.36 1487 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ouminus__class_Ouminus(A,B) = C # label(fact_minus__unique) # label(axiom). [clausify(544)].
% 8.12/8.36 1488 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),B) # label(fact_left__minus) # label(axiom). [clausify(546)].
% 8.12/8.36 1489 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(547)].
% 8.12/8.36 1490 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(547)].
% 8.12/8.36 1491 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_right__minus) # label(axiom). [clausify(548)].
% 8.12/8.36 1492 -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(780)].
% 8.12/8.36 1493 -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(781)].
% 8.12/8.36 1494 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | B = C # label(fact_right__minus__eq) # label(axiom). [clausify(786)].
% 8.12/8.36 1495 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | B != C # label(fact_right__minus__eq) # label(axiom). [clausify(786)].
% 8.12/8.36 1496 -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(788)].
% 8.12/8.36 1497 -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(789)].
% 8.12/8.36 1498 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) # label(fact_diff__minus__eq__add) # label(axiom). [clausify(791)].
% 8.12/8.36 1499 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_diff__def) # label(axiom). [clausify(793)].
% 8.12/8.36 1500 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ouminus__class_Ouminus(A,B) # label(fact_diff__0) # label(axiom). [clausify(794)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ouminus__class_Ouminus(A,C) | B = C. [resolve(1469,b,1470,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ouminus__class_Ouminus(A,C) | B != C. [resolve(1469,b,1471,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B. [resolve(1469,b,1472,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B)) = B. [resolve(1469,b,1476,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = C. [resolve(1469,b,1477,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)) = C. [resolve(1469,b,1478,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B)). [resolve(1469,b,1479,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B. [resolve(1469,b,1480,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B. [resolve(1469,b,1481,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A). [resolve(1469,b,1484,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ouminus__class_Ouminus(A,B) = C. [resolve(1469,b,1485,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ouminus__class_Ouminus(A,B) != C. [resolve(1469,b,1486,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),B). [resolve(1469,b,1488,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B). [resolve(1469,b,1489,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B). [resolve(1469,b,1490,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ouminus__class_Ouminus(A,B)). [resolve(1469,b,1491,a)].
% 8.12/8.36 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),C) = B. [resolve(1469,b,1492,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,B,C)),C) = B. [resolve(1469,b,1493,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | B = C. [resolve(1469,b,1494,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | B != C. [resolve(1469,b,1495,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,B,B) = c_Groups_Ozero__class_Ozero(A). [resolve(1469,b,1496,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A)) = B. [resolve(1469,b,1497,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C). [resolve(1469,b,1498,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,B,C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ouminus__class_Ouminus(A,C)). [resolve(1469,b,1499,a)].
% 8.12/8.37 Derived: -class_Rings_Oidom(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ouminus__class_Ouminus(A,B). [resolve(1469,b,1500,a)].
% 8.12/8.37 1501 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) | A = B. [resolve(1501,a,1470,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) | A != B. [resolve(1501,a,1471,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B) = A. [resolve(1501,a,1472,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) = A. [resolve(1501,a,1476,a)].
% 8.12/8.37 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)) = B. [resolve(1501,a,1477,a)].
% 8.12/8.37 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B)) = B. [resolve(1501,a,1478,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(tc_Int_Oint,B)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1501,a,1479,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1501,a,1480,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1501,a,1481,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1501,a,1484,a)].
% 8.12/8.37 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = B. [resolve(1501,a,1485,a)].
% 8.12/8.37 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B. [resolve(1501,a,1486,a)].
% 8.12/8.37 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),A). [resolve(1501,a,1488,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) != B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(1501,a,1489,a)].
% 8.12/8.37 Derived: c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A) = B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(1501,a,1490,a)].
% 8.12/8.38 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)). [resolve(1501,a,1491,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),B) = A. [resolve(1501,a,1492,a)].
% 8.12/8.38 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),B) = A. [resolve(1501,a,1493,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(1501,a,1494,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | A != B. [resolve(1501,a,1495,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1501,a,1496,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1501,a,1497,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B). [resolve(1501,a,1498,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1501,a,1499,a)].
% 8.12/8.38 Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A). [resolve(1501,a,1500,a)].
% 8.12/8.38 1502 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom). [clausify(1070)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1502,b,1470,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1502,b,1471,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != C | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C) = B. [resolve(1502,b,1472,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) = B. [resolve(1502,b,1476,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)) = C. [resolve(1502,b,1477,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C)) = C. [resolve(1502,b,1478,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)). [resolve(1502,b,1479,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(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(1502,b,1480,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(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(1502,b,1481,a)].
% 8.12/8.38 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1502,b,1484,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = C. [resolve(1502,b,1485,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != C. [resolve(1502,b,1486,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),B). [resolve(1502,b,1488,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),B). [resolve(1502,b,1489,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),B). [resolve(1502,b,1490,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)). [resolve(1502,b,1491,a)].
