TSTP Solution File: SWW247+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW247+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 01:15:58 EDT 2022
% Result : Theorem 8.33s 8.55s
% Output : Refutation 8.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWW247+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 05:00:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.47/1.80 ============================== Prover9 ===============================
% 1.47/1.80 Prover9 (32) version 2009-11A, November 2009.
% 1.47/1.80 Process 24101 was started by sandbox2 on n018.cluster.edu,
% 1.47/1.80 Mon Jun 6 05:00:50 2022
% 1.47/1.80 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23947_n018.cluster.edu".
% 1.47/1.80 ============================== end of head ===========================
% 1.47/1.80
% 1.47/1.80 ============================== INPUT =================================
% 1.47/1.80
% 1.47/1.80 % Reading from file /tmp/Prover9_23947_n018.cluster.edu
% 1.47/1.80
% 1.47/1.80 set(prolog_style_variables).
% 1.47/1.80 set(auto2).
% 1.47/1.80 % set(auto2) -> set(auto).
% 1.47/1.80 % set(auto) -> set(auto_inference).
% 1.47/1.80 % set(auto) -> set(auto_setup).
% 1.47/1.80 % set(auto_setup) -> set(predicate_elim).
% 1.47/1.80 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.47/1.80 % set(auto) -> set(auto_limits).
% 1.47/1.80 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.47/1.80 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.47/1.80 % set(auto) -> set(auto_denials).
% 1.47/1.80 % set(auto) -> set(auto_process).
% 1.47/1.80 % set(auto2) -> assign(new_constants, 1).
% 1.47/1.80 % set(auto2) -> assign(fold_denial_max, 3).
% 1.47/1.80 % set(auto2) -> assign(max_weight, "200.000").
% 1.47/1.80 % set(auto2) -> assign(max_hours, 1).
% 1.47/1.80 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.47/1.80 % set(auto2) -> assign(max_seconds, 0).
% 1.47/1.80 % set(auto2) -> assign(max_minutes, 5).
% 1.47/1.80 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.47/1.80 % set(auto2) -> set(sort_initial_sos).
% 1.47/1.80 % set(auto2) -> assign(sos_limit, -1).
% 1.47/1.80 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.47/1.80 % set(auto2) -> assign(max_megs, 400).
% 1.47/1.80 % set(auto2) -> assign(stats, some).
% 1.47/1.80 % set(auto2) -> clear(echo_input).
% 1.47/1.80 % set(auto2) -> set(quiet).
% 1.47/1.80 % set(auto2) -> clear(print_initial_clauses).
% 1.47/1.80 % set(auto2) -> clear(print_given).
% 1.47/1.80 assign(lrs_ticks,-1).
% 1.47/1.80 assign(sos_limit,10000).
% 1.47/1.80 assign(order,kbo).
% 1.47/1.80 set(lex_order_vars).
% 1.47/1.80 clear(print_given).
% 1.47/1.80
% 1.47/1.80 % formulas(sos). % not echoed (1214 formulas)
% 1.47/1.80
% 1.47/1.80 ============================== end of input ==========================
% 1.47/1.80
% 1.47/1.80 % From the command line: assign(max_seconds, 300).
% 1.47/1.80
% 1.47/1.80 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.47/1.80
% 1.47/1.80 % Formulas that are not ordinary clauses:
% 1.47/1.80 1 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.80 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].
% 1.47/1.80 3 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_C) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.80 4 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].
% 1.47/1.80 5 (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].
% 1.47/1.80 6 (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].
% 1.47/1.80 7 (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].
% 1.47/1.80 8 (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].
% 1.47/1.81 9 (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].
% 1.47/1.81 10 (all V_p all T_a (class_Groups_Ozero(T_a) -> -(all B_a all B_q V_p != hAPP(hAPP(c_Polynomial_OpCons(T_a),B_a),B_q)))) # label(fact_pCons__cases) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 11 (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].
% 1.47/1.81 12 (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].
% 1.47/1.81 13 (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].
% 1.47/1.81 14 (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].
% 1.47/1.81 15 (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].
% 1.47/1.81 16 (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].
% 1.47/1.81 17 (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].
% 1.47/1.81 18 (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].
% 1.47/1.81 19 (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].
% 1.47/1.81 20 (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].
% 1.47/1.81 21 (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].
% 1.47/1.81 22 (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].
% 1.47/1.81 23 (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].
% 1.47/1.81 24 (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].
% 1.47/1.81 25 (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].
% 1.47/1.81 26 (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].
% 1.47/1.81 27 (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].
% 1.47/1.81 28 (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].
% 1.47/1.81 29 (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].
% 1.47/1.81 30 (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].
% 1.47/1.81 31 (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].
% 1.47/1.81 32 (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].
% 1.47/1.81 33 (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].
% 1.47/1.81 34 (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].
% 1.47/1.81 35 (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].
% 1.47/1.81 36 (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].
% 1.47/1.81 37 (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].
% 1.47/1.81 38 (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].
% 1.47/1.81 39 (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].
% 1.47/1.81 40 (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].
% 1.47/1.81 41 (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].
% 1.47/1.81 42 (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].
% 1.47/1.81 43 (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].
% 1.47/1.81 44 (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].
% 1.47/1.81 45 (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].
% 1.47/1.81 46 (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].
% 1.47/1.81 47 (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].
% 1.47/1.81 48 (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].
% 1.47/1.81 49 (all V_ya_2 all V_xa_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_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(T_b) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 50 (all V_d all V_c all V_b all V_a all V_r all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_r != c_Groups_Ozero__class_Ozero(T_a) -> (V_a = V_b & V_c != V_d -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 51 (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].
% 1.47/1.81 52 (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].
% 1.47/1.81 53 (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].
% 1.47/1.81 54 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 55 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 56 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 57 (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].
% 1.47/1.81 58 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 59 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 60 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 61 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 62 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 63 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 64 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 65 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 66 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 67 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 68 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 69 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 70 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 71 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 72 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 73 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 74 (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].
% 1.47/1.81 75 (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),hAPP(hAPP(hAPP(c_If(T_b),hAPP(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].
% 1.47/1.81 76 (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].
% 1.47/1.81 77 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a) | V_b = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 78 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 79 (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].
% 1.47/1.81 80 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 81 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 82 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 83 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 84 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 85 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 86 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 87 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 88 (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].
% 1.47/1.81 89 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 90 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 91 (all V_z_2 all V_xa_2 all V_ya_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_ya_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_xa_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_xa_2),V_ya_2)) <-> V_w_2 = V_xa_2 | V_ya_2 = V_z_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 92 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 93 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 94 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 95 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 96 (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].
% 1.47/1.81 97 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 98 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 99 (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].
% 1.47/1.81 100 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 101 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 102 (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].
% 1.47/1.81 103 (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].
% 1.47/1.81 104 (all T_b (class_Groups_Ozero(T_b) -> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)) = c_Polynomial_OAbs__poly(T_b,hAPP(c_COMBK(T_b,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_zero__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 105 (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),hAPP(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].
% 1.47/1.81 106 (all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 107 (all V_xa_2 all T_b (class_Rings_Oring__1__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_xa_2),V_xa_2) = c_Groups_Oone__class_Oone(T_b) <-> V_xa_2 = c_Groups_Oone__class_Oone(T_b) | V_xa_2 = hAPP(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].
% 1.47/1.81 108 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a)) # label(fact_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 109 (all V_xa_2 all T_b (class_Groups_Oone(T_b) -> (c_Groups_Oone__class_Oone(T_b) = V_xa_2 <-> V_xa_2 = c_Groups_Oone__class_Oone(T_b)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 110 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) <-> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 111 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2 <-> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 112 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(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].
% 1.47/1.81 113 (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].
% 1.47/1.81 114 (all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_n))) # label(fact_minus__monom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 115 (all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)))) # label(fact_minus__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 116 (all V_p all V_a all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a)),hAPP(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].
% 1.47/1.81 117 (all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_minus__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 118 (all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = hAPP(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].
% 1.47/1.81 119 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (V_a_2 = hAPP(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].
% 1.47/1.81 120 (all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(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].
% 1.47/1.81 121 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hAPP(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].
% 1.47/1.81 122 (all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_p) = hAPP(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].
% 1.47/1.81 123 (all V_x all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)),V_x) = hAPP(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].
% 1.47/1.81 124 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 125 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))) # label(fact_minus__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 126 (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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b)) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 127 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(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].
% 1.47/1.81 128 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 129 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 130 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 131 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 132 (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].
% 1.47/1.81 133 (all V_m_2 all V_a_2 all T_b (class_Groups_Ozero(T_b) -> c_Polynomial_Omonom(T_b,V_a_2,V_m_2) = c_Polynomial_OAbs__poly(T_b,hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b,hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_fun(T_b,T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Nat_Onat),c_If(T_b)),c_fequal(V_m_2))),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_monom__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 134 (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].
% 1.47/1.81 135 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 136 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 137 (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(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(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].
% 1.47/1.81 138 (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(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = hAPP(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].
% 1.47/1.81 139 (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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(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].
% 1.47/1.81 140 (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(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(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].
% 1.47/1.81 141 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 142 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(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].
% 1.47/1.81 143 (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 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 144 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 145 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a))) # label(fact_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 146 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 147 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 148 (all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(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].
% 1.47/1.81 149 (all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)) = hAPP(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].
% 1.47/1.81 150 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_right__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 151 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (V_a_2 = hAPP(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].
% 1.47/1.81 152 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 153 (all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 154 (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) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b))) # label(fact_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 155 (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].
% 1.47/1.81 156 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 157 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 158 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 159 (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].
% 1.47/1.81 160 (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].
% 1.47/1.81 161 (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].
% 1.47/1.81 162 (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].
% 1.47/1.81 163 (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].
% 1.47/1.81 164 (all V_xa_2 all T_b (class_Groups_Ozero(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = V_xa_2 <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 165 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 166 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 167 (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].
% 1.47/1.81 168 (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].
% 1.47/1.81 169 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 170 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 171 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 172 (all V_ya_2 all V_xa_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_xa_2),V_ya_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_ya_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_xa_2)))) # label(fact_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 173 (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),hAPP(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].
% 1.47/1.81 174 (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),hAPP(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].
% 1.47/1.81 175 (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].
% 1.47/1.81 176 (all V_xa_2 all V_A_2 all T_c all T_b (class_Groups_Ouminus(T_b) -> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_xa_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_xa_2)))) # label(fact_fun__Compl__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 177 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].
% 1.47/1.81 178 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 179 (all V_q_2 all V_pa_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2) = c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))),c_Polynomial_Ocoeff(T_b,V_q_2))))) # label(fact_plus__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 180 (all V_pa_2 all V_a_2 all T_b (class_Rings_Ocomm__semiring__0(T_b) -> hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2) = c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2)),c_Polynomial_Ocoeff(T_b,V_pa_2))))) # label(fact_smult__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 181 (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].
% 1.47/1.81 182 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))) # label(fact_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 183 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 184 (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].
% 1.47/1.81 185 (all V_q_2 all V_pa_2 all T_b (class_Groups_Ozero(T_b) -> (V_pa_2 = V_q_2 <-> (all B_n hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),B_n))))) # label(fact_expand__poly__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 186 (all V_ya_2 all V_xa_2 all T_b (class_Groups_Ozero(T_b) -> (c_Polynomial_Ocoeff(T_b,V_xa_2) = c_Polynomial_Ocoeff(T_b,V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_coeff__inject) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 187 (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].
% 1.47/1.81 188 (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].
% 1.47/1.81 189 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 190 (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,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)))))) # label(fact_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 191 (all V_ya_2 all V_xa_2 all T_b (class_Lattices_Oboolean__algebra(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_xa_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ya_2),V_xa_2))))) # label(fact_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.81 192 (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].
% 1.47/1.81 193 (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].
% 1.47/1.81 194 (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].
% 1.47/1.81 195 (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].
% 1.47/1.81 196 (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].
% 1.47/1.82 197 (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].
% 1.47/1.82 198 (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].
% 1.47/1.82 199 (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].
% 1.47/1.82 200 (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].
% 1.47/1.82 201 (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].
% 1.47/1.82 202 (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].
% 1.47/1.82 203 (all V_ya_2 all V_xa_2 all T_b (class_Rings_Ocomm__ring__1(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_xa_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ya_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_xa_2),V_ya_2))))) # label(fact_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 204 (all V_ya_2 all V_xa_2 all T_b (class_Rings_Ocomm__ring__1(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_xa_2)),V_ya_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_xa_2),V_ya_2))))) # label(fact_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 205 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 206 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 207 (all V_n all V_p all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)),V_n) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)))) # label(fact_coeff__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 208 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 209 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 210 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 211 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 212 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 213 (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].
% 1.47/1.82 214 (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].
% 1.47/1.82 215 (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,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))))) # label(fact_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 216 (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,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(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].
% 1.47/1.82 217 (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,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))))) # label(fact_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 218 (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),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))))) # label(fact_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 219 (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].
% 1.47/1.82 220 (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].
% 1.47/1.82 221 (all V_xa_2 all T_b (class_Groups_Ozero(T_b) -> c_Polynomial_OAbs__poly(T_b,c_Polynomial_Ocoeff(T_b,V_xa_2)) = V_xa_2)) # label(fact_coeff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 222 (all V_n all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(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))))),V_n)),V_n) = c_Groups_Oone__class_Oone(T_a))) # label(fact_coeff__linear__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 223 (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].
% 1.47/1.82 224 (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].
% 1.47/1.82 225 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 226 (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].
% 1.47/1.82 227 (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].
% 1.47/1.82 228 (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].
% 1.47/1.82 229 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 230 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 231 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 232 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 233 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 234 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 235 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 236 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 237 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 238 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 239 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 240 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 241 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 242 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 243 (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].
% 1.47/1.82 244 (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].
% 1.47/1.82 245 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 246 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 247 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 248 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 249 (all V_ya_2 all V_xa_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_xa_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ya_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_xa_2),V_ya_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 250 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 251 (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].
% 1.47/1.82 252 (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].
% 1.47/1.82 253 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 254 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 255 (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(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].
% 1.47/1.82 256 (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,hAPP(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].
% 1.47/1.82 257 (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),hAPP(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].
% 1.47/1.82 258 (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)),hAPP(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].
% 1.47/1.82 259 (all V_n all T_a (class_Groups_Ozero(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_coeff__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 260 (all V_p all V_a all T_a (class_Groups_Ozero(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)) # label(fact_coeff__pCons__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 261 (all V_n all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)))) # label(fact_coeff__smult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 262 (all V_a all V_n all V_m all T_a (class_Groups_Ozero(T_a) -> (V_m = V_n -> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = V_a) & (V_m != V_n -> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_coeff__monom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 263 (all V_n all V_q all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)))) # label(fact_coeff__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 264 (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),hAPP(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].
% 1.47/1.82 265 (all V_pa_2 all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),V_pa_2) = c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))))) # label(fact_uminus__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 266 (all V_n all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_coeff__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 267 (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].
% 1.47/1.82 268 (all V_ya_2 all V_xa_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_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ya_2),V_ya_2))),c_Groups_Ozero__class_Ozero(T_b))) <-> V_xa_2 = c_Groups_Ozero__class_Ozero(T_b) & V_ya_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 269 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 270 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x))))))) # label(fact_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 271 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x))))))) # label(fact_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 272 (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].
% 1.47/1.82 273 (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].
% 1.47/1.82 274 (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].
% 1.47/1.82 275 (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].
% 1.47/1.82 276 (all V_ya_2 all V_xa_2 all T_b (class_Lattices_Oboolean__algebra(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_xa_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ya_2) <-> V_xa_2 = V_ya_2))) # label(fact_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 277 (all V_xa_2 all V_A_2 all T_c all T_b (class_Groups_Ouminus(T_b) -> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_xa_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_xa_2)))) # label(fact_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 278 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x)) # label(fact_double__compl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 279 (all V_n all V_a all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(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),hAPP(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].
% 1.47/1.82 280 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 281 (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].
% 1.47/1.82 282 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))))) # label(fact_power__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 283 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 284 (all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 285 (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].
% 1.47/1.82 286 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 287 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z) # label(fact_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 288 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z) # label(fact_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 289 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 290 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 291 (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].
% 1.47/1.82 292 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(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].
% 1.47/1.82 293 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))) # label(fact_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 294 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))) # label(fact_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 295 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 296 (all V_ca_2 all V_t_2 all V_xa_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_xa_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_xa_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].
% 1.47/1.82 297 (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].
% 1.47/1.82 298 (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].
% 1.47/1.82 299 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n))) # label(fact_power__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 300 (all V_n all V_a all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_field__power__not__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 301 (all V_n all V_b all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 302 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 303 (all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__one) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 304 (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].
% 1.47/1.82 305 (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].
% 1.47/1.82 306 (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].
% 1.47/1.82 307 (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].
% 1.47/1.82 308 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a)) # label(fact_power__one__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 309 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_zero__le__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 310 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))))) # label(fact_power__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 311 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))))) # label(fact_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 312 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_le0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 313 (all V_n all V_m (V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) -> V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 314 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 315 (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),hAPP(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),hAPP(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].
% 1.47/1.82 316 (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),hAPP(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].
% 1.47/1.82 317 (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].
% 1.47/1.82 318 (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].
% 1.47/1.82 319 (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].
% 1.47/1.82 320 (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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))))) # label(fact_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 321 (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),hAPP(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].
% 1.47/1.82 322 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 323 (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].
% 1.47/1.82 324 (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].
% 1.47/1.82 325 (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].
% 1.47/1.82 326 (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].
% 1.47/1.82 327 (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].
% 1.47/1.82 328 (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].
% 1.47/1.82 329 (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].
% 1.47/1.82 330 (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].
% 1.47/1.82 331 (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].
% 1.47/1.82 332 (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].
% 1.47/1.82 333 (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].
% 1.47/1.82 334 (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].
% 1.47/1.82 335 (all V_n hAPP(c_Nat_OSuc,V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 336 (all V_n V_n != hAPP(c_Nat_OSuc,V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 337 (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].
% 1.47/1.82 338 (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].
% 1.47/1.82 339 (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].
% 1.47/1.82 340 (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].
% 1.47/1.82 341 (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].
% 1.47/1.82 342 (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].
% 1.47/1.82 343 (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].
% 1.47/1.82 344 (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].
% 1.47/1.82 345 (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].
% 1.47/1.82 346 (all V_w all V_z hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) # label(fact_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 347 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 348 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 349 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 350 (all V_z hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z) # label(fact_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 351 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 352 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z) # label(fact_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 353 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 354 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 355 (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].
% 1.47/1.82 356 (all V_m_2 all V_xa_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_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_xa_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].
% 1.47/1.82 357 (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].
% 1.47/1.82 358 (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].