% 8.25/8.55 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(1502,b,1492,a)].
% 8.25/8.55 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(1502,b,1493,a)].
% 8.25/8.55 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)) | B = C. [resolve(1502,b,1494,a)].
% 8.25/8.55 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)) | B != C. [resolve(1502,b,1495,a)].
% 8.25/8.55 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(1502,b,1496,a)].
% 8.25/8.55 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(1502,b,1497,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C). [resolve(1502,b,1498,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)). [resolve(1502,b,1499,a)].
% 8.25/8.55 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B). [resolve(1502,b,1500,a)].
% 8.25/8.55 1503 -class_Rings_Oidom(A) | class_Rings_Oring(A) # label(clrel_Rings_Oidom__Rings_Oring) # label(axiom). [clausify(1018)].
% 8.25/8.55 1504 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__right) # label(axiom). [clausify(514)].
% 8.25/8.55 1505 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C) # label(fact_minus__mult__left) # label(axiom). [clausify(515)].
% 8.32/8.56 1506 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__commute) # label(axiom). [clausify(516)].
% 8.32/8.56 1507 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) # label(fact_minus__mult__minus) # label(axiom). [clausify(517)].
% 8.32/8.56 1508 -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__iff2) # label(axiom). [clausify(795)].
% 8.32/8.56 1509 -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__iff2) # label(axiom). [clausify(795)].
% 8.32/8.56 1510 -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__iff1) # label(axiom). [clausify(796)].
% 8.32/8.56 1511 -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__iff1) # label(axiom). [clausify(796)].
% 8.32/8.56 1512 -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(798)].
% 8.32/8.56 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C)). [resolve(1503,b,1504,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(A) | c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C). [resolve(1503,b,1505,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C)). [resolve(1503,b,1506,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C). [resolve(1503,b,1507,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(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. [resolve(1503,b,1508,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(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. [resolve(1503,b,1509,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(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. [resolve(1503,b,1510,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(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. [resolve(1503,b,1511,a)].
% 8.32/8.56 Derived: -class_Rings_Oidom(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)). [resolve(1503,b,1512,a)].
% 8.32/8.56 1513 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption].
% 8.32/8.56 Derived: c_Groups_Ouminus__class_Ouminus(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_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1513,a,1504,a)].
% 8.32/8.56 Derived: c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(tc_Int_Oint,A)),B). [resolve(1513,a,1505,a)].
% 8.32/8.56 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)). [resolve(1513,a,1506,a)].
% 8.32/8.56 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B). [resolve(1513,a,1507,a)].
% 8.32/8.56 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(1513,a,1508,a)].
% 8.32/8.56 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(1513,a,1509,a)].
% 8.32/8.56 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(1513,a,1510,a)].
% 8.32/8.56 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(1513,a,1511,a)].
% 8.32/8.57 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(1513,a,1512,a)].
% 8.32/8.57 1514 -class_Rings_Ocomm__ring(A) | class_Rings_Oring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom). [clausify(1084)].
% 8.32/8.57 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Ouminus__class_Ouminus(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),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)). [resolve(1514,b,1504,a)].
% 8.32/8.57 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C). [resolve(1514,b,1505,a)].
% 8.32/8.57 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)). [resolve(1514,b,1506,a)].
% 8.32/8.57 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C). [resolve(1514,b,1507,a)].
% 8.32/8.57 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(1514,b,1508,a)].
% 8.32/8.57 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(1514,b,1509,a)].
% 8.32/8.57 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(1514,b,1510,a)].
% 8.32/8.57 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(1514,b,1511,a)].
% 8.49/8.74 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(1514,b,1512,a)].
% 8.49/8.74 1515 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 8.49/8.74 1516 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_neg__less__iff__less) # label(axiom). [clausify(523)].
% 8.49/8.74 1517 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_neg__less__iff__less) # label(axiom). [clausify(523)].
% 8.49/8.74 1518 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)) # label(fact_minus__less__iff) # label(axiom). [clausify(524)].
% 8.49/8.74 1519 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)) # label(fact_minus__less__iff) # label(axiom). [clausify(524)].
% 8.49/8.74 1520 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ouminus__class_Ouminus(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ouminus__class_Ouminus(A,B))) # label(fact_less__minus__iff) # label(axiom). [clausify(525)].
% 8.49/8.74 1521 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ouminus__class_Ouminus(A,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ouminus__class_Ouminus(A,B))) # label(fact_less__minus__iff) # label(axiom). [clausify(525)].
% 8.49/8.74 1522 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ouminus__class_Ouminus(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ouminus__class_Ouminus(A,B))) # label(fact_le__minus__iff) # label(axiom). [clausify(526)].
% 8.49/8.74 1523 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ouminus__class_Ouminus(A,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),c_Groups_Ouminus__class_Ouminus(A,B))) # label(fact_le__minus__iff) # label(axiom). [clausify(526)].
% 8.49/8.74 1524 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)) # label(fact_minus__le__iff) # label(axiom). [clausify(527)].
% 8.49/8.74 1525 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)) # label(fact_minus__le__iff) # label(axiom). [clausify(527)].
% 8.49/8.74 1526 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_neg__le__iff__le) # label(axiom). [clausify(528)].
% 8.49/8.74 1527 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),B)) # label(fact_neg__le__iff__le) # label(axiom). [clausify(528)].
% 8.49/8.74 1528 -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_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B))) # label(fact_le__imp__neg__le) # label(axiom). [clausify(529)].
% 8.49/8.74 1529 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(535)].
% 8.49/8.74 1530 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(535)].
% 8.49/8.74 1531 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(537)].
% 8.49/8.74 1532 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(537)].
% 8.49/8.74 1533 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(540)].
% 8.49/8.74 1534 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(540)].
% 8.49/8.74 1535 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(541)].
% 8.49/8.74 1536 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(541)].
% 8.49/8.74 1537 -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(758)].
% 8.49/8.74 1538 -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(758)].
% 8.49/8.74 1539 -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(799)].
% 8.49/8.74 1540 -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(799)].
% 8.49/8.74 1541 -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(800)].
% 8.49/8.74 1542 -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(800)].
% 8.49/8.74 1543 -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(801)].
% 8.49/8.74 1544 -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(801)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1515,a,1516,a)].
% 8.49/8.74 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1515,a,1517,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)),A)). [resolve(1515,a,1518,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))). [resolve(1515,a,1520,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))). [resolve(1515,a,1522,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)),A)). [resolve(1515,a,1524,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1515,a,1526,a)].
% 8.49/8.74 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1515,a,1527,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1515,a,1529,a)].
% 8.49/8.74 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1515,a,1530,a)].
% 8.49/8.74 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1515,a,1531,a)].
% 8.49/8.75 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1515,a,1532,a)].
% 8.49/8.75 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1515,a,1533,a)].
% 8.49/8.75 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(1515,a,1534,a)].
% 8.49/8.75 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1515,a,1535,a)].
% 8.49/8.75 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1515,a,1536,a)].
% 8.49/8.75 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(1515,a,1537,a)].
% 8.49/8.75 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(1515,a,1538,a)].
% 8.49/8.75 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(1515,a,1539,a)].
% 8.49/8.75 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(1515,a,1540,a)].
% 8.49/8.75 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(1515,a,1541,a)].
% 8.49/8.75 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(1515,a,1542,a)].
% 8.49/8.75 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(1515,a,1543,a)].
% 8.49/8.75 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(1515,a,1544,a)].
% 8.49/8.75 1545 -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(1045)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1545,b,1516,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1545,b,1517,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)),B)). [resolve(1545,b,1518,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))). [resolve(1545,b,1520,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))). [resolve(1545,b,1522,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)),B)). [resolve(1545,b,1524,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),B)). [resolve(1545,b,1526,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),B)). [resolve(1545,b,1527,a)].
% 8.49/8.75 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_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1545,b,1529,a)].
% 8.49/8.75 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_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1545,b,1530,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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))),B)). [resolve(1545,b,1531,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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))),B)). [resolve(1545,b,1532,a)].
% 8.49/8.75 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1545,b,1533,a)].
% 8.49/8.76 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(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_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)). [resolve(1545,b,1534,a)].
% 8.49/8.76 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_Ouminus__class_Ouminus(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(1545,b,1535,a)].
% 8.49/8.76 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_Ouminus__class_Ouminus(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(1545,b,1536,a)].
% 8.49/8.76 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(1545,b,1537,a)].
% 8.49/8.76 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(1545,b,1538,a)].
% 8.49/8.76 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(1545,b,1539,a)].
% 8.49/8.76 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(1545,b,1540,a)].
% 8.49/8.76 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(1545,b,1541,a)].
% 8.49/8.76 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(1545,b,1542,a)].
% 8.49/8.76 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(1545,b,1543,a)].
% 8.49/8.76 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(1545,b,1544,a)].
% 8.85/9.12 1546 -class_Rings_Oidom(A) | class_Rings_Oring__1(A) # label(clrel_Rings_Oidom__Rings_Oring__1) # label(axiom). [clausify(1014)].
% 8.85/9.12 1547 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,C)),B) # label(fact_power__minus) # label(axiom). [clausify(553)].
% 8.85/9.12 1548 -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(809)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,C)),B). [resolve(1546,b,1547,a)].
% 8.85/9.12 Derived: -class_Rings_Oidom(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))). [resolve(1546,b,1548,a)].
% 8.85/9.12 1549 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 8.85/9.12 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)),A). [resolve(1549,a,1547,a)].
% 8.85/9.12 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(1549,a,1548,a)].
% 8.85/9.12 1550 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom). [clausify(1080)].
% 8.85/9.12 Derived: -class_Rings_Ocomm__ring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(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)),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)),B). [resolve(1550,b,1547,a)].