% 1.47/1.82 359 (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].
% 1.47/1.82 360 (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].
% 1.47/1.82 361 (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].
% 1.47/1.82 362 (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].
% 1.47/1.82 363 (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].
% 1.47/1.82 364 (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].
% 1.47/1.82 365 (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].
% 1.47/1.82 366 (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].
% 1.47/1.82 367 (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].
% 1.47/1.82 368 (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].
% 1.47/1.82 369 (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].
% 1.47/1.82 370 (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].
% 1.47/1.82 371 (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].
% 1.47/1.82 372 (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].
% 1.47/1.82 373 (all V_n all V_p all V_a all T_a (class_Groups_Ozero(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))) # label(fact_coeff__pCons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 374 (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].
% 1.47/1.82 375 (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].
% 1.47/1.82 376 (all V_ya_2 all V_xa_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_xa_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_ya_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_xa_2 = V_ya_2 | V_xa_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ya_2)))) # label(fact_realpow__two__disj) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 377 (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].
% 1.47/1.82 378 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 379 (all V_xa_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_xa_2)),hAPP(V_g_2,V_xa_2)))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 380 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 381 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 382 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 383 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 384 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.82 385 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 386 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 387 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 388 (all V_xa_2 all V_ya_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ya_2),V_xa_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) <-> V_xa_2 = V_ya_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 389 (all V_xa_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_xa_2)),hAPP(V_g_2,V_xa_2)))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 390 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 391 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Oorder(T_b) -> (V_xa_2 = V_ya_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ya_2),V_xa_2))))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 392 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 393 (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].
% 1.47/1.83 394 (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].
% 1.47/1.83 395 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 396 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 397 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 398 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 399 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 400 (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].
% 1.47/1.83 401 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n))) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 402 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 403 (all V_n all V_m (V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 404 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k))))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 405 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 406 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 407 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 408 (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].
% 1.47/1.83 409 (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].
% 1.47/1.83 410 (all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 411 (all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 412 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 413 (all V_n all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 414 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 415 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 416 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 417 (all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 418 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 419 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 420 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 421 (all V_m all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 422 (all V_m all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 423 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> (exists B_k V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 424 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 425 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 426 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 427 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 428 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 429 (all V_n all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 430 (all V_n all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 431 (all V_n all V_k all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 432 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 433 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 434 (all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 435 (all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 436 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 437 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 438 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 439 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n) # label(fact_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 440 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 441 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 442 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 443 (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),hAPP(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].
% 1.47/1.83 444 (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].
% 1.47/1.83 445 (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].
% 1.47/1.83 446 (all V_n all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 447 (all V_k all V_j all V_u all V_i hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k)) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 448 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 449 (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].
% 1.47/1.83 450 (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].
% 1.47/1.83 451 (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].
% 1.47/1.83 452 (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].
% 1.47/1.83 453 (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].
% 1.47/1.83 454 (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].
% 1.47/1.83 455 (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].
% 1.47/1.83 456 (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].
% 1.47/1.83 457 (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].
% 1.47/1.83 458 (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].
% 1.47/1.83 459 (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].
% 1.47/1.83 460 (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].
% 1.47/1.83 461 (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].
% 1.47/1.83 462 (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].
% 1.47/1.83 463 (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].
% 1.47/1.83 464 (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].
% 1.47/1.83 465 (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].
% 1.47/1.83 466 (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].
% 1.47/1.83 467 (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].
% 1.47/1.83 468 (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].
% 1.47/1.83 469 (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].
% 1.47/1.83 470 (all V_xa_2 all V_ya_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ya_2),V_xa_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) <-> V_xa_2 = V_ya_2))) # label(fact_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 471 (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].
% 1.47/1.83 472 (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].
% 1.47/1.83 473 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ya_2),V_xa_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) & V_xa_2 != V_ya_2)) # label(fact_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 474 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ya_2),V_xa_2)) | V_xa_2 = V_ya_2)) # label(fact_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 475 (all V_ya_2 all V_xa_2 (V_xa_2 = V_ya_2 <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ya_2),V_xa_2)))) # label(fact_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 476 (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].
% 1.47/1.83 477 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) -> V_z = V_w))) # label(fact_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 478 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k))))) # label(fact_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 479 (all V_w all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 480 (all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w))) # label(fact_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 481 (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].
% 1.47/1.83 482 (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].
% 1.47/1.83 483 (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].
% 1.47/1.83 484 (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].
% 1.47/1.83 485 (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].
% 1.47/1.83 486 (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].
% 1.47/1.83 487 (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].
% 1.47/1.83 488 (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].
% 1.47/1.83 489 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 490 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 491 (all V_y all V_z all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 492 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 493 (all V_l_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2)) <-> (exists B_n V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 494 (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_Polynomial_OAbs__poly(T_b,c_Nat_Onat_Onat__case(T_b,V_a_2,c_Polynomial_Ocoeff(T_b,V_pa_2))))) # label(fact_pCons__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 495 (all V_f2_2 all V_f1_2 all T_b hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2) # label(fact_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 496 (all V_nat_2 all V_f2_2 all V_f1_2 all T_b hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2)) # label(fact_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 497 (all V_pa_2 all V_a_2 all T_b (class_Groups_Ozero(T_b) -> c_Polynomial_Ocoeff(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)) = c_Nat_Onat_Onat__case(T_b,V_a_2,c_Polynomial_Ocoeff(T_b,V_pa_2)))) # label(fact_coeff__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 498 (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_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2)),V_n_2)))) # label(fact_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 499 (all V_ya_2 all V_xa_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_xa_2),V_ya_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2)),hAPP(V_f_2,V_ya_2))))))) # label(fact_dvd_OmonoD) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 500 (all V_z_H all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))))) # label(fact_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 501 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 502 (all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))) # label(fact_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 503 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 504 (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].
% 1.47/1.83 505 (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].
% 1.47/1.83 506 (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].
% 1.47/1.83 507 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 508 (all V_z all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 509 (all V_y all V_z all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 510 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2))))) # label(fact_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 511 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))))) # label(fact_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 512 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_one__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 513 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,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_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 514 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)))) # label(fact_zless__nat__conj) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 515 (all V_w_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))))) # label(fact_nat__mono__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 516 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> (V_x != V_y -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 517 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 518 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 519 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 520 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 521 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 522 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 523 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 524 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 525 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 526 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 527 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 528 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 529 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 530 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 531 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 532 (all V_xa_2 all V_ya_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ya_2),V_xa_2)) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 533 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) | V_x = V_y | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 534 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ya_2),V_xa_2)) | V_xa_2 = V_ya_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 535 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Olinorder(T_b) -> (V_xa_2 != V_ya_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ya_2),V_xa_2))))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 536 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 537 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)))) # label(fact_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 538 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 539 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 540 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) | V_m = V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 541 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> (V_m != V_n -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 542 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 543 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 544 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 545 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 546 (all V_n all V_m all V_l all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 547 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 548 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 549 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 550 (all V_m all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 551 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 552 (all V_i all V_j -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i))) # label(fact_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 553 (all V_j all V_i -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i))) # label(fact_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 554 (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].
% 1.47/1.83 555 (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].
% 1.47/1.83 556 (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].
% 1.47/1.83 557 (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].
% 1.47/1.83 558 (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].
% 1.47/1.83 559 (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].
% 1.47/1.83 560 (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].
% 1.47/1.83 561 (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].
% 1.47/1.83 562 (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].
% 1.47/1.83 563 (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].
% 1.47/1.83 564 (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].
% 1.47/1.83 565 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 566 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 567 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 568 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 569 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 570 (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,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(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].
% 1.47/1.83 571 (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,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))))) # label(fact_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 572 (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),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))))) # label(fact_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 573 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 574 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 575 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 576 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 577 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 578 (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].
% 1.47/1.83 579 (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].
% 1.47/1.83 580 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 581 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 582 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 583 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 584 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> (V_a != V_b -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 585 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (V_a != V_b -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 586 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 587 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 588 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 589 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 590 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 591 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 592 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) <-> V_xa_2 = V_ya_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 593 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 594 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 595 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) | V_xa_2 = V_ya_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 596 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Opreorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) & -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ya_2),V_xa_2))))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 597 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) & V_xa_2 != V_ya_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 598 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 599 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_xa_2),V_ya_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ya_2),V_xa_2))))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 600 (all V_ya_2 all V_xa_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_xa_2),V_ya_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,V_ya_2),V_xa_2))))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 601 (all V_w_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2)) & V_z_2 != V_w_2)) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 602 (all V_ya_2 all V_xa_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_xa_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2),V_ya_2)))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 603 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))))) # label(fact_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 604 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))))) # label(fact_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.83 605 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2)),hAPP(c_Int_Onat,V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2),V_ya_2)))))) # label(fact_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 606 (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].
% 1.47/1.84 607 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))))) # label(fact_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 608 (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].
% 1.47/1.84 609 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))))) # label(fact_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 610 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2)) -> (hAPP(c_Int_Onat,V_xa_2) = hAPP(c_Int_Onat,V_ya_2) <-> V_xa_2 = V_ya_2)))) # label(fact_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 611 (all V_P_2 ((all B_x1 hBOOL(hAPP(V_P_2,B_x1))) <-> (all B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))))))) # label(fact_all__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 612 (all V_P_2 ((exists B_x1 hBOOL(hAPP(V_P_2,B_x1))) <-> (exists B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))))))) # label(fact_ex__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 613 (all V_z_H_2 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) -> (hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) <-> V_z_2 = V_z_H_2)))) # label(fact_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 614 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 615 (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].
% 1.47/1.84 616 (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].
% 1.47/1.84 617 (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].
% 1.47/1.84 618 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 619 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 620 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 621 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 622 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 623 (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].
% 1.47/1.84 624 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 625 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 626 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 627 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 628 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 629 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 630 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 631 (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].
% 1.47/1.84 632 (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].
% 1.47/1.84 633 (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].
% 1.47/1.84 634 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 635 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 636 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 637 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 638 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 639 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 640 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 641 (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)),hAPP(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].
% 1.47/1.84 642 (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),hAPP(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].
% 1.47/1.84 643 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(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].
% 1.47/1.84 644 (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(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].
% 1.47/1.84 645 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 646 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 647 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 648 (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].
% 1.47/1.84 649 (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].
% 1.47/1.84 650 (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].
% 1.47/1.84 651 (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].
% 1.47/1.84 652 (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].
% 1.47/1.84 653 (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].
% 1.47/1.84 654 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 655 (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].
% 1.47/1.84 656 (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].
% 1.47/1.84 657 (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].
% 1.47/1.84 658 (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].
% 1.47/1.84 659 (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].
% 1.47/1.84 660 (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].
% 1.47/1.84 661 (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].
% 1.47/1.84 662 (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].
% 1.47/1.84 663 (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].
% 1.47/1.84 664 (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].
% 1.47/1.84 665 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 666 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 667 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 668 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 669 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 670 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 671 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 672 (all V_k all V_j all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 673 (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].
% 1.47/1.84 674 (all V_z all V_z_H all V_w all V_w_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 675 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) | V_w_2 = V_z_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 676 (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].
% 1.47/1.84 677 (all V_n all V_m all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))) # label(fact_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 678 (all V_n_2 all V_xa_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_xa_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xa_2)) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 679 (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].
% 1.47/1.84 680 (all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 681 (all V_i_2 (hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_nat__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 682 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2)),hAPP(c_Int_Onat,V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2),V_ya_2)))))) # label(fact_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 683 (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].
% 1.47/1.84 684 (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].
% 1.47/1.84 685 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 686 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 687 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 688 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 689 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 690 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 691 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 692 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 693 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)))))) # label(fact_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 694 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)))))) # label(fact_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 695 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 696 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 697 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 698 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 699 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 700 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 701 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 702 (all V_ya_2 all V_xa_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_xa_2),V_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ya_2),V_ya_2)))) <-> V_xa_2 != c_Groups_Ozero__class_Ozero(T_b) | V_ya_2 != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 703 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))))) # label(fact_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 704 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 705 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 706 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 707 (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].
% 1.47/1.84 708 (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].
% 1.47/1.84 709 (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].
% 1.47/1.84 710 (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].
% 1.47/1.84 711 (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].
% 1.47/1.84 712 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 713 (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].
% 1.47/1.84 714 (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].
% 1.47/1.84 715 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 716 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 717 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 718 (all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 719 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 720 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 721 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 722 (all V_z all V_w (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)))) # label(fact_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 723 (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].
% 1.47/1.84 724 (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)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 725 (all V_z_H 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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))))) # label(fact_nat__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 726 (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)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 727 (all V_z_H all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)))) # label(fact_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 728 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_xa_2)),hAPP(c_Int_Onat,V_ya_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_xa_2),V_ya_2)))))) # label(fact_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 729 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 730 (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].
% 1.47/1.84 731 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))))) # label(fact_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 732 (all V_ya_2 all V_xa_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_xa_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2),V_ya_2)))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 733 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> V_a = V_b)))))) # label(fact_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 734 (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].
% 1.47/1.84 735 (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)) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 736 (all V_n all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n))) # label(fact_nat__power__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 737 (all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))))) # label(fact_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 738 (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].
% 1.47/1.84 739 (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].
% 1.47/1.84 740 (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].
% 1.47/1.84 741 (all V_q all V_r all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)))))) # label(fact_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 742 (all V_q all V_r all V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) # label(fact_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 743 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)))))) # label(fact_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 744 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) # label(fact_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 745 (all V_P_2 all V_n_2 all V_m_2 ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 746 (all V_t all V_s (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t)) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 747 (all V_m all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m)) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 748 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 749 (all V_y all V_x (V_x != V_y -> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x))))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 750 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 751 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 752 (all V_y all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y)) | V_x = V_y | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 753 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q))))))))) # label(fact_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 754 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H))))))) # label(fact_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 755 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H))))))))) # label(fact_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 756 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q))))))) # label(fact_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 757 (all V_n all V_i c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n)) # label(fact_nat__aux__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 758 (all V_n_2 all V_xa_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_xa_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_xa_2)))) # label(fact_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 759 (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].
% 1.47/1.84 760 (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].
% 1.47/1.84 761 (all V_ya_2 all V_xa_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_xa_2),V_ya_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ya_2),V_xa_2)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2)),hAPP(V_f_2,V_ya_2))))))) # label(fact_dvd_Ostrict__monoD) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 762 (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].
% 1.47/1.84 763 (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].
% 1.47/1.84 764 (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].
% 1.47/1.84 765 (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].
% 1.47/1.84 766 (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].