% 8.85/9.12 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(1550,b,1548,a)].
% 8.85/9.12 1551 -class_Rings_Oidom(A) | class_Rings_Odvd(A) # label(clrel_Rings_Oidom__Rings_Odvd) # label(axiom). [clausify(1020)].
% 8.85/9.12 1552 -class_Rings_Odvd(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) != D | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvdI) # label(axiom). [clausify(630)].
% 8.85/9.12 1553 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),f10(C,B,A)),c_Groups_Ozero__class_Ozero(A)))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(657)].
% 8.85/9.12 1554 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(B,f10(C,B,A))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(657)].
% 8.85/9.12 1555 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),f11(C,B,A)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Groups_Ozero__class_Ozero(A)))) | -hBOOL(hAPP(B,D)) # label(fact_unity__coeff__ex) # label(axiom). [clausify(657)].
% 8.85/9.12 1556 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I4_J) # label(axiom). [clausify(810)].
% 8.85/9.12 1557 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I4_J) # label(axiom). [clausify(810)].
% 8.85/9.12 1558 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I3_J) # label(axiom). [clausify(811)].
% 8.85/9.12 1559 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I3_J) # label(axiom). [clausify(811)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) != D | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)). [resolve(1551,b,1552,a)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),f10(C,B,A)),c_Groups_Ozero__class_Ozero(A)))). [resolve(1551,b,1553,a)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(B,f10(C,B,A))). [resolve(1551,b,1554,a)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),f11(C,B,A)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Groups_Ozero__class_Ozero(A)))) | -hBOOL(hAPP(B,D)). [resolve(1551,b,1555,a)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | -class_Rings_Ocomm__ring(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))). [resolve(1551,b,1556,b)].
% 8.85/9.12 Derived: -class_Rings_Oidom(A) | -class_Rings_Ocomm__ring(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ominus__class_Ominus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))). [resolve(1551,b,1557,b)].
% 8.85/9.13 1560 class_Rings_Odvd(tc_Int_Oint) # label(arity_Int__Oint__Rings_Odvd) # label(axiom). [assumption].
% 8.85/9.13 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) != C | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(1560,a,1552,a)].
% 8.85/9.13 Derived: -class_Rings_Osemiring__0(tc_Int_Oint) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),f10(B,A,tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). [resolve(1560,a,1553,a)].
% 8.85/9.13 Derived: -class_Rings_Osemiring__0(tc_Int_Oint) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))) | hBOOL(hAPP(A,f10(B,A,tc_Int_Oint))). [resolve(1560,a,1554,a)].
% 8.85/9.13 Derived: -class_Rings_Osemiring__0(tc_Int_Oint) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),f11(B,A,tc_Int_Oint)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) | -hBOOL(hAPP(A,C)). [resolve(1560,a,1555,a)].
% 8.85/9.13 Derived: -class_Rings_Ocomm__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B))),D))). [resolve(1560,a,1556,b)].
% 8.85/9.13 Derived: -class_Rings_Ocomm__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B))),D))). [resolve(1560,a,1557,b)].
% 8.85/9.13 1561 class_Rings_Odvd(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Odvd) # label(axiom). [assumption].
% 8.85/9.13 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B) != C | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)). [resolve(1561,a,1552,a)].
% 8.85/9.13 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),f10(B,A,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). [resolve(1561,a,1553,a)].
% 8.85/9.13 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))) | hBOOL(hAPP(A,f10(B,A,tc_Nat_Onat))). [resolve(1561,a,1554,a)].
% 8.85/9.13 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),f11(B,A,tc_Nat_Onat)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | -hBOOL(hAPP(A,C)). [resolve(1561,a,1555,a)].
% 8.85/9.13 Derived: -class_Rings_Ocomm__ring(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),E),B))),D))). [resolve(1561,a,1556,b)].
% 8.85/9.13 Derived: -class_Rings_Ocomm__ring(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),E),B))),D))). [resolve(1561,a,1557,b)].
% 9.41/9.67 1562 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Odvd(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Odvd) # label(axiom). [clausify(1087)].
% 9.41/9.67 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) != D | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),D)). [resolve(1562,b,1552,a)].
% 9.41/9.67 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),f10(C,B,tc_Polynomial_Opoly(A))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))). [resolve(1562,b,1553,a)].
% 9.41/9.67 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))) | hBOOL(hAPP(B,f10(C,B,tc_Polynomial_Opoly(A)))). [resolve(1562,b,1554,a)].
% 9.41/9.67 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),f11(C,B,tc_Polynomial_Opoly(A))))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))) | -hBOOL(hAPP(B,D)). [resolve(1562,b,1555,a)].
% 9.41/9.67 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ocomm__ring(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),C))),E))). [resolve(1562,b,1556,b)].
% 9.41/9.67 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ocomm__ring(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),C))),E))). [resolve(1562,b,1557,b)].
% 9.41/9.67 1563 class_Orderings_Owellorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Owellorder) # label(axiom). [assumption].
% 9.41/9.67 1564 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(A,B))) # label(fact_LeastI__ex) # label(axiom). [clausify(666)].
% 9.41/9.67 1565 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(A,B))) # label(fact_LeastI) # label(axiom). [clausify(667)].
% 9.41/9.67 1566 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Orderings_Oord__class_OLeast(A,B)),C)) # label(fact_Least__le) # label(axiom). [clausify(676)].
% 9.41/9.67 1567 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Orderings_Oord__class_OLeast(A,C))) | -hBOOL(hAPP(C,B)) # label(fact_not__less__Least) # label(axiom). [clausify(677)].
% 9.41/9.67 Derived: -hBOOL(hAPP(A,B)) | hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,A))). [resolve(1563,a,1564,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(A,B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,A)),B)). [resolve(1563,a,1566,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Orderings_Oord__class_OLeast(tc_Nat_Onat,B))) | -hBOOL(hAPP(B,A)). [resolve(1563,a,1567,a)].
% 9.59/9.85 1568 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 9.59/9.85 1569 -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)].
% 9.59/9.85 1570 -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(856)].
% 9.59/9.85 1571 -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(857)].
% 9.59/9.85 1572 -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(858)].
% 9.59/9.85 1573 -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(859)].
% 9.59/9.85 1574 -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(859)].
% 9.59/9.85 1575 -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(860)].
% 9.59/9.85 1576 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B)) = C # label(fact_dvd__mult__div__cancel) # label(axiom). [clausify(861)].
% 9.59/9.85 1577 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__swap) # label(axiom). [clausify(862)].
% 9.59/9.85 1578 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,C,B)),B) = C # label(fact_dvd__div__mult__self) # label(axiom). [clausify(863)].
% 9.59/9.85 1579 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,C,B)),D) # label(fact_dvd__div__mult) # label(axiom). [clausify(864)].
% 9.59/9.85 1580 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),D),E)) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Odiv(A,E,D)) # label(fact_div__mult__div__if__dvd) # label(axiom). [clausify(865)].
% 9.59/9.85 1581 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Odiv(A,D,B)) # label(fact_div__add) # label(axiom). [clausify(866)].
% 9.59/9.85 1582 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(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),c_Divides_Odiv__class_Odiv(A,C,B)),D) # label(fact_div__power) # label(axiom). [clausify(869)].
% 9.59/9.85 1583 -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(873)].
% 9.59/9.85 1584 -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(874)].
% 9.59/9.85 1585 -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(875)].
% 9.59/9.85 1586 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Odiv(A,D,B))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)) # label(fact_div__dvd__div) # label(axiom). [clausify(877)].
% 9.59/9.85 1587 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Odiv(A,D,B))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)) # label(fact_div__dvd__div) # label(axiom). [clausify(877)].
% 9.59/9.85 1588 -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(894)].
% 9.59/9.85 1589 -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(895)].
% 9.59/9.85 1590 -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(896)].
% 9.59/9.85 1591 -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(897)].
% 9.59/9.85 1592 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),E)) | c_Divides_Odiv__class_Odiv(A,E,C) != c_Divides_Odiv__class_Odiv(A,D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) # label(fact_dvd__div__div__eq__mult) # label(axiom). [clausify(898)].
% 9.59/9.85 1593 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),E)) | c_Divides_Odiv__class_Odiv(A,E,C) = c_Divides_Odiv__class_Odiv(A,D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) # label(fact_dvd__div__div__eq__mult) # label(axiom). [clausify(898)].
% 9.59/9.85 1594 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(A,C,B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_dvd__div__eq__mult) # label(axiom). [clausify(899)].
% 9.59/9.85 1595 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(A,C,B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_dvd__div__eq__mult) # label(axiom). [clausify(899)].
% 9.59/9.85 1596 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__div__trivial) # label(axiom). [clausify(949)].
% 9.59/9.85 1597 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)) = B # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(951)].
% 9.59/9.85 1598 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B))),c_Divides_Odiv__class_Omod(A,C,B)) = C # label(fact_mod__div__equality2) # label(axiom). [clausify(952)].
% 9.59/9.85 1599 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)),c_Divides_Odiv__class_Omod(A,B,C)) = B # label(fact_mod__div__equality) # label(axiom). [clausify(953)].
% 9.59/9.85 1600 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B))),c_Divides_Odiv__class_Omod(A,C,B))),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D) # label(fact_div__mod__equality2) # label(axiom). [clausify(954)].
% 9.59/9.85 1601 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)),c_Divides_Odiv__class_Omod(A,B,C))),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) # label(fact_div__mod__equality) # label(axiom). [clausify(955)].
% 9.59/9.85 1602 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Divides_Odiv__class_Omod(A,D,C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvd__mod__iff) # label(axiom). [clausify(962)].