% 1.47/1.84 767 (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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)))) # label(fact_pos__poly__total) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 768 (all V_n_2 all V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_P_2,V_n_2)) -> (exists B_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2)) & (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) -> -hBOOL(hAPP(V_P_2,B_i)))) & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 769 (all V_m_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2)) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)))) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 770 (all V_m all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n))),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)))) # label(fact_negative__zle) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.84 771 (all V_m all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,V_n)))),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)))) # label(fact_negative__zless) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 772 (all V_n hAPP(c_Int_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)) = V_n) # label(fact_nat__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 773 (all V_ya_2 all V_xa_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_xa_2) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_ya_2) <-> V_xa_2 = V_ya_2)) # label(fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 774 (all V_n_2 all V_m_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2) <-> V_m_2 = V_n_2)) # label(fact_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 775 (all V_n_2 all V_m_2 all T_b (class_Nat_Osemiring__char__0(T_b) -> (c_Nat_Osemiring__1__class_Oof__nat(T_b,V_m_2) = c_Nat_Osemiring__1__class_Oof__nat(T_b,V_n_2) <-> V_m_2 = V_n_2))) # label(fact_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 776 (all V_n all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x)),V_n) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 777 (all V_n all V_m c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),V_n)) # label(fact_int__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 778 (all V_n all V_m hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),V_n) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))) # label(fact_zpower__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 779 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_xa_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_ya_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)))) # label(fact_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 780 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_xa_2),V_ya_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_xa_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_ya_2))))) # label(fact_zdvd__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 781 (all V_n all V_m all T_a (class_Rings_Osemiring__1(T_a) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),V_n))) # label(fact_of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 782 (all V_y all V_x hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 783 (all V_n all V_m c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n))) # label(fact_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 784 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 785 (all V_m_2 all V_n_2 (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,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))) # label(fact_negative__eq__positive) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 786 (all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 787 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 788 (all V_z all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z)) # label(fact_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 789 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) <-> (exists B_n V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B_n))))) # label(fact_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 790 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_xa_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2),V_ya_2)))) # label(fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 791 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 792 (all V_P_2 ((all B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> hBOOL(hAPP(V_P_2,B_x)))) <-> (all B_x hBOOL(hAPP(V_P_2,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B_x)))))) # label(fact_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 793 (all V_P_2 ((exists B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) & hBOOL(hAPP(V_P_2,B_x)))) <-> (exists B_x hBOOL(hAPP(V_P_2,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B_x)))))) # label(fact_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 794 (all V_z hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_z)))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 795 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)))) # label(fact_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 796 (all V_n_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 797 (all T_a (class_Rings_Osemiring__1(T_a) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_of__nat__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 798 (all V_n all V_m all T_a (class_Rings_Osemiring__1(T_a) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n)))) # label(fact_of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 799 (all V_n all V_m all T_a (class_Rings_Osemiring__1(T_a) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n)))) # label(fact_of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 800 (all V_n_2 all V_m_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(T_b,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 801 (all T_a (class_Rings_Osemiring__1(T_a) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_of__nat__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 802 (all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 803 (all V_m 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_Nat_Osemiring__1__class_Oof__nat(T_a,V_m))))) # label(fact_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 804 (all V_n 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_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))))) # label(fact_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 805 (all V_ya_2 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_xa_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_ya_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2),V_ya_2)))) # label(fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 806 (all V_n_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 807 (all V_m all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m))))) # label(fact_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 808 (all V_n_2 all V_m_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(T_b,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))))) # label(fact_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 809 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n)))))) # label(fact_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 810 (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_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))) # label(fact_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 811 (all V_k -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 812 (all V_m all T_a (class_Rings_Osemiring__1(T_a) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)))) # label(fact_of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 813 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 814 (all V_z_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) <-> (exists B_n V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,B_n)))))) # label(fact_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 815 (all V_m c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m))) # label(fact_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 816 (all V_z ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Int_Onat,V_z)) = V_z) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_int__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 817 (all V_z_2 all V_m_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2) = V_z_2 <-> V_m_2 = hAPP(c_Int_Onat,V_z_2) & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))) # label(fact_int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 818 (all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Int_Onat,V_z)) = V_z)) # label(fact_nat__0__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 819 (all V_m_2 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,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))) # label(fact_int__zle__neg) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 820 (all V_z_2 all V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)),V_z_2)))) # label(fact_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 821 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_negative__zle__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 822 (all V_n hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 823 (all V_n_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))))) # label(fact_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 824 (all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 825 (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_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_k)),V_j)))))) # label(fact_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 826 (all V_w_2 all V_m_2 (V_m_2 = hAPP(c_Int_Onat,V_w_2) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_w_2 = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 827 (all V_m_2 all V_w_2 (hAPP(c_Int_Onat,V_w_2) = V_m_2 <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_w_2 = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 828 (all V_i_2 all V_P_2 (hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) <-> (all B_n (V_i_2 = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B_n) -> hBOOL(hAPP(V_P_2,B_n)))) & (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) # label(fact_split__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 829 (all V_n -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,V_n)))))) # label(fact_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 830 (all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_negative__zless__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 831 (all V_m_2 all V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),V_m_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)))))) # label(fact_nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 832 (all V_n_2 all T_b (class_Rings_Osemiring__1(T_b) -> c_Nat_Osemiring__1__class_Oof__nat(T_b,V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(c_COMBC(T_b,T_b,T_b,c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 833 (all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (exists B_n V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,B_n)))))) # label(fact_negD) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 834 (all V_i_2 all V_inc_2 all T_b (class_Rings_Osemiring__1(T_b) -> c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2)) # label(fact_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 835 (all V_i_2 all V_n_2 all V_inc_2 all T_b (class_Rings_Osemiring__1(T_b) -> c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)))) # label(fact_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 836 (all V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) & V_k = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B_n))))) # label(fact_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 837 (all V_k all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Int_Oring__1__class_Oof__int(T_a,V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))))) & (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Int_Oring__1__class_Oof__int(T_a,V_k) = c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(c_Int_Onat,V_k))))) # label(fact_of__int__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 838 (all V_n all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)) = c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))) # label(fact_of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 839 (all V_n c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)) # label(fact_of__int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 840 (all V_z_2 all V_w_2 all T_b (class_Int_Oring__char__0(T_b) -> (c_Int_Oring__1__class_Oof__int(T_b,V_w_2) = c_Int_Oring__1__class_Oof__int(T_b,V_z_2) <-> V_w_2 = V_z_2))) # label(fact_of__int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 841 (all V_n all V_z all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z)),V_n))) # label(fact_of__int__power) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 842 (all V_z all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z)))) # label(fact_of__int__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 843 (all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_of__int__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 844 (all V_z all V_w all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_w)),c_Int_Oring__1__class_Oof__int(T_a,V_z)))) # label(fact_of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 845 (all V_z all V_w all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_w)),c_Int_Oring__1__class_Oof__int(T_a,V_z)))) # label(fact_of__int__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 846 (all V_z_2 all V_w_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Int_Oring__1__class_Oof__int(T_b,V_w_2)),c_Int_Oring__1__class_Oof__int(T_b,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2))))) # label(fact_of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 847 (all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_of__int__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 848 (all V_z_2 all T_b (class_Int_Oring__char__0(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = c_Int_Oring__1__class_Oof__int(T_b,V_z_2) <-> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_of__int__0__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 849 (all V_z_2 all T_b (class_Int_Oring__char__0(T_b) -> (c_Int_Oring__1__class_Oof__int(T_b,V_z_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_of__int__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 850 (all V_z_2 all V_w_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Int_Oring__1__class_Oof__int(T_b,V_w_2)),c_Int_Oring__1__class_Oof__int(T_b,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))))) # label(fact_of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 851 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_Oof__int(T_b,V_z_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))))) # label(fact_of__int__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 852 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,c_Int_Oring__1__class_Oof__int(T_b,V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_of__int__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 853 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Int_Oring__1__class_Oof__int(T_b,V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_of__int__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 854 (all V_z_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_Int_Oring__1__class_Oof__int(T_b,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_of__int__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 855 (all V_z all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(c_Int_Onat,V_z)) = c_Int_Oring__1__class_Oof__int(T_a,V_z)))) # label(fact_of__nat__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 856 (all V_f_2 all T_b (class_Orderings_Oorder(T_b) -> ((all B_x all B_y (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) -> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))))) -> 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)))) # label(fact_dvd_Ostrict__monoI) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 857 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))) # label(fact_realpow__minus__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 858 (all V_z all V_w all T_a (class_Rings_Oring__1(T_a) -> c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_w)),c_Int_Oring__1__class_Oof__int(T_a,V_z)))) # label(fact_of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 859 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 860 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)))) # label(fact_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 861 (all V_n all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(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].
% 1.47/1.85 862 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 863 (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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 864 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 865 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)))) # label(fact_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 866 (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) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(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].
% 1.47/1.85 867 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c)))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 868 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 869 (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,hAPP(hAPP(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].
% 1.47/1.85 870 (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,hAPP(hAPP(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].
% 1.47/1.85 871 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 872 (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),hAPP(hAPP(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].
% 1.47/1.85 873 (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),hAPP(hAPP(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].
% 1.47/1.85 874 (all V_b all V_a all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))))) # label(fact_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 875 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) # label(fact_diff__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 876 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 877 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 878 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(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].
% 1.47/1.85 879 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(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].
% 1.47/1.85 880 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 881 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 882 (all V_n all V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 883 (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_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 884 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(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].
% 1.47/1.85 885 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(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].
% 1.47/1.85 886 (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_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 887 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k))) # label(fact_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 888 (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_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 889 (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)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 <-> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)))) # label(fact_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 890 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m)) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 891 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))))) # label(fact_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 892 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))) # label(fact_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 893 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 894 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))))) # label(fact_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 895 (all V_i_2 all V_k_2 all V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))))) # label(fact_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 896 (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_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))) # label(fact_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 897 (all V_n hAPP(hAPP(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].
% 1.47/1.85 898 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) # label(fact_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 899 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 900 (all V_xa_2 all V_B_2 all V_A_2 all T_c all T_b (class_Groups_Ominus(T_b) -> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_xa_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_xa_2)),hAPP(V_B_2,V_xa_2)))) # label(fact_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 901 (all V_n all V_q all V_p all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)))) # label(fact_coeff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 902 (all V_xa_2 all V_B_2 all V_A_2 all T_c all T_b (class_Groups_Ominus(T_b) -> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_xa_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_xa_2)),hAPP(V_B_2,V_xa_2)))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 903 (all V_b all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_n))) # label(fact_diff__monom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 904 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(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].
% 1.47/1.85 905 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_p) = hAPP(hAPP(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].
% 1.47/1.85 906 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)))) # label(fact_diff__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 907 (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) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(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].
% 1.47/1.85 908 (all V_q_2 all V_pa_2 all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2) = c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))),c_Polynomial_Ocoeff(T_b,V_q_2))))) # label(fact_minus__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 909 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 910 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 911 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)))))) # label(fact_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 912 (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)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 913 (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)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 914 (all V_n all V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i)) # label(fact_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 915 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 916 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 917 (all V_n all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 918 (all V_n all V_k all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 919 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 920 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) # label(fact_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 921 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m) # label(fact_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 922 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m) # label(fact_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 923 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 924 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 925 (all V_n all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 926 (all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 927 (all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 928 (all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 929 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))))))) # label(fact_dvd__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 930 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))) # label(fact_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 931 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a)) # label(fact_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 932 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 933 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 934 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 935 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 936 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 937 (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) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(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].
% 1.47/1.85 938 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(hAPP(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].
% 1.47/1.85 939 (all V_b_2 all V_a_2 all T_b (class_Groups_Oab__group__add(T_b) -> (V_a_2 = V_b_2 <-> hAPP(hAPP(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].
% 1.47/1.85 940 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 941 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 942 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))))) # label(fact_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 943 (all V_n_2 all V_m_2 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2))) # label(fact_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 944 (all V_m all V_n all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) -> c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))))) # label(fact_of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 945 (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),hAPP(hAPP(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].
% 1.47/1.85 946 (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),hAPP(hAPP(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].
% 1.47/1.85 947 (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),hAPP(hAPP(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].
% 1.47/1.85 948 (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),hAPP(hAPP(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].
% 1.47/1.85 949 (all V_x all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))))) # label(fact_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 950 (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),hAPP(hAPP(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].
% 1.47/1.85 951 (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),hAPP(hAPP(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].
% 1.47/1.85 952 (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,hAPP(hAPP(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].
% 1.47/1.85 953 (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,hAPP(hAPP(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].
% 1.47/1.85 954 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) <-> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2)) & -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_d (V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) & -hBOOL(hAPP(V_P_2,B_d))))))) # label(fact_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 955 (all V_b_2 all V_a_2 all V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) <-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2)) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (all B_d (V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) -> hBOOL(hAPP(V_P_2,B_d)))))) # label(fact_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.85 956 (all V_m 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_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(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].
% 1.47/1.85 957 (all V_m 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_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 958 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))))) # label(fact_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 959 (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)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n))) # label(fact_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 960 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2))) # label(fact_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 961 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))))) # label(fact_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 962 (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)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)))) # label(fact_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 963 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))) # label(fact_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 964 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n)) # label(fact_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 965 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 966 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))))) # label(fact_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 967 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))))) # label(fact_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 968 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))))) # label(fact_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 969 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))))) # label(fact_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 970 (all V_p all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) # label(fact_power__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 971 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)))) # label(fact_realpow__two__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 972 (all V_m all V_n all T_a (class_Power_Opower(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) # label(fact_realpow__num__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 973 (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),hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_p))),V_y)))) # label(fact_lemma__realpow__diff) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 974 (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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 975 (all V_w all V_z hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) # label(fact_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 976 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w)) # label(fact_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 977 (all V_q all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = hAPP(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].
% 1.47/1.86 978 (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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = hAPP(hAPP(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].
% 1.47/1.86 979 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(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].
% 1.47/1.86 980 (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].
% 1.47/1.86 981 (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].
% 1.47/1.86 982 (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].
% 1.47/1.86 983 (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].
% 1.47/1.86 984 (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].
% 1.47/1.86 985 (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].
% 1.47/1.86 986 (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].
% 1.47/1.86 987 (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].
% 1.47/1.86 988 (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].
% 1.47/1.86 989 (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].
% 1.47/1.86 990 (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].
% 1.47/1.86 991 (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].
% 1.47/1.86 992 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__semiring(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 993 (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].
% 1.47/1.86 994 (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].
% 1.47/1.86 995 (all T (class_Rings_Oidom(T) -> class_Groups_Omonoid__mult(T))) # label(clrel_Rings_Oidom__Groups_Omonoid__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 996 (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].
% 1.47/1.86 997 (all T (class_Rings_Oidom(T) -> class_Groups_Omonoid__add(T))) # label(clrel_Rings_Oidom__Groups_Omonoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 998 (all T (class_Rings_Oidom(T) -> class_Rings_Osemiring__1(T))) # label(clrel_Rings_Oidom__Rings_Osemiring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 999 (all T (class_Rings_Oidom(T) -> class_Rings_Osemiring__0(T))) # label(clrel_Rings_Oidom__Rings_Osemiring__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1000 (all T (class_Rings_Oidom(T) -> class_Groups_Ogroup__add(T))) # label(clrel_Rings_Oidom__Groups_Ogroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1001 (all T (class_Rings_Oidom(T) -> class_Rings_Omult__zero(T))) # label(clrel_Rings_Oidom__Rings_Omult__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1002 (all T (class_Rings_Oidom(T) -> class_Rings_Ocomm__ring(T))) # label(clrel_Rings_Oidom__Rings_Ocomm__ring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1003 (all T (class_Rings_Oidom(T) -> class_Rings_Osemiring(T))) # label(clrel_Rings_Oidom__Rings_Osemiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1004 (all T (class_Rings_Oidom(T) -> class_Groups_Ouminus(T))) # label(clrel_Rings_Oidom__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1005 (all T (class_Rings_Oidom(T) -> class_Rings_Oring__1(T))) # label(clrel_Rings_Oidom__Rings_Oring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1006 (all T (class_Rings_Oidom(T) -> class_Groups_Ominus(T))) # label(clrel_Rings_Oidom__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1007 (all T (class_Rings_Oidom(T) -> class_Power_Opower(T))) # label(clrel_Rings_Oidom__Power_Opower) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1008 (all T (class_Rings_Oidom(T) -> class_Groups_Ozero(T))) # label(clrel_Rings_Oidom__Groups_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1009 (all T (class_Rings_Oidom(T) -> class_Rings_Oring(T))) # label(clrel_Rings_Oidom__Rings_Oring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1010 (all T (class_Rings_Oidom(T) -> class_Groups_Oone(T))) # label(clrel_Rings_Oidom__Groups_Oone) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1011 (all T (class_Rings_Oidom(T) -> class_Rings_Odvd(T))) # label(clrel_Rings_Oidom__Rings_Odvd) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1012 (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].
% 1.47/1.86 1013 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1014 (all T_2 all T_1 (class_Lattices_Oboolean__algebra(T_1) -> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1015 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1016 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1017 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1018 (all T_2 all T_1 (class_Groups_Ouminus(T_1) -> class_Groups_Ouminus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1019 (all T_2 all T_1 (class_Groups_Ominus(T_1) -> class_Groups_Ominus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1020 (all T_1 (class_Rings_Oidom(T_1) -> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1021 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1022 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1023 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1024 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1025 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1026 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1027 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1028 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1029 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1030 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1031 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1032 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1033 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1034 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1035 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1036 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1037 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1038 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1039 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1040 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1041 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1042 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1043 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1044 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1045 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1046 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1047 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1048 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1049 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1050 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1051 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Nat_Osemiring__char__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1052 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__group__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1053 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1054 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1055 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1056 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1057 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1058 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1059 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1060 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1061 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1062 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1063 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Omult__zero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1064 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1065 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1066 (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].
% 1.47/1.86 1067 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1068 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1069 (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].
% 1.47/1.86 1070 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1071 (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].
% 1.47/1.86 1072 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Power_Opower(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Power_Opower) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1073 (all T_1 (class_Groups_Ozero(T_1) -> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1074 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Oring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1075 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oidom) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1076 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Oone(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oone) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1077 (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].
% 1.47/1.86 1078 (all V_P all T_a hAPP(c_COMBI(T_a),V_P) = V_P) # label(help_c__COMBI__1) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.86 1079 (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].
% 1.47/1.86 1080 (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].
% 1.47/1.95 1081 (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].
% 1.47/1.95 1082 (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].
% 1.47/1.95 1083 (all V_y_2 all V_x_2 (-hBOOL(hAPP(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].
% 1.47/1.95 1084 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(c_fequal(V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption].
% 1.47/1.95 1085 (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].
% 1.47/1.95 1086 (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].
% 1.47/1.95 1087 (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].
% 1.47/1.95 1088 (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].
% 1.47/1.95 1089 (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].
% 1.47/1.95
% 1.47/1.95 ============================== end of process non-clausal formulas ===
% 1.47/1.95
% 1.47/1.95 ============================== PROCESS INITIAL CLAUSES ===============
% 1.47/1.95
% 1.47/1.95 ============================== PREDICATE ELIMINATION =================
% 1.47/1.95 1090 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 1.47/1.95 1091 -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(5)].
% 1.47/1.95 1092 -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(5)].
% 1.47/1.95 1093 -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(14)].
% 1.47/1.95 1094 -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(14)].
% 1.47/1.95 1095 -class_Int_Oring__char__0(A) | c_Int_Oring__1__class_Oof__int(A,B) != c_Int_Oring__1__class_Oof__int(A,C) | B = C # label(fact_of__int__eq__iff) # label(axiom). [clausify(840)].
% 1.47/1.95 1096 -class_Int_Oring__char__0(A) | c_Int_Oring__1__class_Oof__int(A,B) = c_Int_Oring__1__class_Oof__int(A,C) | B != C # label(fact_of__int__eq__iff) # label(axiom). [clausify(840)].
% 1.47/1.95 1097 -class_Int_Oring__char__0(A) | c_Int_Oring__1__class_Oof__int(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B # label(fact_of__int__0__eq__iff) # label(axiom). [clausify(848)].
% 1.47/1.95 1098 -class_Int_Oring__char__0(A) | c_Int_Oring__1__class_Oof__int(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B # label(fact_of__int__0__eq__iff) # label(axiom). [clausify(848)].
% 1.47/1.95 1099 -class_Int_Oring__char__0(A) | c_Int_Oring__1__class_Oof__int(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B # label(fact_of__int__eq__0__iff) # label(axiom). [clausify(849)].
% 1.47/1.95 1100 -class_Int_Oring__char__0(A) | c_Int_Oring__1__class_Oof__int(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B # label(fact_of__int__eq__0__iff) # label(axiom). [clausify(849)].
% 1.47/2.05 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) != c_Polynomial_Opoly(tc_Int_Oint,B) | A = B. [resolve(1090,a,1091,a)].
% 1.47/2.05 Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) = c_Polynomial_Opoly(tc_Int_Oint,B) | A != B. [resolve(1090,a,1092,a)].
% 1.47/2.05 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) != c_Int_Oring__1__class_Oof__int(tc_Int_Oint,B) | A = B. [resolve(1090,a,1095,a)].
% 1.47/2.05 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint,B) | A != B. [resolve(1090,a,1096,a)].
% 1.47/2.05 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1090,a,1097,a)].
% 1.47/2.05 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1090,a,1098,a)].
% 1.47/2.05 1101 -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(1066)].
% 1.47/2.05 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(1101,b,1091,a)].
% 1.47/2.05 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(1101,b,1092,a)].
% 1.47/2.05 Derived: -class_Rings_Olinordered__idom(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) != c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1101,b,1095,a)].
% 1.47/2.05 Derived: -class_Rings_Olinordered__idom(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) = c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1101,b,1096,a)].
% 1.47/2.05 Derived: -class_Rings_Olinordered__idom(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1101,b,1097,a)].
% 1.47/2.05 Derived: -class_Rings_Olinordered__idom(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1101,b,1098,a)].
% 1.47/2.05 1102 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 1.47/2.05 1103 -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(49)].
% 1.47/2.05 1104 -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(49)].
% 1.47/2.05 1105 -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(49)].
% 1.47/2.05 1106 -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(243)].
% 1.47/2.05 1107 -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(243)].
% 1.47/2.05 1108 -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(243)].
% 1.47/2.05 1109 -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(243)].
% 1.47/2.05 1110 -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(243)].
% 1.47/2.05 1111 -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(243)].
% 1.47/2.05 1112 -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(244)].
% 1.47/2.05 1113 -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(244)].
% 1.47/2.05 1114 -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(244)].
% 1.47/2.05 1115 -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(244)].
% 1.47/2.05 1116 -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(244)].
% 1.47/2.05 1117 -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(244)].
% 1.47/2.05 1118 -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(268)].
% 1.47/2.05 1119 -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(268)].
% 1.47/2.05 1120 -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(268)].
% 1.47/2.05 1121 -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(615)].
% 1.47/2.05 1122 -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(615)].
% 1.47/2.05 1123 -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(615)].
% 1.47/2.05 1124 -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(615)].
% 1.47/2.05 1125 -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(615)].
% 1.47/2.05 1126 -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(615)].
% 1.47/2.05 1127 -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(616)].
% 1.47/2.05 1128 -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(616)].
% 1.47/2.05 1129 -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(616)].
% 1.47/2.05 1130 -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(616)].
% 1.47/2.05 1131 -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(616)].
% 1.47/2.05 1132 -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(616)].
% 1.47/2.05 1133 -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(617)].
% 1.47/2.05 1134 -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(617)].
% 1.47/2.05 1135 -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(623)].
% 1.47/2.05 1136 -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(623)].
% 1.47/2.05 1137 -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(625)].
% 1.47/2.05 1138 -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(629)].
% 1.47/2.05 1139 -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(630)].
% 1.47/2.05 1140 -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(683)].
% 1.47/2.05 1141 -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(683)].
% 1.47/2.05 1142 -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(684)].
% 1.47/2.05 1143 -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(684)].
% 1.47/2.05 1144 -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(702)].
% 1.47/2.05 1145 -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(702)].
% 1.47/2.05 1146 -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(702)].
% 1.47/2.05 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(1102,a,1103,a)].
% 1.47/2.05 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(1102,a,1104,a)].
% 1.47/2.05 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(1102,a,1105,a)].
% 1.47/2.05 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(1102,a,1106,a)].
% 1.47/2.05 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(1102,a,1107,a)].
% 1.47/2.05 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(1102,a,1108,a)].
% 1.47/2.05 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(1102,a,1109,a)].
% 1.47/2.05 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(1102,a,1110,a)].
% 1.47/2.05 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(1102,a,1111,a)].
% 1.47/2.05 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_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(1102,a,1112,a)].
% 1.47/2.05 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_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(1102,a,1113,a)].
% 1.47/2.05 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_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(1102,a,1114,a)].
% 1.47/2.05 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_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(1102,a,1115,a)].
% 1.47/2.05 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_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(1102,a,1116,a)].
% 1.47/2.05 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_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(1102,a,1117,a)].
% 1.47/2.05 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(1102,a,1118,a)].
% 1.47/2.05 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(1102,a,1119,a)].
% 1.47/2.05 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(1102,a,1120,a)].
% 1.47/2.05 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(1102,a,1121,a)].
% 1.47/2.05 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(1102,a,1122,a)].
% 1.47/2.05 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(1102,a,1123,a)].
% 1.47/2.05 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(1102,a,1124,a)].
% 1.47/2.05 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(1102,a,1125,a)].
% 1.47/2.05 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(1102,a,1126,a)].
% 1.47/2.05 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(1102,a,1127,a)].
% 1.47/2.05 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(1102,a,1128,a)].
% 1.47/2.05 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(1102,a,1129,a)].
% 1.47/2.05 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(1102,a,1130,a)].
% 1.47/2.05 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(1102,a,1131,a)].
% 1.47/2.05 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(1102,a,1132,a)].
% 1.47/2.05 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(1102,a,1133,a)].
% 1.47/2.05 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(1102,a,1135,a)].
% 1.47/2.05 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(1102,a,1137,a)].
% 1.47/2.06 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(1102,a,1140,a)].
% 1.47/2.06 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(1102,a,1141,a)].
% 1.47/2.06 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(1102,a,1142,a)].
% 1.47/2.06 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(1102,a,1143,a)].
% 1.47/2.06 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(1102,a,1144,a)].
% 1.47/2.06 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(1102,a,1145,a)].
% 1.47/2.06 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(1102,a,1146,a)].
% 1.47/2.06 1147 -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(1032)].
% 1.47/2.06 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)),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(1147,b,1103,a)].
% 1.47/2.06 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)),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(1147,b,1104,a)].
% 1.47/2.06 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)),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(1147,b,1105,a)].
% 1.47/2.06 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(1147,b,1106,a)].
% 1.47/2.06 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(1147,b,1107,a)].
% 1.47/2.06 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(1147,b,1108,a)].
% 1.47/2.06 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(1147,b,1109,a)].
% 1.47/2.06 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(1147,b,1110,a)].
% 1.47/2.06 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(1147,b,1111,a)].
% 1.47/2.06 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),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(1147,b,1112,a)].
% 1.47/2.06 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),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(1147,b,1113,a)].
% 1.47/2.06 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),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(1147,b,1114,a)].
% 1.47/2.06 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),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(1147,b,1115,a)].
% 1.47/2.06 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),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(1147,b,1116,a)].
% 1.47/2.06 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),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(1147,b,1117,a)].
% 1.47/2.06 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)),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(1147,b,1118,a)].
% 1.47/2.06 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)),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(1147,b,1119,a)].
% 1.47/2.06 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)),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(1147,b,1120,a)].
% 1.47/2.06 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),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(1147,b,1121,a)].
% 1.47/2.06 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),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(1147,b,1122,a)].
% 1.47/2.06 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),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(1147,b,1123,a)].
% 1.47/2.06 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),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(1147,b,1124,a)].
% 1.47/2.06 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),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(1147,b,1125,a)].
% 1.47/2.06 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),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(1147,b,1126,a)].
% 1.47/2.06 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),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(1147,b,1127,a)].
% 1.47/2.06 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),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(1147,b,1128,a)].
% 1.47/2.06 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),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(1147,b,1129,a)].
% 1.47/2.06 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),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(1147,b,1130,a)].
% 1.47/2.06 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),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(1147,b,1131,a)].
% 1.47/2.06 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),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(1147,b,1132,a)].
% 1.47/2.06 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))),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(1147,b,1133,a)].
% 1.47/2.06 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(1147,b,1135,a)].
% 1.47/2.06 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(1147,b,1137,a)].
% 1.47/2.06 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))),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(1147,b,1140,a)].
% 1.47/2.06 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))),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(1147,b,1141,a)].
% 1.47/2.06 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(1147,b,1142,a)].
% 1.47/2.16 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(1147,b,1143,a)].
% 1.47/2.16 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(1147,b,1144,a)].
% 1.47/2.16 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(1147,b,1145,a)].
% 1.47/2.16 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(1147,b,1146,a)].
% 1.47/2.16 1148 -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(980)].
% 1.47/2.16 1149 -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(50)].
% 1.47/2.16 1150 -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(57)].
% 1.47/2.16 1151 -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(57)].
% 1.47/2.16 1152 -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(57)].
% 1.47/2.16 1153 -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(88)].
% 1.97/2.17 1154 -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(88)].
% 1.97/2.17 1155 -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(91)].
% 1.97/2.17 1156 -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(91)].
% 1.97/2.17 1157 -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(91)].
% 1.97/2.17 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(1148,b,1149,a)].
% 1.97/2.17 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(1148,b,1150,a)].
% 1.97/2.17 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(1148,b,1151,a)].
% 1.97/2.17 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(1148,b,1152,a)].
% 1.97/2.17 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != B | c_Groups_Ozero__class_Ozero(A) = C. [resolve(1148,b,1153,a)].
% 1.97/2.17 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = B | c_Groups_Ozero__class_Ozero(A) != C. [resolve(1148,b,1154,a)].
% 1.97/2.17 1158 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].
% 1.97/2.17 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(1158,a,1149,a)].
% 1.97/2.17 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(1158,a,1150,a)].
% 1.97/2.18 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(1158,a,1151,a)].
% 1.97/2.18 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(1158,a,1152,a)].
% 1.97/2.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(1158,a,1153,a)].
% 1.97/2.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(1158,a,1154,a)].
% 1.97/2.18 1159 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].
% 1.97/2.18 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(1159,a,1149,a)].
% 1.97/2.18 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(1159,a,1150,a)].
% 1.97/2.18 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(1159,a,1151,a)].
% 1.97/2.18 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(1159,a,1152,a)].
% 1.97/2.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1159,a,1153,a)].
% 1.97/2.18 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1159,a,1154,a)].
% 1.97/2.18 1160 -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(1020)].
% 1.97/2.18 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(1160,b,1149,a)].
% 1.97/2.18 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(1160,b,1150,a)].
% 2.14/2.41 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(1160,b,1151,a)].
% 2.14/2.41 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(1160,b,1152,a)].
% 2.14/2.41 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(1160,b,1153,a)].
% 2.14/2.41 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(1160,b,1154,a)].
% 2.14/2.41 1161 -class_Rings_Oidom(A) | class_Rings_Ocomm__semiring(A) # label(clrel_Rings_Oidom__Rings_Ocomm__semiring) # label(axiom). [clausify(992)].
% 2.14/2.41 1162 -class_Rings_Ocomm__semiring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(58)].
% 2.14/2.41 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)). [resolve(1161,b,1162,a)].
% 2.14/2.41 1163 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 2.14/2.41 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(1163,a,1162,a)].
% 2.14/2.41 1164 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 2.14/2.41 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(1164,a,1162,a)].
% 2.14/2.41 1165 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1050)].
% 2.14/2.41 Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(1165,b,1162,a)].
% 2.14/2.41 1166 -class_Rings_Oidom(A) | class_Rings_Ono__zero__divisors(A) # label(clrel_Rings_Oidom__Rings_Ono__zero__divisors) # label(axiom). [clausify(988)].
% 2.14/2.42 1167 -class_Rings_Ono__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_divisors__zero) # label(axiom). [clausify(77)].
% 2.14/2.42 1168 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) # label(fact_no__zero__divisors) # label(axiom). [clausify(78)].
% 2.14/2.42 1169 -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(285)].
% 2.14/2.42 1170 -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(285)].
% 2.14/2.42 1171 -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(285)].
% 2.14/2.42 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(1166,b,1167,a)].
% 2.14/2.42 Derived: -class_Rings_Oidom(A) | -class_Power_Opower(A) | -class_Rings_Omult__zero(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. [resolve(1166,b,1169,c)].
% 2.14/2.42 Derived: -class_Rings_Oidom(A) | -class_Power_Opower(A) | -class_Rings_Omult__zero(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(1166,b,1170,c)].
% 2.14/2.42 Derived: -class_Rings_Oidom(A) | -class_Power_Opower(A) | -class_Rings_Omult__zero(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(1166,b,1171,c)].
% 2.14/2.42 1172 class_Rings_Ono__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.14/2.42 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(1172,a,1167,a)].
% 2.14/2.42 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(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. [resolve(1172,a,1169,c)].
% 2.14/2.42 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(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(1172,a,1170,c)].
% 2.14/2.42 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Omult__zero(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(1172,a,1171,c)].
% 2.14/2.42 1173 class_Rings_Ono__zero__divisors(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.30/2.50 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1173,a,1167,a)].
% 2.30/2.50 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(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(1173,a,1169,c)].
% 2.30/2.50 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(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(1173,a,1170,c)].
% 2.30/2.50 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Omult__zero(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(1173,a,1171,c)].
% 2.30/2.50 1174 -class_Rings_Oidom(A) | class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom). [clausify(1044)].
% 2.30/2.50 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(1174,b,1167,a)].
% 2.30/2.50 Derived: -class_Rings_Oidom(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Omult__zero(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(1174,b,1169,c)].
% 2.30/2.50 Derived: -class_Rings_Oidom(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Omult__zero(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(1174,b,1170,c)].
% 2.30/2.50 Derived: -class_Rings_Oidom(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Omult__zero(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(1174,b,1171,c)].
% 2.30/2.50 1175 -class_Rings_Oidom(A) | class_Rings_Oring__no__zero__divisors(A) # label(clrel_Rings_Oidom__Rings_Oring__no__zero__divisors) # label(axiom). [clausify(983)].
% 2.30/2.50 1176 -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(79)].
% 2.30/2.50 1177 -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(79)].
% 2.30/2.50 1178 -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(79)].
% 2.30/2.50 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(1175,b,1177,a)].
% 2.30/2.50 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(1175,b,1178,a)].
% 2.45/2.67 1179 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.45/2.67 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(1179,a,1177,a)].
% 2.45/2.67 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(1179,a,1178,a)].
% 2.45/2.67 1180 -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(1033)].
% 2.45/2.67 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(1180,b,1177,a)].
% 2.45/2.67 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(1180,b,1178,a)].
% 2.45/2.67 1181 -class_Rings_Oidom(A) | class_Rings_Osemiring(A) # label(clrel_Rings_Oidom__Rings_Osemiring) # label(axiom). [clausify(1003)].
% 2.45/2.67 1182 -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(92)].
% 2.45/2.67 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(1181,b,1182,a)].
% 2.45/2.67 1183 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 2.45/2.67 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(1183,a,1182,a)].
% 2.45/2.67 1184 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 2.45/2.67 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(1184,a,1182,a)].
% 2.45/2.67 1185 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom). [clausify(1067)].
% 2.45/2.67 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(1185,b,1182,a)].
% 2.45/2.67 1186 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 2.45/2.67 1187 -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(96)].
% 2.45/2.67 1188 -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(96)].
% 2.45/2.67 1189 -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(99)].
% 2.45/2.67 1190 -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(99)].
% 2.45/2.67 1191 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_equal__neg__zero) # label(axiom). [clausify(119)].
% 2.45/2.67 1192 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_equal__neg__zero) # label(axiom). [clausify(119)].
% 2.45/2.67 1193 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__zero) # label(axiom). [clausify(121)].
% 2.45/2.67 1194 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__zero) # label(axiom). [clausify(121)].
% 2.45/2.67 1195 -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(251)].
% 2.45/2.67 1196 -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(251)].
% 2.45/2.67 1197 -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(252)].
% 2.45/2.67 1198 -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(252)].
% 2.45/2.67 1199 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(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(255)].
% 2.45/2.67 1200 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(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(255)].
% 2.45/2.67 1201 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),hAPP(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(257)].
% 2.45/2.67 1202 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),hAPP(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(257)].
% 2.45/2.67 1203 -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(631)].
% 2.45/2.67 1204 -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(631)].
% 2.45/2.67 1205 -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(633)].
% 2.45/2.67 1206 -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(633)].
% 2.45/2.67 1207 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(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(644)].
% 2.45/2.67 1208 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(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(644)].
% 2.45/2.67 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(1186,a,1187,a)].
% 2.45/2.67 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(1186,a,1188,a)].
% 2.45/2.67 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1186,a,1191,a)].
% 2.45/2.67 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1186,a,1192,a)].
% 2.45/2.67 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(1186,a,1195,a)].
% 2.45/2.67 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(1186,a,1196,a)].
% 2.45/2.67 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(1186,a,1197,a)].
% 2.45/2.67 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(1186,a,1198,a)].
% 2.45/2.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1186,a,1199,a)].
% 2.45/2.67 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1186,a,1200,a)].
% 2.45/2.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),hAPP(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(1186,a,1201,a)].
% 2.45/2.67 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),hAPP(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(1186,a,1202,a)].
% 2.45/2.67 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(1186,a,1203,a)].
% 2.45/2.67 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(1186,a,1204,a)].
% 2.45/2.67 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(1186,a,1205,a)].
% 2.45/2.67 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(1186,a,1206,a)].
% 2.45/2.67 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(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(1186,a,1207,a)].
% 2.45/2.67 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(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(1186,a,1208,a)].
% 2.45/2.67 1209 -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(1028)].
% 2.45/2.67 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(1209,b,1187,a)].
% 2.45/2.67 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(1209,b,1188,a)].
% 2.45/2.67 Derived: -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1209,b,1191,a)].
% 2.45/2.67 Derived: -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1209,b,1192,a)].
% 2.45/2.67 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(1209,b,1195,a)].
% 2.45/2.67 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(1209,b,1196,a)].
% 2.45/2.67 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(1209,b,1197,a)].
% 2.45/2.67 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(1209,b,1198,a)].
% 2.45/2.67 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(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(1209,b,1199,a)].
% 2.45/2.67 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(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(1209,b,1200,a)].
% 2.45/2.67 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),hAPP(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(1209,b,1201,a)].
% 2.45/2.67 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),hAPP(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(1209,b,1202,a)].
% 2.45/2.67 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(1209,b,1203,a)].
% 2.45/2.67 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(1209,b,1204,a)].
% 2.45/2.67 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(1209,b,1205,a)].
% 2.45/2.67 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(1209,b,1206,a)].
% 2.54/2.84 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(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(1209,b,1207,a)].
% 2.54/2.84 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(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(1209,b,1208,a)].
% 2.54/2.84 1210 -class_Rings_Oidom(A) | class_Groups_Omonoid__add(A) # label(clrel_Rings_Oidom__Groups_Omonoid__add) # label(axiom). [clausify(997)].
% 2.54/2.84 1211 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(98)].
% 2.54/2.84 1212 -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(101)].
% 2.54/2.84 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B. [resolve(1210,b,1211,a)].
% 2.54/2.84 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B. [resolve(1210,b,1212,a)].
% 2.54/2.84 1213 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.54/2.84 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1213,a,1211,a)].
% 2.54/2.84 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(1213,a,1212,a)].
% 2.54/2.84 1214 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.54/2.84 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1214,a,1211,a)].
% 2.54/2.84 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A. [resolve(1214,a,1212,a)].
% 2.54/2.84 1215 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom). [clausify(1059)].
% 2.54/2.84 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1215,b,1211,a)].
% 2.54/2.84 Derived: -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = B. [resolve(1215,b,1212,a)].
% 2.54/2.84 1216 -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(982)].
% 2.54/2.84 1217 -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 | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) = B # label(fact_square__eq__1__iff) # label(axiom). [clausify(107)].
% 2.54/2.84 1218 -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(107)].
% 2.54/2.84 1219 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(107)].
% 2.71/2.93 1220 -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(300)].
% 2.71/2.93 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 | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) = B. [resolve(1216,b,1217,a)].
% 2.71/2.93 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(1216,b,1218,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) != B. [resolve(1216,b,1219,a)].
% 2.71/2.93 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(1216,b,1220,a)].
% 2.71/2.93 1221 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.71/2.93 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 | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1221,a,1217,a)].
% 2.71/2.93 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(1221,a,1218,a)].
% 2.71/2.93 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) != A. [resolve(1221,a,1219,a)].
% 2.71/2.93 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(1221,a,1220,a)].
% 2.71/2.93 1222 -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(1030)].
% 2.71/2.93 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 | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1222,b,1217,a)].
% 2.71/2.93 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(1222,b,1218,a)].
% 2.71/2.93 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) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) != B. [resolve(1222,b,1219,a)].
% 2.71/2.93 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(1222,b,1220,a)].
% 2.71/2.93 1223 -class_Rings_Oidom(A) | class_Groups_Ogroup__add(A) # label(clrel_Rings_Oidom__Groups_Ogroup__add) # label(axiom). [clausify(1000)].