% 9.59/9.85 1603 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Divides_Odiv__class_Omod(A,D,C))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvd__mod__iff) # label(axiom). [clausify(962)].
% 9.59/9.85 1604 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,D,C),B) = c_Divides_Odiv__class_Omod(A,D,B) # label(fact_mod__mod__cancel) # label(axiom). [clausify(963)].
% 9.59/9.85 1605 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Divides_Odiv__class_Omod(A,C,D))) # label(fact_dvd__mod) # label(axiom). [clausify(965)].
% 9.59/9.85 1606 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Divides_Odiv__class_Omod(A,C,D))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_dvd__mod__imp__dvd) # label(axiom). [clausify(966)].
% 9.59/9.85 1607 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__imp__mod__0) # label(axiom). [clausify(968)].
% 9.59/9.85 1608 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom). [clausify(969)].
% 9.59/9.85 1609 -class_Divides_Osemiring__div(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,C,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom). [clausify(969)].
% 9.59/9.85 1610 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self2__is__0) # label(axiom). [clausify(972)].
% 9.59/9.85 1611 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self1__is__0) # label(axiom). [clausify(973)].
% 9.59/9.85 1612 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Oone__class_Oone(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__by__1) # label(axiom). [clausify(974)].
% 9.59/9.85 1613 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mult__self2) # label(axiom). [clausify(975)].
% 9.59/9.85 1614 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),D) = c_Divides_Odiv__class_Omod(A,B,D) # label(fact_mod__mult__self1) # label(axiom). [clausify(976)].
% 9.59/9.85 1615 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__0) # label(axiom). [clausify(979)].
% 9.59/9.85 1616 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_mod__by__0) # label(axiom). [clausify(980)].
% 9.59/9.85 1617 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__self) # label(axiom). [clausify(981)].
% 9.59/9.85 1618 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__add__self2) # label(axiom). [clausify(982)].
% 9.59/9.85 1619 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),B) = c_Divides_Odiv__class_Omod(A,C,B) # label(fact_mod__add__self1) # label(axiom). [clausify(983)].
% 9.59/9.85 1620 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),D) # label(fact_mod__add__right__eq) # label(axiom). [clausify(984)].
% 9.59/9.85 1621 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_mod__add__left__eq) # label(axiom). [clausify(985)].
% 9.59/9.85 1622 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_mod__add__eq) # label(axiom). [clausify(986)].
% 9.59/9.85 1623 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),D) # label(fact_zmod__simps_I2_J) # label(axiom). [clausify(987)].
% 9.59/9.85 1624 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_zmod__simps_I1_J) # label(axiom). [clausify(988)].
% 9.59/9.85 1625 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),F),C) # label(fact_mod__add__cong) # label(axiom). [clausify(989)].
% 9.59/9.85 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(1568,a,1569,a)].
% 9.59/9.85 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(1568,a,1570,a)].
% 9.59/9.85 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(1568,a,1571,a)].
% 9.59/9.85 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(1568,a,1572,a)].
% 9.59/9.85 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(1568,a,1573,a)].
% 9.59/9.85 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(1568,a,1575,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)) = B. [resolve(1568,a,1576,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1568,a,1577,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),A) = B. [resolve(1568,a,1578,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),C). [resolve(1568,a,1579,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),C),D)) | c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,D,C)). [resolve(1568,a,1580,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A)). [resolve(1568,a,1581,a)].
% 9.59/9.85 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),C). [resolve(1568,a,1582,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1568,a,1583,a)].
% 9.59/9.86 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(1568,a,1584,a)].
% 9.59/9.86 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(1568,a,1585,a)].
% 9.59/9.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),C)). [resolve(1568,a,1586,a)].
% 9.59/9.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),C)). [resolve(1568,a,1587,a)].
% 9.59/9.86 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(1568,a,1588,a)].
% 9.59/9.86 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(1568,a,1589,a)].
% 9.59/9.86 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(1568,a,1590,a)].
% 9.59/9.86 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(1568,a,1591,a)].
% 9.59/9.86 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),D)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B). [resolve(1568,a,1592,a)].
% 9.59/9.86 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),D)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,D,B) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B). [resolve(1568,a,1593,a)].
% 9.59/9.86 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A) = B. [resolve(1568,a,1594,a)].
% 9.59/9.86 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A) != B. [resolve(1568,a,1595,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1596,a)].
% 9.59/9.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)) = A. [resolve(1568,a,1597,a)].
% 9.59/9.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)) = B. [resolve(1568,a,1598,a)].
% 9.59/9.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)) = A. [resolve(1568,a,1599,a)].
% 9.59/9.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C). [resolve(1568,a,1600,a)].
% 9.59/9.86 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C). [resolve(1568,a,1601,a)].
% 9.59/9.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(1568,a,1602,a)].
% 9.59/9.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(1568,a,1603,a)].
% 9.59/9.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,C,A). [resolve(1568,a,1604,a)].
% 9.59/9.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1607,a)].