% 2.71/2.93 1224 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) = B # label(fact_minus__minus) # label(axiom). [clausify(108)].
% 2.71/2.93 1225 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) = B # label(fact_equation__minus__iff) # label(axiom). [clausify(110)].
% 2.71/2.93 1226 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) != B # label(fact_equation__minus__iff) # label(axiom). [clausify(110)].
% 2.71/2.93 1227 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) = B # label(fact_minus__equation__iff) # label(axiom). [clausify(111)].
% 2.71/2.93 1228 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) != B # label(fact_minus__equation__iff) # label(axiom). [clausify(111)].
% 2.71/2.93 1229 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != hAPP(c_Groups_Ouminus__class_Ouminus(A),C) | B = C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(112)].
% 2.71/2.93 1230 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),C) | B != C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(112)].
% 2.71/2.93 1231 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_minus__zero) # label(axiom). [clausify(117)].
% 2.71/2.93 1232 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(118)].
% 2.71/2.93 1233 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(118)].
% 2.71/2.93 1234 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(120)].
% 2.71/2.93 1235 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(120)].
% 2.71/2.93 1236 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_minus__add) # label(axiom). [clausify(125)].
% 2.71/2.93 1237 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) = C # label(fact_add__minus__cancel) # label(axiom). [clausify(126)].
% 2.71/2.93 1238 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(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(127)].
% 2.71/2.93 1239 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_right__minus) # label(axiom). [clausify(150)].
% 2.71/2.93 1240 -class_Groups_Ogroup__add(A) | hAPP(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(151)].
% 2.71/2.93 1241 -class_Groups_Ogroup__add(A) | hAPP(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(151)].
% 2.71/2.93 1242 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B) # label(fact_left__minus) # label(axiom). [clausify(152)].
% 2.71/2.93 1243 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C # label(fact_minus__unique) # label(axiom). [clausify(154)].
% 2.71/2.93 1244 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C # label(fact_add__eq__0__iff) # label(axiom). [clausify(172)].
% 2.71/2.93 1245 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C # label(fact_add__eq__0__iff) # label(axiom). [clausify(172)].
% 2.71/2.93 1246 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_diff__0) # label(axiom). [clausify(875)].
% 2.71/2.93 1247 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_diff__def) # label(axiom). [clausify(876)].
% 2.71/2.93 1248 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),hAPP(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(878)].
% 2.71/2.93 1249 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),C) = B # label(fact_add__diff__cancel) # label(axiom). [clausify(931)].
% 2.71/2.93 1250 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(932)].
% 2.71/2.93 1251 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | B = C # label(fact_right__minus__eq) # label(axiom). [clausify(938)].
% 2.71/2.93 1252 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | B != C # label(fact_right__minus__eq) # label(axiom). [clausify(938)].
% 2.71/2.93 1253 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),B) # label(fact_diff__self) # label(axiom). [clausify(940)].
% 2.71/2.93 1254 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(941)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) = B. [resolve(1223,b,1224,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) = B. [resolve(1223,b,1225,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != hAPP(c_Groups_Ouminus__class_Ouminus(A),C) | B = C. [resolve(1223,b,1229,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),C) | B != C. [resolve(1223,b,1230,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Ozero__class_Ozero(A)). [resolve(1223,b,1231,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) = B. [resolve(1223,b,1232,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) != B. [resolve(1223,b,1233,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). [resolve(1223,b,1236,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) = C. [resolve(1223,b,1237,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = C. [resolve(1223,b,1238,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)). [resolve(1223,b,1239,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(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(1223,b,1240,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(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(1223,b,1241,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B). [resolve(1223,b,1242,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C. [resolve(1223,b,1243,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C. [resolve(1223,b,1245,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Groups_Ozero__class_Ozero(A)),B). [resolve(1223,b,1246,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)). [resolve(1223,b,1247,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C). [resolve(1223,b,1248,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),C) = B. [resolve(1223,b,1249,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),C) = B. [resolve(1223,b,1250,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | B = C. [resolve(1223,b,1251,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | B != C. [resolve(1223,b,1252,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),B). [resolve(1223,b,1253,a)].
% 2.71/2.93 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Ozero__class_Ozero(A)) = B. [resolve(1223,b,1254,a)].
% 2.71/2.93 1255 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 2.71/2.93 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = A. [resolve(1255,a,1224,a)].
% 2.71/2.93 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != B | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B) = A. [resolve(1255,a,1225,a)].
% 2.71/2.93 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B) | A = B. [resolve(1255,a,1229,a)].
% 2.71/2.93 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B) | A != B. [resolve(1255,a,1230,a)].
% 2.71/2.93 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(1255,a,1231,a)].
% 2.71/2.93 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(1255,a,1232,a)].
% 2.71/2.93 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(1255,a,1233,a)].
% 2.71/2.93 Derived: hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(1255,a,1236,a)].
% 2.71/2.93 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = B. [resolve(1255,a,1237,a)].
% 2.71/2.94 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)) = B. [resolve(1255,a,1238,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(1255,a,1239,a)].
% 2.71/2.94 Derived: hAPP(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(1255,a,1240,a)].
% 2.71/2.94 Derived: hAPP(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(1255,a,1241,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),A). [resolve(1255,a,1242,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = B. [resolve(1255,a,1243,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != B. [resolve(1255,a,1245,a)].
% 2.71/2.94 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(1255,a,1246,a)].
% 2.71/2.94 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(1255,a,1247,a)].
% 2.71/2.94 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B). [resolve(1255,a,1248,a)].
% 2.71/2.94 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),B) = A. [resolve(1255,a,1249,a)].
% 2.71/2.94 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A. [resolve(1255,a,1250,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) | A = B. [resolve(1255,a,1251,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) | A != B. [resolve(1255,a,1252,a)].
% 2.71/2.94 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),A). [resolve(1255,a,1253,a)].
% 2.71/2.94 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(1255,a,1254,a)].
% 2.71/2.94 1256 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom). [clausify(1062)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)) = B. [resolve(1256,b,1224,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) != C | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C) = B. [resolve(1256,b,1225,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C) | B = C. [resolve(1256,b,1229,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C) | B != C. [resolve(1256,b,1230,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1256,b,1231,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1256,b,1232,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1256,b,1233,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(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)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)). [resolve(1256,b,1236,a)].
% 2.71/2.94 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)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C)) = C. [resolve(1256,b,1237,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(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(1256,b,1238,a)].
% 2.71/2.94 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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)). [resolve(1256,b,1239,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(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(1256,b,1240,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(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(1256,b,1241,a)].
% 2.71/2.94 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)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),B). [resolve(1256,b,1242,a)].
% 2.71/2.94 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) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) = C. [resolve(1256,b,1243,a)].
% 2.71/2.94 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) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) != C. [resolve(1256,b,1245,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B). [resolve(1256,b,1246,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)). [resolve(1256,b,1247,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C). [resolve(1256,b,1248,a)].
% 2.71/2.94 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),C) = B. [resolve(1256,b,1249,a)].
% 2.77/3.02 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),C) = B. [resolve(1256,b,1250,a)].
% 2.77/3.02 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) | B = C. [resolve(1256,b,1251,a)].
% 2.77/3.02 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) | B != C. [resolve(1256,b,1252,a)].
% 2.77/3.02 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),B). [resolve(1256,b,1253,a)].
% 2.77/3.02 Derived: -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1256,b,1254,a)].
% 2.77/3.02 1257 -class_Rings_Oidom(A) | class_Groups_Omonoid__mult(A) # label(clrel_Rings_Oidom__Groups_Omonoid__mult) # label(axiom). [clausify(995)].
% 2.77/3.02 1258 -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(128)].
% 2.77/3.02 1259 -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(130)].
% 2.77/3.02 1260 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(fact_power__add) # label(axiom). [clausify(283)].
% 2.77/3.02 1261 -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(299)].
% 2.77/3.02 1262 -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(302)].
% 2.77/3.02 1263 -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(303)].
% 2.77/3.02 1264 -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(308)].
% 2.77/3.02 1265 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(fact_power__Suc2) # label(axiom). [clausify(367)].
% 2.77/3.02 1266 -class_Groups_Omonoid__mult(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C) # label(fact_realpow__minus__mult) # label(axiom). [clausify(857)].
% 2.77/3.02 1267 -class_Groups_Omonoid__mult(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,C)),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B))),D) # label(fact_lemma__realpow__diff) # label(axiom). [clausify(973)].
% 2.77/3.03 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B. [resolve(1257,b,1258,a)].
% 2.77/3.03 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B. [resolve(1257,b,1259,a)].
% 2.77/3.03 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)). [resolve(1257,b,1260,a)].
% 2.77/3.03 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(1257,b,1261,a)].
% 2.77/3.03 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(1257,b,1262,a)].
% 2.77/3.03 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(1257,b,1263,a)].
% 2.77/3.03 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B. [resolve(1257,b,1264,a)].
% 2.77/3.03 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B). [resolve(1257,b,1265,a)].
% 2.77/3.03 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_Power_Opower__class_Opower(A),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C). [resolve(1257,b,1266,a)].
% 2.77/3.03 Derived: -class_Rings_Oidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,C)),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B))),D). [resolve(1257,b,1267,a)].
% 2.77/3.03 1268 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.77/3.03 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(1268,a,1258,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(1268,a,1259,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)). [resolve(1268,a,1260,a)].
% 2.77/3.03 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(1268,a,1261,a)].
% 2.77/3.03 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(1268,a,1262,a)].
% 2.77/3.03 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(1268,a,1263,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1268,a,1264,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A). [resolve(1268,a,1265,a)].
% 2.77/3.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B). [resolve(1268,a,1266,a)].
% 2.77/3.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,B)),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A))),C). [resolve(1268,a,1267,a)].
% 2.77/3.03 1269 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.77/3.03 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(1269,a,1258,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1269,a,1259,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)). [resolve(1269,a,1260,a)].
% 2.77/3.03 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(1269,a,1261,a)].
% 2.77/3.03 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(1269,a,1262,a)].
% 2.77/3.03 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(1269,a,1263,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1269,a,1264,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A). [resolve(1269,a,1265,a)].
% 2.77/3.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),B). [resolve(1269,a,1266,a)].
% 2.77/3.03 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,B)),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A))),C). [resolve(1269,a,1267,a)].
% 2.77/3.03 1270 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1057)].
% 2.77/3.03 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(1270,b,1258,a)].
% 2.77/3.03 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(1270,b,1259,a)].
% 2.90/3.12 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)). [resolve(1270,b,1260,a)].
% 2.90/3.12 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(1270,b,1261,a)].
% 2.90/3.12 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(1270,b,1262,a)].
% 2.90/3.12 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(1270,b,1263,a)].
% 2.90/3.12 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(1270,b,1264,a)].
% 2.90/3.12 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B). [resolve(1270,b,1265,a)].
% 2.90/3.12 Derived: -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C). [resolve(1270,b,1266,a)].
% 2.90/3.12 Derived: -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,C)),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B))),D). [resolve(1270,b,1267,a)].
% 2.90/3.12 1271 -class_Rings_Oidom(A) | class_Groups_Ocomm__monoid__mult(A) # label(clrel_Rings_Oidom__Groups_Ocomm__monoid__mult) # label(axiom). [clausify(986)].
% 2.90/3.12 1272 -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(129)].
% 2.90/3.12 1273 -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(131)].
% 2.90/3.12 1274 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__mult__distrib) # label(axiom). [clausify(301)].
% 2.90/3.12 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)). [resolve(1271,b,1274,a)].
% 2.90/3.12 1275 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.92/3.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(1275,a,1274,a)].
% 2.92/3.21 1276 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.92/3.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)). [resolve(1276,a,1274,a)].
% 2.92/3.21 1277 -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(1041)].
% 2.92/3.21 Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)). [resolve(1277,b,1274,a)].
% 2.92/3.21 1278 -class_Rings_Oidom(A) | class_Rings_Oring(A) # label(clrel_Rings_Oidom__Rings_Oring) # label(axiom). [clausify(1009)].
% 2.92/3.21 1279 -class_Rings_Oring(A) | hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__mult__right) # label(axiom). [clausify(135)].
% 2.92/3.21 1280 -class_Rings_Oring(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) # label(fact_minus__mult__left) # label(axiom). [clausify(136)].
% 2.92/3.21 1281 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__mult__commute) # label(axiom). [clausify(141)].
% 2.92/3.21 1282 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(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(142)].
% 2.92/3.21 1283 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),E)) # label(fact_mult__diff__mult) # label(axiom). [clausify(871)].
% 2.92/3.21 1284 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(fact_eq__add__iff1) # label(axiom). [clausify(872)].
% 2.92/3.21 1285 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) != F # label(fact_eq__add__iff1) # label(axiom). [clausify(872)].
% 2.92/3.21 1286 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) = D # label(fact_eq__add__iff2) # label(axiom). [clausify(873)].
% 2.92/3.22 1287 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) != D # label(fact_eq__add__iff2) # label(axiom). [clausify(873)].
% 2.92/3.22 Derived: -class_Rings_Oidom(A) | hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)). [resolve(1278,b,1279,a)].
% 2.92/3.22 Derived: -class_Rings_Oidom(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C). [resolve(1278,b,1280,a)].
% 2.92/3.22 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)). [resolve(1278,b,1281,a)].
% 2.92/3.22 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C). [resolve(1278,b,1282,a)].
% 2.92/3.22 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),E)). [resolve(1278,b,1283,a)].
% 2.92/3.22 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) = F. [resolve(1278,b,1284,a)].
% 2.92/3.22 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) != F. [resolve(1278,b,1285,a)].
% 2.92/3.22 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) = D. [resolve(1278,b,1286,a)].
% 2.92/3.22 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) != D. [resolve(1278,b,1287,a)].
% 2.92/3.22 1288 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption].
% 2.92/3.22 Derived: hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(1288,a,1279,a)].
% 2.92/3.22 Derived: hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B). [resolve(1288,a,1280,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(1288,a,1281,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B). [resolve(1288,a,1282,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C)),D)). [resolve(1288,a,1283,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) = E. [resolve(1288,a,1284,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) != E. [resolve(1288,a,1285,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E) = C. [resolve(1288,a,1286,a)].
% 2.92/3.22 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E) != C. [resolve(1288,a,1287,a)].
% 2.92/3.22 1289 -class_Rings_Ocomm__ring(A) | class_Rings_Oring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom). [clausify(1074)].
% 2.92/3.22 Derived: -class_Rings_Ocomm__ring(A) | hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)). [resolve(1289,b,1279,a)].
% 2.92/3.22 Derived: -class_Rings_Ocomm__ring(A) | hAPP(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)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C). [resolve(1289,b,1280,a)].
% 2.92/3.22 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)). [resolve(1289,b,1281,a)].
% 3.10/3.31 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C). [resolve(1289,b,1282,a)].
% 3.10/3.31 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),D)),E)). [resolve(1289,b,1283,a)].
% 3.10/3.31 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D) = F. [resolve(1289,b,1284,a)].
% 3.10/3.31 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D) != F. [resolve(1289,b,1285,a)].
% 3.10/3.31 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F) = D. [resolve(1289,b,1286,a)].
% 3.10/3.31 Derived: -class_Rings_Ocomm__ring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F) != D. [resolve(1289,b,1287,a)].
% 3.10/3.31 1290 -class_Rings_Oidom(A) | class_Groups_Oab__semigroup__mult(A) # label(clrel_Rings_Oidom__Groups_Oab__semigroup__mult) # label(axiom). [clausify(985)].
% 3.10/3.31 1291 -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(165)].
% 3.10/3.31 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(1290,b,1291,a)].
% 3.10/3.31 1292 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.27/3.49 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(1292,a,1291,a)].
% 3.27/3.49 1293 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.27/3.49 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(1293,a,1291,a)].
% 3.27/3.49 1294 -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(1040)].
% 3.27/3.49 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(1294,b,1291,a)].
% 3.27/3.49 1295 -class_Rings_Oidom(A) | class_Groups_Oab__semigroup__add(A) # label(clrel_Rings_Oidom__Groups_Oab__semigroup__add) # label(axiom). [clausify(987)].
% 3.27/3.49 1296 -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(166)].
% 3.27/3.49 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(1295,b,1296,a)].
% 3.27/3.49 1297 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 3.27/3.49 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(1297,a,1296,a)].
% 3.27/3.49 1298 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 3.27/3.49 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(1298,a,1296,a)].
% 3.27/3.49 1299 -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(1042)].
% 3.27/3.49 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(1299,b,1296,a)].
% 3.27/3.49 1300 -class_Rings_Oidom(A) | class_Groups_Ocancel__semigroup__add(A) # label(clrel_Rings_Oidom__Groups_Ocancel__semigroup__add) # label(axiom). [clausify(984)].
% 3.27/3.49 1301 -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(167)].
% 3.27/3.49 1302 -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(167)].
% 3.27/3.49 1303 -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(168)].
% 3.30/3.50 1304 -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(168)].
% 3.30/3.50 1305 -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(169)].
% 3.30/3.50 1306 -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(171)].
% 3.30/3.50 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(1300,b,1301,a)].
% 3.30/3.50 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(1300,b,1302,a)].
% 3.30/3.50 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(1300,b,1303,a)].
% 3.30/3.50 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(1300,b,1304,a)].
% 3.30/3.50 1307 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.30/3.50 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(1307,a,1301,a)].
% 3.30/3.50 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(1307,a,1302,a)].
% 3.30/3.50 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(1307,a,1303,a)].
% 3.30/3.50 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(1307,a,1304,a)].
% 3.30/3.50 1308 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.30/3.50 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(1308,a,1301,a)].
% 3.30/3.50 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(1308,a,1302,a)].
% 3.30/3.50 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(1308,a,1303,a)].
% 3.30/3.50 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(1308,a,1304,a)].
% 3.30/3.50 1309 -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(1037)].
% 3.30/3.50 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(1309,b,1301,a)].
% 3.30/3.50 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(1309,b,1302,a)].
% 3.30/3.50 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(1309,b,1303,a)].
% 3.30/3.50 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(1309,b,1304,a)].
% 3.51/3.78 1310 -class_Rings_Oidom(A) | class_Groups_Ocancel__ab__semigroup__add(A) # label(clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add) # label(axiom). [clausify(981)].
% 3.51/3.78 1311 -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(170)].
% 3.51/3.78 1312 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.51/3.78 1313 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.51/3.78 1314 -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(1029)].
% 3.51/3.78 1315 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 3.51/3.78 1316 -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(178)].
% 3.51/3.78 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),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(1315,a,1316,a)].
% 3.51/3.78 1317 -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(1035)].
% 3.51/3.78 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(1317,b,1316,a)].
% 3.51/3.78 1318 -class_Rings_Oidom(A) | class_Rings_Odvd(A) # label(clrel_Rings_Oidom__Rings_Odvd) # label(axiom). [clausify(1011)].
% 3.51/3.78 1319 -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(195)].
% 3.51/3.78 1320 -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),f7(C,B,A)),c_Groups_Ozero__class_Ozero(A)))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(281)].
% 3.51/3.78 1321 -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,f7(C,B,A))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(281)].
% 3.51/3.78 1322 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),f8(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(281)].
% 3.51/3.78 1323 -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),hAPP(hAPP(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(950)].
% 3.51/3.78 1324 -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),hAPP(hAPP(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(950)].
% 3.51/3.78 1325 -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),hAPP(hAPP(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(951)].
% 3.51/3.78 1326 -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),hAPP(hAPP(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(951)].
% 3.51/3.78 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(1318,b,1319,a)].
% 3.51/3.78 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),f7(C,B,A)),c_Groups_Ozero__class_Ozero(A)))). [resolve(1318,b,1320,a)].
% 3.51/3.78 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,f7(C,B,A))). [resolve(1318,b,1321,a)].
% 3.51/3.78 Derived: -class_Rings_Oidom(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),f8(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(1318,b,1322,a)].
% 3.51/3.78 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))). [resolve(1318,b,1323,b)].
% 3.51/3.78 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))). [resolve(1318,b,1324,b)].
% 3.58/3.78 1327 class_Rings_Odvd(tc_Int_Oint) # label(arity_Int__Oint__Rings_Odvd) # label(axiom). [assumption].
% 3.58/3.78 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(1327,a,1319,a)].
% 3.58/3.78 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),f7(B,A,tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). [resolve(1327,a,1320,a)].
% 3.58/3.78 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,f7(B,A,tc_Int_Oint))). [resolve(1327,a,1321,a)].
% 3.58/3.78 Derived: -class_Rings_Osemiring__0(tc_Int_Oint) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),f8(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(1327,a,1322,a)].
% 3.58/3.78 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B))),D))). [resolve(1327,a,1323,b)].
% 3.58/3.78 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B))),D))). [resolve(1327,a,1324,b)].
% 3.58/3.78 1328 class_Rings_Odvd(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Odvd) # label(axiom). [assumption].
% 3.58/3.78 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(1328,a,1319,a)].
% 3.58/3.78 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),f7(B,A,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). [resolve(1328,a,1320,a)].
% 3.58/3.78 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,f7(B,A,tc_Nat_Onat))). [resolve(1328,a,1321,a)].
% 3.58/3.78 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),f8(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(1328,a,1322,a)].
% 3.58/3.78 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),E),B))),D))). [resolve(1328,a,1323,b)].
% 3.58/3.78 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),E),B))),D))). [resolve(1328,a,1324,b)].
% 3.67/3.88 1329 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Odvd(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Odvd) # label(axiom). [clausify(1077)].
% 3.67/3.88 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(1329,b,1319,a)].
% 3.67/3.88 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)),f7(C,B,tc_Polynomial_Opoly(A))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))). [resolve(1329,b,1320,a)].
% 3.67/3.88 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,f7(C,B,tc_Polynomial_Opoly(A)))). [resolve(1329,b,1321,a)].
% 3.67/3.88 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),f8(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(1329,b,1322,a)].
% 3.67/3.88 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)),hAPP(hAPP(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(1329,b,1323,b)].
% 3.67/3.88 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)),hAPP(hAPP(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(1329,b,1324,b)].
% 3.67/3.88 1330 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 3.67/3.88 1331 -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(208)].
% 3.67/3.88 1332 -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(209)].
% 3.67/3.88 1333 -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(213)].
% 3.67/3.88 1334 -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(213)].
% 3.67/3.88 1335 -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(214)].
% 3.67/3.88 1336 -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(214)].
% 3.67/3.88 1337 -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(573)].
% 3.67/3.88 1338 -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(574)].
% 3.67/3.88 1339 -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(578)].
% 3.67/3.88 1340 -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(578)].
% 3.67/3.88 1341 -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(579)].
% 3.67/3.88 1342 -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(579)].
% 3.67/3.88 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(1330,a,1331,a)].
% 3.67/3.88 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(1330,a,1332,a)].
% 3.67/3.88 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(1330,a,1334,a)].
% 3.67/3.88 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(1330,a,1336,a)].
% 3.68/3.88 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(1330,a,1337,a)].
% 3.68/3.88 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(1330,a,1338,a)].
% 3.68/3.88 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(1330,a,1340,a)].
% 3.68/3.88 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(1330,a,1342,a)].
% 3.68/3.88 1343 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 3.68/3.88 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(1343,a,1331,a)].
% 3.68/3.88 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(1343,a,1332,a)].
% 3.68/3.88 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(1343,a,1334,a)].
% 3.68/3.88 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(1343,a,1336,a)].
% 3.68/3.88 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(1343,a,1337,a)].
% 3.68/3.88 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(1343,a,1338,a)].
% 3.68/3.88 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(1343,a,1340,a)].
% 3.68/3.88 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(1343,a,1342,a)].
% 3.68/3.88 1344 -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(1022)].
% 3.68/3.88 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(1344,b,1331,a)].
% 3.72/3.98 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(1344,b,1332,a)].
% 3.72/3.98 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(1344,b,1334,a)].
% 3.72/3.98 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(1344,b,1336,a)].
% 3.72/3.98 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(1344,b,1337,a)].
% 3.72/3.98 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(1344,b,1338,a)].
% 3.72/3.98 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(1344,b,1340,a)].
% 3.72/3.98 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(1344,b,1342,a)].
% 3.72/3.98 1345 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.72/3.98 1346 -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(210)].
% 3.72/3.98 1347 -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(211)].
% 3.72/3.98 1348 -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(212)].
% 3.72/3.98 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(1345,a,1346,a)].
% 3.81/4.08 1349 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.81/4.08 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(1349,a,1346,a)].
% 3.81/4.08 1350 -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(1026)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D),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(1350,b,1346,a)].
% 3.81/4.08 1351 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 3.81/4.08 1352 -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,hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_le__imp__neg__le) # label(axiom). [clausify(215)].
% 3.81/4.08 1353 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(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(216)].
% 3.81/4.08 1354 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(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(216)].
% 3.81/4.08 1355 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__le__iff) # label(axiom). [clausify(217)].
% 3.81/4.08 1356 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__le__iff) # label(axiom). [clausify(217)].
% 3.81/4.08 1357 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_le__minus__iff) # label(axiom). [clausify(218)].
% 3.81/4.08 1358 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_le__minus__iff) # label(axiom). [clausify(218)].
% 3.81/4.08 1359 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(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(256)].
% 3.81/4.08 1360 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,hAPP(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(256)].
% 3.81/4.08 1361 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(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(258)].
% 3.81/4.08 1362 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),hAPP(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(258)].
% 3.81/4.08 1363 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(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(570)].
% 3.81/4.08 1364 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(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(570)].
% 3.81/4.08 1365 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__less__iff) # label(axiom). [clausify(571)].
% 3.81/4.08 1366 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__less__iff) # label(axiom). [clausify(571)].
% 3.81/4.08 1367 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_less__minus__iff) # label(axiom). [clausify(572)].
% 3.81/4.08 1368 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_less__minus__iff) # label(axiom). [clausify(572)].
% 3.81/4.08 1369 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(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(641)].
% 3.81/4.08 1370 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(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(641)].
% 3.81/4.08 1371 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(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(643)].
% 3.81/4.08 1372 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(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(643)].
% 3.81/4.08 1373 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | -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(866)].
% 3.81/4.08 1374 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | 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(866)].
% 3.81/4.08 1375 -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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(869)].
% 3.81/4.08 1376 -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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(869)].
% 3.81/4.08 1377 -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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(870)].
% 3.81/4.08 1378 -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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(870)].
% 3.81/4.08 1379 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | -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(937)].
% 3.81/4.08 1380 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | 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(937)].
% 3.81/4.08 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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(1351,a,1352,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(1351,a,1353,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),A)). [resolve(1351,a,1355,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(1351,a,1357,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1351,a,1359,a)].
% 3.81/4.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(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(1351,a,1360,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(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(1351,a,1361,a)].
% 3.81/4.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(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(1351,a,1362,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1351,a,1363,a)].
% 3.81/4.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1351,a,1364,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),A)). [resolve(1351,a,1365,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(1351,a,1367,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(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(1351,a,1369,a)].
% 3.81/4.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(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(1351,a,1370,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(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(1351,a,1371,a)].
% 3.81/4.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(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(1351,a,1372,a)].
% 3.81/4.08 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | -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(1351,a,1373,a)].
% 3.81/4.08 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | 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(1351,a,1374,a)].
% 3.81/4.08 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1351,a,1375,a)].
% 3.81/4.08 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1351,a,1376,a)].
% 3.81/4.08 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1351,a,1377,a)].
% 3.81/4.08 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1351,a,1378,a)].
% 3.81/4.08 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | -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(1351,a,1379,a)].
% 3.81/4.08 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | 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(1351,a,1380,a)].
% 3.81/4.08 1381 -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(1036)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B))). [resolve(1381,b,1352,a)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),hAPP(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(1381,b,1353,a)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)),B)). [resolve(1381,b,1355,a)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B))). [resolve(1381,b,1357,a)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(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(1381,b,1359,a)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(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(1381,b,1360,a)].
% 3.81/4.08 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(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(1381,b,1361,a)].
% 3.81/4.08 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(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(1381,b,1362,a)].
% 3.81/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1381,b,1363,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1381,b,1364,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)),B)). [resolve(1381,b,1365,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B))). [resolve(1381,b,1367,a)].
% 3.88/4.08 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(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(1381,b,1369,a)].
% 3.88/4.08 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(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(1381,b,1370,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(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(1381,b,1371,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(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(1381,b,1372,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | -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(1381,b,1373,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | 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(1381,b,1374,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1381,b,1375,a)].
% 3.88/4.08 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1381,b,1376,a)].
% 3.88/4.08 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1381,b,1377,a)].
% 4.04/4.28 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1381,b,1378,a)].
% 4.04/4.28 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | -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(1381,b,1379,a)].
% 4.04/4.28 Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),D),E) | 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(1381,b,1380,a)].
% 4.04/4.28 1382 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 4.04/4.28 1383 -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(229)].
% 4.04/4.28 1384 -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(229)].
% 4.04/4.28 1385 -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(239)].
% 4.04/4.28 1386 -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(240)].
% 4.04/4.28 1387 -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(241)].
% 4.04/4.28 1388 -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(242)].
% 4.04/4.28 1389 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 4.13/4.37 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(1389,a,1383,a)].
% 4.13/4.37 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | 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(1389,a,1384,a)].
% 4.13/4.37 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(1389,a,1388,a)].
% 4.13/4.37 1390 -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(1031)].
% 4.13/4.37 1391 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 4.13/4.37 1392 -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(230)].
% 4.13/4.37 1393 -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(230)].
% 4.13/4.37 1394 -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(233)].
% 4.13/4.37 1395 -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(234)].
% 4.13/4.37 1396 -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(238)].
% 4.13/4.37 1397 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(945)].
% 4.13/4.37 1398 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(945)].
% 4.13/4.37 1399 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(946)].
% 4.13/4.37 1400 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(946)].
% 4.13/4.37 1401 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(947)].
% 4.13/4.37 1402 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(947)].
% 4.13/4.37 1403 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(948)].
% 4.13/4.37 1404 -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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(948)].
% 4.13/4.37 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(1391,a,1394,a)].
% 4.13/4.37 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(1391,a,1395,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1391,a,1397,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1391,a,1398,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1391,a,1399,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1391,a,1400,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1391,a,1401,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(1391,a,1402,a)].
% 4.13/4.37 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1391,a,1403,a)].
% 4.13/4.38 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(1391,a,1404,a)].
% 4.13/4.38 1405 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom). [clausify(1054)].
% 4.13/4.38 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(1405,b,1394,a)].
% 4.13/4.38 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(1405,b,1395,a)].
% 4.13/4.38 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1405,b,1397,a)].
% 4.13/4.38 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1405,b,1398,a)].
% 4.13/4.38 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1405,b,1399,a)].
% 4.27/4.47 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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1405,b,1400,a)].
% 4.27/4.47 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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1405,b,1401,a)].
% 4.27/4.47 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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),E),B)),C)),F))). [resolve(1405,b,1402,a)].
% 4.27/4.47 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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1405,b,1403,a)].
% 4.27/4.47 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)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),E)),C)),D)),F)). [resolve(1405,b,1404,a)].
% 4.27/4.47 1406 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 4.27/4.47 1407 -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(231)].
% 4.27/4.47 1408 -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(232)].
% 4.27/4.47 1409 -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(236)].
% 4.27/4.47 1410 -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(237)].
% 4.27/4.47 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(1406,a,1407,a)].
% 4.27/4.47 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(1406,a,1408,a)].
% 4.27/4.47 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(1406,a,1409,a)].
% 4.27/4.47 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(1406,a,1410,a)].
% 4.27/4.47 1411 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 4.27/4.47 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(1411,a,1407,a)].
% 4.27/4.47 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(1411,a,1408,a)].
% 4.34/4.57 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(1411,a,1409,a)].
% 4.34/4.57 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(1411,a,1410,a)].
% 4.34/4.57 1412 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom). [clausify(1043)].
% 4.34/4.57 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(1412,b,1407,a)].
% 4.34/4.57 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(1412,b,1408,a)].
% 4.34/4.57 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(1412,b,1409,a)].
% 4.34/4.57 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(1412,b,1410,a)].
% 4.34/4.57 1413 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.34/4.57 1414 -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(235)].
% 4.43/4.67 1415 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.43/4.67 1416 -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(1034)].
% 4.43/4.67 1417 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 4.43/4.67 1418 -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(245)].
% 4.43/4.67 1419 -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(269)].
% 4.43/4.67 1420 -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(614)].
% 4.43/4.67 1421 -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(701)].
% 4.43/4.67 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(1417,a,1418,a)].
% 4.43/4.67 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(1417,a,1419,a)].
% 4.43/4.67 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(1417,a,1420,a)].
% 4.43/4.67 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(1417,a,1421,a)].
% 4.43/4.67 1422 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom). [clausify(1046)].
% 4.43/4.67 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(1422,b,1418,a)].
% 4.43/4.67 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(1422,b,1419,a)].
% 4.43/4.67 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(1422,b,1420,a)].
% 4.43/4.67 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(1422,b,1421,a)].
% 4.55/4.76 1423 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.55/4.76 1424 -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(246)].
% 4.55/4.76 1425 -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(247)].
% 4.55/4.76 1426 -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(248)].
% 4.55/4.76 1427 -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(249)].
% 4.55/4.76 1428 -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(249)].
% 4.55/4.76 1429 -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(249)].
% 4.55/4.76 1430 -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(250)].
% 4.55/4.76 1431 -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(634)].
% 4.55/4.76 1432 -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(635)].
% 4.55/4.76 1433 -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(695)].
% 4.55/4.76 1434 -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(696)].
% 4.55/4.76 1435 -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(697)].
% 4.55/4.76 1436 -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(698)].
% 4.55/4.76 1437 -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(699)].
% 4.55/4.76 1438 -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(700)].
% 4.55/4.76 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(1423,a,1424,a)].
% 4.55/4.76 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(1423,a,1425,a)].
% 4.55/4.76 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(1423,a,1426,a)].
% 4.55/4.76 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(1423,a,1427,a)].
% 4.55/4.76 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(1423,a,1428,a)].
% 4.55/4.76 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(1423,a,1429,a)].
% 4.55/4.76 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B))). [resolve(1423,a,1431,a)].
% 4.55/4.76 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(1423,a,1432,a)].
% 4.55/4.76 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(1423,a,1433,a)].
% 4.55/4.76 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(1423,a,1434,a)].
% 4.55/4.76 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(1423,a,1435,a)].
% 4.55/4.76 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(1423,a,1436,a)].
% 4.55/4.76 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(1423,a,1437,a)].
% 4.55/4.76 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(1423,a,1438,a)].
% 4.55/4.76 1439 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 4.55/4.76 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(1439,a,1424,a)].
% 4.55/4.76 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(1439,a,1425,a)].
% 4.55/4.76 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(1439,a,1426,a)].
% 4.55/4.76 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(1439,a,1427,a)].
% 4.55/4.76 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(1439,a,1428,a)].
% 4.55/4.76 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(1439,a,1429,a)].
% 4.55/4.76 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B))). [resolve(1439,a,1431,a)].
% 4.55/4.76 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(1439,a,1432,a)].
% 4.55/4.76 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(1439,a,1433,a)].
% 4.55/4.76 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(1439,a,1434,a)].
% 4.55/4.76 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(1439,a,1435,a)].
% 4.55/4.76 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(1439,a,1436,a)].
% 4.55/4.77 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(1439,a,1437,a)].
% 4.55/4.77 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(1439,a,1438,a)].
% 4.55/4.77 1440 -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(1027)].
% 4.55/4.77 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(1440,b,1424,a)].
% 4.55/4.77 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(1440,b,1425,a)].
% 4.55/4.77 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(1440,b,1426,a)].
% 4.55/4.77 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(1440,b,1427,a)].
% 4.55/4.77 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(1440,b,1428,a)].
% 4.55/4.77 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(1440,b,1429,a)].
% 4.55/4.77 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C))). [resolve(1440,b,1431,a)].
% 4.65/4.87 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(1440,b,1432,a)].
% 4.65/4.87 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(1440,b,1433,a)].
% 4.65/4.87 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(1440,b,1434,a)].
% 4.65/4.87 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(1440,b,1435,a)].
% 4.65/4.87 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(1440,b,1436,a)].
% 4.65/4.87 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(1440,b,1437,a)].
% 4.65/4.87 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(1440,b,1438,a)].
% 4.65/4.87 1441 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.65/4.87 1442 -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(253)].
% 4.65/4.87 1443 -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(254)].
% 4.65/4.87 1444 -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(282)].
% 4.65/4.87 1445 -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(286)].
% 4.65/4.87 1446 -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(309)].
% 4.65/4.87 1447 -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(310)].
% 4.65/4.87 1448 -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(311)].
% 4.65/4.87 1449 -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(374)].
% 4.65/4.87 1450 -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(375)].
% 4.65/4.87 1451 -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(409)].
% 4.65/4.87 1452 -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(511)].
% 4.65/4.87 1453 -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(512)].
% 4.65/4.87 1454 -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(602)].
% 4.65/4.87 1455 -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(602)].
% 4.65/4.87 1456 -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(603)].
% 4.65/4.87 1457 -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(604)].
% 4.65/4.87 1458 -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(609)].
% 4.65/4.87 1459 -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(636)].
% 4.65/4.87 1460 -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(639)].
% 4.65/4.87 1461 -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(640)].