% 9.59/9.86 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1609,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1610,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1611,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1612,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(1568,a,1613,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C). [resolve(1568,a,1614,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1615,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1568,a,1616,a)].
% 9.59/9.86 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1568,a,1617,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(1568,a,1618,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A). [resolve(1568,a,1619,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),C). [resolve(1568,a,1620,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),B). [resolve(1568,a,1621,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),B). [resolve(1568,a,1622,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),E),B). [resolve(1568,a,1625,a)].
% 9.59/9.87 1626 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption].
% 9.59/9.87 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(1626,a,1569,a)].
% 9.59/9.87 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(1626,a,1570,a)].
% 9.59/9.87 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(1626,a,1571,a)].
% 9.59/9.87 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(1626,a,1572,a)].
% 9.59/9.87 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(1626,a,1573,a)].
% 9.59/9.87 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(1626,a,1575,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)) = B. [resolve(1626,a,1576,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1626,a,1577,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),A) = B. [resolve(1626,a,1578,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),C). [resolve(1626,a,1579,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),C),D)) | c_Divides_Odiv__class_Odiv(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,D,C)). [resolve(1626,a,1580,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A)). [resolve(1626,a,1581,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),C). [resolve(1626,a,1582,a)].
% 9.59/9.87 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1626,a,1583,a)].
% 9.59/9.87 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(1626,a,1584,a)].
% 9.59/9.87 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(1626,a,1585,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),C)). [resolve(1626,a,1586,a)].
% 9.59/9.87 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),C)). [resolve(1626,a,1587,a)].
% 9.59/9.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1626,a,1588,a)].
% 9.59/9.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)). [resolve(1626,a,1589,a)].
% 9.59/9.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),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(1626,a,1590,a)].
% 9.59/9.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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(1626,a,1591,a)].
% 9.59/9.87 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),D)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B). [resolve(1626,a,1592,a)].
% 9.59/9.88 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),D)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,D,B) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B). [resolve(1626,a,1593,a)].
% 9.59/9.88 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A) = B. [resolve(1626,a,1594,a)].
% 9.59/9.88 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A) != B. [resolve(1626,a,1595,a)].
% 9.59/9.88 Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1596,a)].
% 9.59/9.88 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)) = A. [resolve(1626,a,1597,a)].
% 9.59/9.88 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A)) = B. [resolve(1626,a,1598,a)].
% 9.59/9.88 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)) = A. [resolve(1626,a,1599,a)].
% 9.59/9.88 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C). [resolve(1626,a,1600,a)].
% 9.59/9.88 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C). [resolve(1626,a,1601,a)].
% 9.59/9.88 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)). [resolve(1626,a,1602,a)].
% 9.59/9.88 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)). [resolve(1626,a,1603,a)].
% 9.59/9.88 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,A). [resolve(1626,a,1604,a)].
% 9.59/9.88 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1607,a)].
% 9.59/9.88 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1609,a)].
% 9.59/9.88 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1610,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1611,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1612,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1626,a,1613,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C). [resolve(1626,a,1614,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1615,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1626,a,1616,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1626,a,1617,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1626,a,1618,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A). [resolve(1626,a,1619,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C). [resolve(1626,a,1620,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). [resolve(1626,a,1621,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). [resolve(1626,a,1622,a)].
% 9.81/10.06 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E),B). [resolve(1626,a,1625,a)].
% 9.81/10.06 1627 class_Divides_Oring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 9.81/10.06 1628 -class_Divides_Oring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_dvd__div__neg) # label(axiom). [clausify(867)].
% 9.81/10.06 1629 -class_Divides_Oring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Odiv(A,c_Groups_Ouminus__class_Ouminus(A,C),B) = c_Groups_Ouminus__class_Ouminus(A,c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_dvd__neg__div) # label(axiom). [clausify(868)].
% 9.81/10.06 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1627,a,1628,a)].
% 9.81/10.06 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B),A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)). [resolve(1627,a,1629,a)].
% 11.27/11.55 1630 class_Groups_Osgn__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Osgn__if) # label(axiom). [assumption].
% 11.27/11.55 1631 -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(934)].
% 11.27/11.55 1632 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__if) # label(axiom). [clausify(944)].
% 11.27/11.55 1633 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__if) # label(axiom). [clausify(944)].
% 11.27/11.55 1634 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) # label(fact_sgn__if) # label(axiom). [clausify(944)].
% 11.27/11.55 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(1630,a,1631,a)].
% 11.27/11.55 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1630,a,1632,a)].
% 11.27/11.55 Derived: 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)),A)) | c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1630,a,1633,a)].
% 11.27/11.55 Derived: 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)),A)) | c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(1630,a,1634,a)].
% 11.27/11.55 1635 -class_Rings_Olinordered__idom(A) | class_Groups_Osgn__if(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Osgn__if) # label(axiom). [clausify(1079)].
% 11.27/11.55 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(1635,b,1631,a)].