% 4.65/4.87 1462 -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(645)].
% 4.65/4.87 1463 -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(646)].
% 4.65/4.87 1464 -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(647)].
% 4.65/4.87 1465 -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(648)].
% 4.65/4.87 1466 -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(648)].
% 4.65/4.87 1467 -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(703)].
% 4.65/4.87 1468 -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(704)].
% 4.65/4.87 1469 -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(705)].
% 4.65/4.87 1470 -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(706)].
% 4.65/4.87 1471 -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(707)].
% 4.65/4.87 1472 -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(729)].
% 4.65/4.87 1473 -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(730)].
% 4.65/4.87 1474 -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(731)].
% 4.65/4.87 1475 -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(732)].
% 4.65/4.87 1476 -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(732)].
% 4.65/4.87 1477 -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(733)].
% 4.65/4.87 1478 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) # label(fact_of__nat__le__iff) # label(axiom). [clausify(800)].
% 4.65/4.87 1479 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) # label(fact_of__nat__le__iff) # label(axiom). [clausify(800)].
% 4.65/4.87 1480 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_of__nat__less__0__iff) # label(axiom). [clausify(802)].
% 4.65/4.87 1481 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B))) # label(fact_zero__le__imp__of__nat) # label(axiom). [clausify(803)].
% 4.65/4.87 1482 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B))) # label(fact_of__nat__0__le__iff) # label(axiom). [clausify(804)].
% 4.65/4.87 1483 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) # label(fact_of__nat__less__iff) # label(axiom). [clausify(808)].
% 4.65/4.87 1484 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) # label(fact_of__nat__less__iff) # label(axiom). [clausify(808)].
% 4.65/4.87 1485 -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_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))) # label(fact_less__imp__of__nat__less) # label(axiom). [clausify(809)].
% 4.65/4.87 1486 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)) # label(fact_of__nat__less__imp__less) # label(axiom). [clausify(810)].
% 4.65/4.87 1487 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) # label(fact_of__nat__0__less__iff) # label(axiom). [clausify(823)].
% 4.65/4.87 1488 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) # label(fact_of__nat__0__less__iff) # label(axiom). [clausify(823)].
% 4.65/4.87 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(1441,a,1442,a)].
% 4.65/4.87 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(1441,a,1443,a)].
% 4.65/4.87 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(1441,a,1444,a)].
% 4.65/4.87 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(1441,a,1445,a)].
% 4.65/4.87 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(1441,a,1446,a)].
% 4.65/4.87 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(1441,a,1447,a)].
% 4.65/4.87 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(1441,a,1448,a)].
% 4.65/4.87 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(1441,a,1449,a)].
% 4.65/4.87 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(1441,a,1450,a)].
% 4.65/4.87 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(1441,a,1451,a)].
% 4.65/4.87 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(1441,a,1452,a)].
% 4.65/4.87 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(1441,a,1453,a)].
% 4.65/4.87 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(1441,a,1454,a)].
% 4.65/4.87 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(1441,a,1455,a)].
% 4.65/4.87 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(1441,a,1458,a)].
% 4.65/4.87 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(1441,a,1459,a)].
% 4.65/4.87 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(1441,a,1460,a)].
% 4.65/4.87 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(1441,a,1461,a)].
% 4.65/4.87 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(1441,a,1462,a)].
% 4.65/4.87 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(1441,a,1463,a)].
% 4.65/4.87 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(1441,a,1464,a)].
% 4.65/4.87 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(1441,a,1465,a)].
% 4.65/4.87 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(1441,a,1466,a)].
% 4.65/4.87 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(1441,a,1467,a)].
% 4.65/4.87 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(1441,a,1468,a)].
% 4.65/4.87 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(1441,a,1469,a)].
% 4.65/4.87 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(1441,a,1470,a)].
% 4.65/4.87 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(1441,a,1471,a)].
% 4.65/4.87 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(1441,a,1472,a)].
% 4.65/4.87 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(1441,a,1473,a)].
% 4.65/4.87 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(1441,a,1474,a)].
% 4.65/4.87 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(1441,a,1476,a)].
% 4.65/4.87 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(1441,a,1477,a)].
% 4.65/4.87 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)). [resolve(1441,a,1478,a)].
% 4.65/4.87 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)). [resolve(1441,a,1479,a)].
% 4.65/4.87 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1441,a,1480,a)].
% 4.65/4.87 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A))). [resolve(1441,a,1481,a)].
% 4.65/4.87 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)). [resolve(1441,a,1483,a)].
% 4.65/4.88 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)). [resolve(1441,a,1484,a)].
% 4.65/4.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(1441,a,1487,a)].
% 4.65/4.88 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(1441,a,1488,a)].
% 4.65/4.88 1489 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.65/4.88 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(1489,a,1442,a)].
% 4.65/4.88 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(1489,a,1443,a)].
% 4.65/4.88 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(1489,a,1444,a)].
% 4.65/4.88 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(1489,a,1445,a)].
% 4.65/4.88 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(1489,a,1446,a)].
% 4.65/4.88 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(1489,a,1447,a)].
% 4.65/4.88 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(1489,a,1448,a)].
% 4.65/4.88 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(1489,a,1449,a)].
% 4.65/4.88 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(1489,a,1450,a)].
% 4.65/4.88 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(1489,a,1451,a)].
% 4.65/4.88 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(1489,a,1452,a)].
% 4.65/4.88 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(1489,a,1453,a)].
% 4.65/4.88 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(1489,a,1454,a)].
% 4.65/4.88 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(1489,a,1455,a)].
% 4.65/4.88 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(1489,a,1458,a)].
% 4.65/4.88 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(1489,a,1459,a)].
% 4.65/4.88 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(1489,a,1460,a)].
% 4.65/4.88 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(1489,a,1461,a)].
% 4.65/4.88 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(1489,a,1462,a)].
% 4.65/4.88 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(1489,a,1463,a)].
% 4.65/4.88 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(1489,a,1464,a)].
% 4.65/4.88 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(1489,a,1465,a)].
% 4.65/4.88 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(1489,a,1466,a)].
% 4.65/4.88 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(1489,a,1467,a)].
% 4.65/4.88 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(1489,a,1468,a)].
% 4.65/4.88 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(1489,a,1469,a)].
% 4.65/4.88 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(1489,a,1470,a)].
% 4.65/4.88 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(1489,a,1471,a)].
% 4.65/4.88 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(1489,a,1472,a)].
% 4.65/4.88 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(1489,a,1473,a)].
% 4.65/4.88 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(1489,a,1474,a)].
% 4.65/4.88 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(1489,a,1476,a)].
% 4.65/4.88 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(1489,a,1477,a)].
% 4.65/4.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)). [resolve(1489,a,1478,a)].
% 4.65/4.88 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)). [resolve(1489,a,1479,a)].
% 4.65/4.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1489,a,1480,a)].
% 4.65/4.88 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A))). [resolve(1489,a,1481,a)].
% 4.65/4.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)). [resolve(1489,a,1483,a)].
% 4.65/4.88 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)). [resolve(1489,a,1484,a)].
% 4.65/4.88 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(1489,a,1487,a)].
% 4.65/4.88 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(1489,a,1488,a)].
% 4.65/4.88 1490 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(1039)].
% 4.65/4.88 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(1490,b,1442,a)].
% 4.65/4.88 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(1490,b,1443,a)].
% 4.65/4.88 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(1490,b,1444,a)].
% 4.65/4.88 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(1490,b,1445,a)].
% 4.65/4.88 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(1490,b,1446,a)].
% 4.65/4.88 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(1490,b,1447,a)].
% 4.65/4.88 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(1490,b,1448,a)].
% 4.65/4.88 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(1490,b,1449,a)].
% 4.65/4.88 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(1490,b,1450,a)].
% 4.65/4.88 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(1490,b,1451,a)].
% 4.65/4.88 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(1490,b,1452,a)].
% 4.65/4.88 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(1490,b,1453,a)].
% 4.65/4.88 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(1490,b,1454,a)].
% 4.65/4.89 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(1490,b,1455,a)].
% 4.65/4.89 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(1490,b,1458,a)].
% 4.65/4.89 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(1490,b,1459,a)].
% 4.65/4.89 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(1490,b,1460,a)].
% 4.65/4.89 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(1490,b,1461,a)].
% 4.65/4.89 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(1490,b,1462,a)].
% 4.65/4.89 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(1490,b,1463,a)].
% 4.65/4.89 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(1490,b,1464,a)].
% 4.65/4.89 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(1490,b,1465,a)].
% 4.65/4.89 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(1490,b,1466,a)].
% 4.65/4.89 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(1490,b,1467,a)].
% 4.65/4.89 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(1490,b,1468,a)].
% 4.65/4.89 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(1490,b,1469,a)].
% 4.65/4.89 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(1490,b,1470,a)].
% 4.65/4.89 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(1490,b,1471,a)].
% 4.65/4.89 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(1490,b,1472,a)].
% 4.65/4.89 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(1490,b,1473,a)].
% 4.65/4.89 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(1490,b,1474,a)].
% 4.65/4.89 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(1490,b,1476,a)].
% 4.65/4.89 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(1490,b,1477,a)].
% 4.87/5.10 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1490,b,1478,a)].
% 4.87/5.10 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)). [resolve(1490,b,1479,a)].
% 4.87/5.10 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1490,b,1480,a)].
% 4.87/5.10 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_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B))). [resolve(1490,b,1481,a)].
% 4.87/5.10 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1490,b,1483,a)].
% 4.87/5.10 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)). [resolve(1490,b,1484,a)].
% 4.87/5.10 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_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B))) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(1490,b,1487,a)].
% 4.87/5.10 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_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B))) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(1490,b,1488,a)].
% 4.87/5.10 1491 -class_Rings_Oidom(A) | class_Rings_Oring__1(A) # label(clrel_Rings_Oidom__Rings_Oring__1) # label(axiom). [clausify(1005)].
% 4.87/5.10 1492 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__minus) # label(axiom). [clausify(279)].
% 4.87/5.10 1493 -class_Rings_Oring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(A,B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)))) # label(fact_of__int__of__nat) # label(axiom). [clausify(837)].
% 4.87/5.10 1494 -class_Rings_Oring__1(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(A,B) = c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Int_Onat,B)) # label(fact_of__int__of__nat) # label(axiom). [clausify(837)].
% 4.87/5.10 1495 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)) = c_Nat_Osemiring__1__class_Oof__nat(A,B) # label(fact_of__int__of__nat__eq) # label(axiom). [clausify(838)].
% 4.87/5.10 1496 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Oring__1__class_Oof__int(A,B)),C) # label(fact_of__int__power) # label(axiom). [clausify(841)].
% 4.87/5.10 1497 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Int_Oring__1__class_Oof__int(A,B)) # label(fact_of__int__minus) # label(axiom). [clausify(842)].
% 4.87/5.10 1498 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(A) # label(fact_of__int__1) # label(axiom). [clausify(843)].
% 4.87/5.10 1499 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)) # label(fact_of__int__mult) # label(axiom). [clausify(844)].
% 4.87/5.10 1500 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)) # label(fact_of__int__add) # label(axiom). [clausify(845)].
% 4.87/5.10 1501 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(A) # label(fact_of__int__0) # label(axiom). [clausify(847)].
% 4.87/5.10 1502 -class_Rings_Oring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Int_Oring__1__class_Oof__int(A,B) = c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Int_Onat,B)) # label(fact_of__nat__nat) # label(axiom). [clausify(855)].
% 4.87/5.10 1503 -class_Rings_Oring__1(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)) # label(fact_of__int__diff) # label(axiom). [clausify(858)].
% 4.87/5.10 1504 -class_Rings_Oring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Nat_Osemiring__1__class_Oof__nat(A,C)),c_Nat_Osemiring__1__class_Oof__nat(A,B)) # label(fact_of__nat__diff) # label(axiom). [clausify(944)].
% 4.87/5.10 1505 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Oone__class_Oone(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Oone__class_Oone(A))) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(949)].
% 4.87/5.10 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)). [resolve(1491,b,1492,a)].
% 4.87/5.10 Derived: -class_Rings_Oidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(A,B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)))). [resolve(1491,b,1493,a)].
% 4.87/5.10 Derived: -class_Rings_Oidom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(A,B) = c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Int_Onat,B)). [resolve(1491,b,1494,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)) = c_Nat_Osemiring__1__class_Oof__nat(A,B). [resolve(1491,b,1495,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Oring__1__class_Oof__int(A,B)),C). [resolve(1491,b,1496,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Int_Oring__1__class_Oof__int(A,B)). [resolve(1491,b,1497,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(A). [resolve(1491,b,1498,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)). [resolve(1491,b,1499,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)). [resolve(1491,b,1500,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(A). [resolve(1491,b,1501,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Int_Oring__1__class_Oof__int(A,B) = c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Int_Onat,B)). [resolve(1491,b,1502,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)). [resolve(1491,b,1503,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Nat_Osemiring__1__class_Oof__nat(A,C)),c_Nat_Osemiring__1__class_Oof__nat(A,B)). [resolve(1491,b,1504,a)].
% 4.87/5.11 Derived: -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Oone__class_Oone(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Oone__class_Oone(A))). [resolve(1491,b,1505,a)].
% 4.87/5.11 1506 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 4.87/5.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(1506,a,1492,a)].
% 4.87/5.11 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)))). [resolve(1506,a,1493,a)].
% 4.87/5.11 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Int_Onat,A)). [resolve(1506,a,1494,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A). [resolve(1506,a,1495,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(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_Int_Oring__1__class_Oof__int(tc_Int_Oint,A)),B). [resolve(1506,a,1496,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A)). [resolve(1506,a,1497,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1506,a,1498,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(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_Int_Oring__1__class_Oof__int(tc_Int_Oint,A)),c_Int_Oring__1__class_Oof__int(tc_Int_Oint,B)). [resolve(1506,a,1499,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(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_Int_Oring__1__class_Oof__int(tc_Int_Oint,A)),c_Int_Oring__1__class_Oof__int(tc_Int_Oint,B)). [resolve(1506,a,1500,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1506,a,1501,a)].
% 4.87/5.11 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Int_Onat,A)). [resolve(1506,a,1502,a)].
% 4.87/5.11 Derived: c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Oring__1__class_Oof__int(tc_Int_Oint,A)),c_Int_Oring__1__class_Oof__int(tc_Int_Oint,B)). [resolve(1506,a,1503,a)].
% 4.87/5.11 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)). [resolve(1506,a,1504,a)].
% 4.87/5.11 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(1506,a,1505,a)].
% 4.87/5.11 1507 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom). [clausify(1070)].
% 4.87/5.11 Derived: -class_Rings_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(1507,b,1492,a)].
% 4.87/5.11 Derived: -class_Rings_Ocomm__ring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)))). [resolve(1507,b,1493,a)].
% 4.87/5.11 Derived: -class_Rings_Ocomm__ring__1(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) = c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(c_Int_Onat,B)). [resolve(1507,b,1494,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B). [resolve(1507,b,1495,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B)),C). [resolve(1507,b,1496,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B)). [resolve(1507,b,1497,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(1507,b,1498,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),C)). [resolve(1507,b,1499,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),C)). [resolve(1507,b,1500,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1507,b,1501,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B) = c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(c_Int_Onat,B)). [resolve(1507,b,1502,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),B)),c_Int_Oring__1__class_Oof__int(tc_Polynomial_Opoly(A),C)). [resolve(1507,b,1503,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C)) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)). [resolve(1507,b,1504,a)].
% 4.96/5.21 Derived: -class_Rings_Ocomm__ring__1(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1507,b,1505,a)].
% 4.96/5.21 1508 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 4.96/5.21 1509 -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(378)].
% 4.96/5.21 1510 -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(392)].
% 4.96/5.21 1511 -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(516)].
% 4.96/5.21 1512 -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(531)].
% 4.96/5.21 1513 -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(532)].
% 4.96/5.21 1514 -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(532)].
% 4.96/5.21 1515 -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(533)].
% 4.96/5.21 1516 -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(534)].
% 4.96/5.21 1517 -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(534)].
% 4.96/5.21 1518 -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(534)].
% 4.96/5.21 1519 -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(535)].
% 4.96/5.21 1520 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(535)].
% 4.96/5.21 1521 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(535)].
% 4.96/5.21 1522 -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(587)].
% 4.96/5.21 1523 -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(587)].
% 4.96/5.21 1524 -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(589)].
% 4.96/5.21 1525 -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(592)].
% 4.96/5.21 1526 -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(592)].
% 4.96/5.21 1527 -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(593)].
% 4.96/5.21 1528 -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(594)].
% 4.96/5.22 1529 -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(598)].
% 4.96/5.22 1530 -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(599)].
% 4.96/5.22 1531 -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(599)].
% 4.96/5.22 1532 -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(600)].
% 4.96/5.22 1533 -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(600)].
% 4.96/5.22 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(1508,a,1509,a)].
% 4.96/5.22 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(1508,a,1511,a)].
% 4.96/5.22 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(1508,a,1514,a)].
% 4.96/5.22 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(1508,a,1517,a)].
% 4.96/5.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)) | A != B. [resolve(1508,a,1518,a)].
% 4.96/5.22 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1508,a,1521,a)].
% 4.96/5.22 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(1508,a,1522,a)].
% 4.96/5.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1508,a,1524,a)].
% 4.96/5.22 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(1508,a,1526,a)].
% 4.96/5.22 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A)). [resolve(1508,a,1527,a)].
% 4.96/5.22 1534 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 4.96/5.22 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(1534,a,1509,a)].
% 4.96/5.22 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(1534,a,1511,a)].
% 4.96/5.22 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(1534,a,1514,a)].
% 4.96/5.22 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(1534,a,1517,a)].
% 4.96/5.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | A != B. [resolve(1534,a,1518,a)].
% 4.96/5.22 Derived: A != B | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1534,a,1521,a)].
% 4.96/5.22 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(1534,a,1522,a)].
% 4.96/5.22 Derived: -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1534,a,1524,a)].
% 4.96/5.22 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(1534,a,1526,a)].
% 5.19/5.44 Derived: hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)). [resolve(1534,a,1527,a)].
% 5.19/5.44 1535 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1056)].
% 5.19/5.44 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(1535,b,1509,a)].
% 5.19/5.44 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(1535,b,1511,a)].
% 5.19/5.44 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(1535,b,1514,a)].
% 5.19/5.44 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(1535,b,1517,a)].
% 5.19/5.44 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B),C)) | B != C. [resolve(1535,b,1518,a)].
% 5.19/5.44 Derived: -class_Rings_Olinordered__idom(A) | B != C | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1535,b,1521,a)].
% 5.19/5.44 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(1535,b,1522,a)].
% 5.19/5.44 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1535,b,1524,a)].