% 11.27/11.55 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1635,b,1632,a)].
% 11.27/11.55 Derived: -class_Rings_Olinordered__idom(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))),B)) | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(1635,b,1633,a)].
% 11.27/11.55 Derived: -class_Rings_Olinordered__idom(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))),B)) | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1635,b,1634,a)].
% 11.27/11.55
% 11.27/11.55 ============================== end predicate elimination =============
% 11.27/11.55
% 11.27/11.55 Auto_denials: (non-Horn, no changes).
% 11.27/11.55
% 11.27/11.55 Term ordering decisions:
% 11.27/11.55 Function symbol KB weights: tc_Int_Oint=1. tc_Nat_Onat=1. c_Nat_OSuc=1. t_a=1. tc_HOL_Obool=1. v_cs____=1. v_k=1. c_fconj=1. c_fNot=1. v_q=1. v_a=1. v_c____=1. v_p=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. hAPP=1. c_Orderings_Oord__class_Oless=1. c_Orderings_Oord__class_Oless__eq=1. c_Groups_Ouminus__class_Ouminus=1. tc_fun=1. c_Polynomial_Opoly=1. c_Groups_Osgn__class_Osgn=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Orderings_Oord__class_OLeast=1. c_COMBK=1. c_Nat__Transfer_Otsub=1. c_fequal=1. c_SMT_Oz3div=1. f1=1. f4=1. f6=1. f7=1. f8=1. f12=1. f28=1. tc_Polynomial_Opoly=1. c_Groups_Ozero__class_Ozero=1. c_Groups_Otimes__class_Otimes=1. c_Groups_Oplus__class_Oplus=1. c_Power_Opower__class_Opower=1. c_Rings_Odvd__class_Odvd=1. c_Groups_Oone__class_Oone=1. c_Polynomial_OpCons=1. c_Polynomial_Osmult=1. f5=1. c_Groups_Ominus__class_Ominus=1. c_Divides_Odiv__class_Odiv=1. c_Divides_Odiv__class_Omod=1. c_COMBB=1. c_Polynomial_Omonom=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. c_Polynomial_Oorder=1. c_Polynomial_Osynthetic__div=1. c_Power_Opower_Opower=1. c_COMBS=1. c_Polynomial_Opcompose=1. f2=1. f3=1. f10=1. f11=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. c_COMBC=1. c_If=1. f9=1. c_Polynomial_Opoly__rec=1.
% 161.50/161.81
% 161.50/161.81 ============================== end of process initial clauses ========
% 161.50/161.81
% 161.50/161.81 ============================== CLAUSES FOR SEARCH ====================
% 161.50/161.81
% 161.50/161.81 ============================== end of clauses for search =============
% 161.50/161.81
% 161.50/161.81 ============================== SEARCH ================================
% 161.50/161.81
% 161.50/161.81 % Starting search at 9.06 seconds.
% 161.50/161.81
% 161.50/161.81 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 54 (0.00 of 9.68 sec).
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=72.000, iters=3574
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=63.000, iters=3466
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=52.000, iters=3369
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=51.000, iters=3405
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=50.000, iters=3491
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=47.000, iters=3481
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=45.000, iters=3401
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=44.000, iters=3343
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=43.000, iters=3369
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=42.000, iters=3398
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=40.000, iters=3335
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=39.000, iters=3368
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=38.000, iters=3342
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=37.000, iters=3342
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=36.000, iters=3393
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=35.000, iters=3346
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=34.000, iters=3701
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=32.000, iters=3347
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=31.000, iters=3373
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=30.000, iters=3365
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=29.000, iters=3420
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=28.000, iters=3363
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=27.000, iters=3346
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=26.000, iters=3385
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=25.000, iters=3371
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=24.000, iters=3347
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=23.000, iters=3366
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=22.000, iters=3351
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=21.000, iters=3366
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=20.000, iters=3346
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=19.000, iters=3335
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16259, wt=79.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=14314, wt=72.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16252, wt=68.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=13465, wt=65.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=14307, wt=62.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=12675, wt=58.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16258, wt=57.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=14466, wt=56.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16251, wt=53.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=14313, wt=52.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=11949, wt=51.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=12663, wt=50.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=14306, wt=48.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=13464, wt=47.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=11934, wt=44.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=13455, wt=43.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=12674, wt=42.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=15900, wt=41.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16013, wt=40.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=15808, wt=39.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16321, wt=38.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16549, wt=37.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16595, wt=36.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16699, wt=35.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16905, wt=34.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=16559, wt=33.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=17211, wt=18.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=17600, wt=16.000
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=17667, wt=14.000
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=18.000, iters=3376
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=17.000, iters=3333
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=16.000, iters=3361
% 161.50/161.81
% 161.50/161.81 Low Water (displace): id=24011, wt=13.000
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=15.000, iters=3334
% 161.50/161.81
% 161.50/161.81 Low Water (keep): wt=14.0Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------