% 5.19/5.44 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(1535,b,1526,a)].
% 5.19/5.44 Derived: -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B),C)) | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C),B)). [resolve(1535,b,1527,a)].
% 5.19/5.44 1536 class_Orderings_Owellorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Owellorder) # label(axiom). [assumption].
% 5.19/5.44 1537 -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(476)].
% 5.19/5.44 1538 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(A,B))) # label(fact_LeastI) # label(axiom). [clausify(481)].
% 5.19/5.44 1539 -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(482)].
% 5.19/5.44 1540 -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(608)].
% 5.19/5.44 Derived: -hBOOL(hAPP(A,B)) | hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,A))). [resolve(1536,a,1537,a)].
% 5.19/5.44 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(1536,a,1539,a)].
% 5.19/5.44 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(1536,a,1540,a)].
% 5.19/5.44 1541 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 5.19/5.44 1542 -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(501)].
% 5.32/5.55 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(1541,a,1542,a)].
% 5.32/5.55 1543 -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(1024)].
% 5.32/5.55 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(1543,b,1542,a)].
% 5.32/5.55 1544 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.32/5.55 1545 -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(575)].
% 5.32/5.55 1546 -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(576)].
% 5.32/5.55 1547 -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(577)].
% 5.32/5.55 1548 -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(637)].
% 5.32/5.55 1549 -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(638)].
% 5.45/5.65 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(1544,a,1545,a)].
% 5.45/5.65 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(1544,a,1548,a)].
% 5.45/5.65 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(1544,a,1549,a)].
% 5.45/5.65 1550 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.45/5.65 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(1550,a,1545,a)].
% 5.45/5.65 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(1550,a,1548,a)].
% 5.45/5.65 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(1550,a,1549,a)].
% 5.45/5.65 1551 -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(1021)].
% 5.45/5.65 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(1551,b,1545,a)].
% 5.45/5.65 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(1551,b,1548,a)].
% 5.45/5.65 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(1551,b,1549,a)].
% 5.45/5.65 1552 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 5.45/5.65 1553 -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(618)].
% 5.45/5.65 1554 -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(619)].
% 5.45/5.65 1555 -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(620)].
% 5.45/5.65 1556 -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(621)].
% 5.45/5.65 1557 -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(622)].
% 5.45/5.65 1558 -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(624)].
% 5.45/5.65 1559 -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(626)].
% 5.45/5.65 1560 -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(627)].
% 5.45/5.65 1561 -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(685)].
% 5.45/5.65 1562 -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(686)].
% 5.45/5.65 1563 -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(687)].
% 5.45/5.65 1564 -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(688)].
% 5.45/5.65 1565 -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(690)].
% 5.45/5.65 1566 -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(692)].
% 5.45/5.65 1567 -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(693)].
% 5.45/5.65 1568 -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(694)].
% 5.45/5.65 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(1552,a,1553,a)].
% 5.45/5.65 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(1552,a,1554,a)].
% 5.45/5.65 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(1552,a,1555,a)].
% 5.45/5.66 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(1552,a,1556,a)].
% 5.45/5.66 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(1552,a,1557,a)].
% 5.45/5.66 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(1552,a,1561,a)].
% 5.45/5.66 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(1552,a,1562,a)].
% 5.45/5.66 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(1552,a,1563,a)].
% 5.45/5.66 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(1552,a,1564,a)].
% 5.45/5.66 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(1552,a,1565,a)].
% 5.45/5.66 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(1552,a,1566,a)].
% 5.45/5.66 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(1552,a,1567,a)].
% 5.45/5.66 1569 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 5.45/5.66 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(1569,a,1553,a)].
% 5.45/5.66 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(1569,a,1554,a)].
% 5.45/5.66 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(1569,a,1555,a)].
% 5.45/5.66 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(1569,a,1556,a)].
% 5.45/5.66 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(1569,a,1557,a)].
% 5.45/5.66 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(1569,a,1559,a)].
% 5.45/5.66 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(1569,a,1560,a)].
% 5.45/5.66 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(1569,a,1561,a)].
% 5.45/5.66 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(1569,a,1562,a)].
% 5.45/5.66 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(1569,a,1563,a)].
% 5.45/5.66 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(1569,a,1564,a)].
% 5.45/5.66 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(1569,a,1565,a)].
% 5.45/5.66 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(1569,a,1566,a)].
% 5.45/5.66 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(1569,a,1567,a)].
% 5.45/5.66 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(1569,a,1568,a)].
% 5.45/5.66 1570 -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(1025)].
% 5.45/5.66 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(1570,b,1553,a)].
% 5.45/5.66 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(1570,b,1554,a)].
% 5.45/5.66 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(1570,b,1555,a)].
% 5.45/5.66 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(1570,b,1556,a)].
% 5.45/5.66 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(1570,b,1557,a)].
% 5.45/5.66 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(1570,b,1561,a)].
% 5.45/5.66 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(1570,b,1562,a)].
% 5.45/5.66 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(1570,b,1563,a)].
% 5.45/5.66 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(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(1570,b,1564,a)].
% 5.45/5.66 Derived: -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),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(1570,b,1565,a)].
% 5.85/6.09 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(1570,b,1566,a)].
% 5.85/6.09 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(1570,b,1567,a)].
% 5.85/6.09 1571 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 5.85/6.09 1572 -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(628)].
% 5.85/6.09 1573 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 5.85/6.09 1574 -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(1023)].
% 5.85/6.09 1575 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 5.85/6.09 1576 -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(689)].
% 5.85/6.09 1577 -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(691)].
% 5.85/6.09 1578 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 5.85/6.09 1579 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom). [clausify(1038)].
% 5.85/6.09 1580 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 5.85/6.09 1581 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(A,B) != c_Nat_Osemiring__1__class_Oof__nat(A,C) | B = C # label(fact_of__nat__eq__iff) # label(axiom). [clausify(775)].
% 5.85/6.09 1582 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(A,B) = c_Nat_Osemiring__1__class_Oof__nat(A,C) | B != C # label(fact_of__nat__eq__iff) # label(axiom). [clausify(775)].
% 5.85/6.09 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B) | A = B. [resolve(1580,a,1581,a)].
% 6.00/6.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B) | A != B. [resolve(1580,a,1582,a)].
% 6.00/6.20 1583 class_Nat_Osemiring__char__0(tc_Nat_Onat) # label(arity_Nat__Onat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 6.00/6.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A) != c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B) | A = B. [resolve(1583,a,1581,a)].
% 6.00/6.20 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A) = c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B) | A != B. [resolve(1583,a,1582,a)].
% 6.00/6.20 1584 -class_Rings_Olinordered__idom(A) | class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Nat_Osemiring__char__0) # label(axiom). [clausify(1051)].
% 6.00/6.20 Derived: -class_Rings_Olinordered__idom(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B) != c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1584,b,1581,a)].
% 6.00/6.20 Derived: -class_Rings_Olinordered__idom(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B) = c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1584,b,1582,a)].
% 6.00/6.20 1585 -class_Rings_Oidom(A) | class_Rings_Osemiring__1(A) # label(clrel_Rings_Oidom__Rings_Osemiring__1) # label(axiom). [clausify(998)].
% 6.00/6.20 1586 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),C) # label(fact_of__nat__power) # label(axiom). [clausify(781)].
% 6.00/6.20 1587 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(A) # label(fact_of__nat__1) # label(axiom). [clausify(797)].
% 6.00/6.20 1588 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)) # label(fact_of__nat__mult) # label(axiom). [clausify(798)].
% 6.00/6.20 1589 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)) # label(fact_of__nat__add) # label(axiom). [clausify(799)].
% 6.00/6.20 1590 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(A) # label(fact_of__nat__0) # label(axiom). [clausify(801)].
% 6.00/6.20 1591 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B)) # label(fact_of__nat__Suc) # label(axiom). [clausify(812)].
% 6.00/6.20 1592 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,hAPP(c_COMBC(A,A,A,c_Groups_Oplus__class_Oplus(A)),c_Groups_Oone__class_Oone(A)),B,c_Groups_Ozero__class_Ozero(A)) = c_Nat_Osemiring__1__class_Oof__nat(A,B) # label(fact_semiring__1__class_Oof__nat__code) # label(axiom). [clausify(832)].
% 6.00/6.20 1593 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) = C # label(fact_of__nat__aux_Osimps_I1_J) # label(axiom). [clausify(834)].
% 6.00/6.20 1594 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,hAPP(c_Nat_OSuc,C),D) = c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,C,hAPP(B,D)) # label(fact_of__nat__aux_Osimps_I2_J) # label(axiom). [clausify(835)].
% 6.00/6.20 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),C). [resolve(1585,b,1586,a)].
% 6.00/6.20 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(A). [resolve(1585,b,1587,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)). [resolve(1585,b,1588,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)). [resolve(1585,b,1589,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(A). [resolve(1585,b,1590,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B)). [resolve(1585,b,1591,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,hAPP(c_COMBC(A,A,A,c_Groups_Oplus__class_Oplus(A)),c_Groups_Oone__class_Oone(A)),B,c_Groups_Ozero__class_Ozero(A)) = c_Nat_Osemiring__1__class_Oof__nat(A,B). [resolve(1585,b,1592,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) = C. [resolve(1585,b,1593,a)].
% 6.00/6.21 Derived: -class_Rings_Oidom(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,hAPP(c_Nat_OSuc,C),D) = c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,C,hAPP(B,D)). [resolve(1585,b,1594,a)].
% 6.00/6.21 1595 class_Rings_Osemiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__1) # label(axiom). [assumption].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),B). [resolve(1595,a,1586,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint). [resolve(1595,a,1587,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)). [resolve(1595,a,1588,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)). [resolve(1595,a,1589,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(1595,a,1590,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)). [resolve(1595,a,1591,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A). [resolve(1595,a,1592,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) = B. [resolve(1595,a,1593,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,A,hAPP(c_Nat_OSuc,B),C) = c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,A,B,hAPP(A,C)). [resolve(1595,a,1594,a)].
% 6.00/6.21 1596 class_Rings_Osemiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__1) # label(axiom). [assumption].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(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_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),B). [resolve(1596,a,1586,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat). [resolve(1596,a,1587,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(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_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B)). [resolve(1596,a,1588,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(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_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,B)). [resolve(1596,a,1589,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1596,a,1590,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A)). [resolve(1596,a,1591,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat,A). [resolve(1596,a,1592,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) = B. [resolve(1596,a,1593,a)].
% 6.00/6.21 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B),C) = c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,A,B,hAPP(A,C)). [resolve(1596,a,1594,a)].
% 6.00/6.21 1597 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Osemiring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring__1) # label(axiom). [clausify(1060)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),C). [resolve(1597,b,1586,a)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(1597,b,1587,a)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C)). [resolve(1597,b,1588,a)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),C)). [resolve(1597,b,1589,a)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1597,b,1590,a)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B)). [resolve(1597,b,1591,a)].
% 6.00/6.21 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Polynomial_Opoly(A),hAPP(c_COMBC(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Nat_Osemiring__1__class_Oof__nat(tc_Polynomial_Opoly(A),B). [resolve(1597,b,1592,a)].
% 8.33/8.55 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) = C. [resolve(1597,b,1593,a)].
% 8.33/8.55 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Polynomial_Opoly(A),B,hAPP(c_Nat_OSuc,C),D) = c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Polynomial_Opoly(A),B,C,hAPP(B,D)). [resolve(1597,b,1594,a)].
% 8.33/8.55
% 8.33/8.55 ============================== end predicate elimination =============
% 8.33/8.55
% 8.33/8.55 Auto_denials: (non-Horn, no changes).
% 8.33/8.55
% 8.33/8.55 Term ordering decisions:
% 8.33/8.55 Function symbol KB weights: tc_Nat_Onat=1. tc_Int_Oint=1. c_Nat_OSuc=1. c_Int_Onat=1. tc_HOL_Obool=1. t_a=1. c_fconj=1. v_cs____=1. c_fNot=1. c_fFalse=1. v_c____=1. v_p=1. v_x____=1. v_y____=1. c1=1. c2=1. c3=1. hAPP=1. c_Orderings_Oord__class_Oless=1. c_Orderings_Oord__class_Oless__eq=1. c_Nat_Osemiring__1__class_Oof__nat=1. tc_fun=1. c_Int_Oring__1__class_Oof__int=1. c_Polynomial_Opoly=1. c_Polynomial_Ocoeff=1. c_Polynomial_OAbs__poly=1. c_COMBK=1. c_Orderings_Oord__class_OLeast=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Int_Onat__aux=1. f1=1. f4=1. f5=1. f10=1. f11=1. f17=1. f18=1. f20=1. f21=1. f26=1. f27=1. f30=1. f31=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_Groups_Ominus__class_Ominus=1. c_Rings_Odvd__class_Odvd=1. c_Groups_Oone__class_Oone=1. c_Groups_Ouminus__class_Ouminus=1. c_Polynomial_OpCons=1. c_Polynomial_Osmult=1. c_fequal=1. c_COMBI=1. c_If=1. f12=1. f13=1. f14=1. f15=1. f16=1. f22=1. f23=1. f24=1. f25=1. f28=1. f29=1. c_COMBB=1. c_Polynomial_Omonom=1. c_COMBS=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. c_Nat_Onat_Onat__case=1. c_Polynomial_Oorder=1. c_Polynomial_Osynthetic__div=1. c_Polynomial_Opcompose=1. c_Power_Opower_Opower=1. f2=1. f3=1. f6=1. f7=1. f8=1. f19=1. f32=1. f33=1. c_COMBC=1. c_Nat_Osemiring__1__class_Oof__nat__aux=1. f9=1. c_Polynomial_Opoly__rec=1.
% 8.33/8.55
% 8.33/8.55 ============================== end of process initial clauses ========
% 8.33/8.55
% 8.33/8.55 ============================== CLAUSES FOR SEARCH ====================
% 8.33/8.55
% 8.33/8.55 ============================== end of clauses for search =============
% 8.33/8.55
% 8.33/8.55 ============================== SEARCH ================================
% 8.33/8.55
% 8.33/8.55 % Starting search at 5.00 seconds.
% 8.33/8.55
% 8.33/8.55 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 5.25 sec).
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=58.000, iters=3412
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=57.000, iters=3454
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=51.000, iters=3446
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=50.000, iters=3394
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% 8.33/8.55 Low Water (keep): wt=48.000, iters=3472
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=47.000, iters=3505
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=45.000, iters=3417
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=43.000, iters=3337
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=42.000, iters=3532
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=41.000, iters=3510
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=39.000, iters=3390
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=37.000, iters=3355
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=36.000, iters=3389
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=35.000, iters=3407
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=34.000, iters=3358
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=33.000, iters=3363
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=32.000, iters=3364
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=31.000, iters=3349
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=30.000, iters=3349
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=29.000, iters=3409
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=28.000, iters=3396
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=27.000, iters=3405
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=26.000, iters=3359
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=25.000, iters=3366
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=24.000, iters=3338
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=23.000, iters=3357
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=22.000, iters=3333
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=21.000, iters=3357
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=20.000, iters=3341
% 8.33/8.55
% 8.33/8.55 Low Water (keep): wt=19.000, iters=3336
% 8.33/8.55
% 8.33/8.55 ============================== PROOF =================================
% 8.33/8.55 % SZS status Theorem
% 8.33/8.55 % SZS output start Refutation
% 8.33/8.55
% 8.33/8.55 % Proof 1 at 6.82 (+ 0.05) seconds.
% 8.33/8.55 % Length of proof is 15.
% 8.33/8.55 % Level of proof is 5.
% 8.33/8.55 % Maximum clause weight is 23.000.
% 8.33/8.55 % Given clauses 2331.
% 8.33/8.55
% 8.33/8.55 496 (all V_nat_2 all V_f2_2 all V_f1_2 all T_b hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2)) # label(fact_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 8.33/8.55 544 (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].
% 8.33/8.55 656 (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].
% 8.33/8.55 1080 (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].
% 8.33/8.55 1082 (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].
% 8.33/8.55 2122 hAPP(c_Nat_Onat_Onat__case(A,B,C),hAPP(c_Nat_OSuc,D)) = hAPP(C,D) # label(fact_nat__case__Suc) # label(axiom). [clausify(496)].
% 8.33/8.55 2165 -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)) | A != B # label(fact_nat__less__le) # label(axiom). [clausify(544)].
% 8.33/8.55 2237 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A)))) # label(fact_less__add__Suc2) # label(axiom). [clausify(656)].
% 8.33/8.55 2676 hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)) # label(help_c__COMBB__1) # label(axiom). [clausify(1080)].
% 8.33/8.55 2678 hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)) # label(help_c__COMBS__1) # label(axiom). [clausify(1082)].
% 8.33/8.55 5018 hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) != B. [resolve(2237,a,2165,a),flip(a)].
% 8.33/8.55 8322 hAPP(hAPP(hAPP(c_COMBS(A,B,C),hAPP(c_COMBB(D,E,F),V6)),V7),V8) = hAPP(V6,hAPP(V8,hAPP(V7,V8))). [para(2678(a,2),2676(a,1))].
% 8.33/8.55 10661 hAPP(c_Nat_OSuc,hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),D),E)) != hAPP(D,E). [para(2678(a,2),5018(a,1,2))].
% 8.33/8.55 13040 hAPP(c_Nat_OSuc,hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Onat_Onat__case(D,E,F)),hAPP(c_Nat_OSuc,V6))) != hAPP(F,V6). [para(2122(a,1),10661(a,2))].
% 8.33/8.55 13041 $F. [resolve(13040,a,8322,a(flip))].
% 8.33/8.55
% 8.33/8.55 % SZS output end Refutation
% 8.33/8.55 ============================== end of proof ==========================
% 8.33/8.55
% 8.33/8.55 ============================== STATISTICS ============================
% 8.33/8.55
% 8.33/8.55 Given=2331. Generated=53439. Kept=11003. proofs=1.
% 8.33/8.55 Usable=2319. Sos=8270. Demods=1061. Limbo=22, Disabled=2852. Hints=0.
% 8.33/8.55 Megabytes=36.42.
% 8.33/8.55 User_CPU=6.82, System_CPU=0.05, Wall_clock=7.
% 8.33/8.55
% 8.33/8.55 ============================== end of statistics =====================
% 8.33/8.55
% 8.33/8.55 ============================== end of search =========================
% 8.33/8.55
% 8.33/8.55 THEOREM PROVED
% 8.33/8.55 % SZS status Theorem
% 8.33/8.55
% 8.33/8.55 Exiting with 1 proof.
% 8.33/8.55
% 8.33/8.55 Process 24101 exit (max_proofs) Mon Jun 6 05:00:57 2022
% 8.33/8.55 Prover9 interrupted
%------------------------------------------------------------------------------