TSTP Solution File: SWW189+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW189+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 01:15:46 EDT 2022
% Result : Timeout 300.03s 300.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW189+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % 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 02:40:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.52/1.75 ============================== Prover9 ===============================
% 1.52/1.75 Prover9 (32) version 2009-11A, November 2009.
% 1.52/1.75 Process 7184 was started by sandbox2 on n018.cluster.edu,
% 1.52/1.75 Mon Jun 6 02:40:05 2022
% 1.52/1.75 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7031_n018.cluster.edu".
% 1.52/1.75 ============================== end of head ===========================
% 1.52/1.75
% 1.52/1.75 ============================== INPUT =================================
% 1.52/1.75
% 1.52/1.75 % Reading from file /tmp/Prover9_7031_n018.cluster.edu
% 1.52/1.75
% 1.52/1.75 set(prolog_style_variables).
% 1.52/1.75 set(auto2).
% 1.52/1.75 % set(auto2) -> set(auto).
% 1.52/1.75 % set(auto) -> set(auto_inference).
% 1.52/1.75 % set(auto) -> set(auto_setup).
% 1.52/1.75 % set(auto_setup) -> set(predicate_elim).
% 1.52/1.75 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.52/1.75 % set(auto) -> set(auto_limits).
% 1.52/1.75 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.52/1.75 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.52/1.75 % set(auto) -> set(auto_denials).
% 1.52/1.75 % set(auto) -> set(auto_process).
% 1.52/1.75 % set(auto2) -> assign(new_constants, 1).
% 1.52/1.75 % set(auto2) -> assign(fold_denial_max, 3).
% 1.52/1.75 % set(auto2) -> assign(max_weight, "200.000").
% 1.52/1.75 % set(auto2) -> assign(max_hours, 1).
% 1.52/1.75 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.52/1.75 % set(auto2) -> assign(max_seconds, 0).
% 1.52/1.75 % set(auto2) -> assign(max_minutes, 5).
% 1.52/1.75 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.52/1.75 % set(auto2) -> set(sort_initial_sos).
% 1.52/1.75 % set(auto2) -> assign(sos_limit, -1).
% 1.52/1.75 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.52/1.75 % set(auto2) -> assign(max_megs, 400).
% 1.52/1.75 % set(auto2) -> assign(stats, some).
% 1.52/1.75 % set(auto2) -> clear(echo_input).
% 1.52/1.75 % set(auto2) -> set(quiet).
% 1.52/1.75 % set(auto2) -> clear(print_initial_clauses).
% 1.52/1.75 % set(auto2) -> clear(print_given).
% 1.52/1.75 assign(lrs_ticks,-1).
% 1.52/1.75 assign(sos_limit,10000).
% 1.52/1.75 assign(order,kbo).
% 1.52/1.75 set(lex_order_vars).
% 1.52/1.75 clear(print_given).
% 1.52/1.75
% 1.52/1.75 % formulas(sos). % not echoed (1150 formulas)
% 1.52/1.75
% 1.52/1.75 ============================== end of input ==========================
% 1.52/1.75
% 1.52/1.75 % From the command line: assign(max_seconds, 300).
% 1.52/1.75
% 1.52/1.75 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.52/1.75
% 1.52/1.75 % Formulas that are not ordinary clauses:
% 1.52/1.75 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].
% 1.52/1.75 2 (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_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = 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].
% 1.52/1.75 3 (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),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x)))) # label(fact_poly__offset__poly) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 4 (all V_q_2 all V_pa_2 all T_a (class_Int_Oring__char__0(T_a) & class_Rings_Oidom(T_a) -> (c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2) <-> V_pa_2 = V_q_2))) # label(fact_poly__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 5 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 6 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 7 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 8 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 9 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 10 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 11 (all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2) <-> V_b_2 = V_c_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 12 (all V_c_2 all V_aa_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2) <-> V_b_2 = V_c_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 13 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 14 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 15 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 16 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 17 (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].
% 1.52/1.75 18 (all V_b all V_n all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n))) # label(fact_add__monom) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 19 (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,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].
% 1.52/1.75 20 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)))) # label(fact_smult__add__left) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 21 (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,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = 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].
% 1.52/1.75 22 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)))) # label(fact_add__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 23 (all V_c_2 all V_b_2 all V_aa_2 all V_f_2 all T_a (c_Groups_Osemigroup(T_a,V_f_2) -> hAPP(hAPP(V_f_2,hAPP(hAPP(V_f_2,V_aa_2),V_b_2)),V_c_2) = hAPP(hAPP(V_f_2,V_aa_2),hAPP(hAPP(V_f_2,V_b_2),V_c_2)))) # label(fact_semigroup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 24 (all V_aa_2 all V_z_2 all V_f_2 all T_a (c_Groups_Ocomm__monoid(T_a,V_f_2,V_z_2) -> hAPP(hAPP(V_f_2,V_aa_2),V_z_2) = V_aa_2)) # label(fact_comm__monoid_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 25 (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].
% 1.52/1.75 26 (all V_h_2 all V_pa_2 all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_offset__poly__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.75 27 (all V_q all T_a (class_Groups_Ocomm__monoid__add(T_a) -> 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].
% 1.52/1.75 28 (all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> 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].
% 1.52/1.75 29 (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].
% 1.52/1.75 30 (all T_a (class_Groups_Ozero(T_a) -> 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].
% 1.52/1.75 31 (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].
% 1.52/1.75 32 (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].
% 1.52/1.75 33 (all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> 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].
% 1.52/1.75 34 (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].
% 1.54/1.75 35 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = V_x_2 <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 36 (all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> 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].
% 1.54/1.75 37 (all V_q_2 all V_pa_2 all T_a (class_Groups_Ozero(T_a) -> (V_pa_2 = V_q_2 <-> (all B_n hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),B_n))))) # label(fact_expand__poly__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 38 (all V_y_2 all V_x_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_Ocoeff(T_a,V_x_2) = c_Polynomial_Ocoeff(T_a,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_coeff__inject) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 39 (all V_n_2 all V_aa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_monom__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 40 (all V_pa_2 all V_aa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_pCons__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 41 (all V_pa_2 all V_aa_2 all T_a (class_Rings_Oidom(T_a) -> (c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_smult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 42 (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].
% 1.54/1.75 43 (all V_b_2 all V_n_2 all V_aa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_Omonom(T_a,V_aa_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2) <-> V_aa_2 = V_b_2))) # label(fact_monom__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 44 (all V_q_2 all V_b_2 all V_pa_2 all V_aa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2) <-> V_aa_2 = V_b_2 & V_pa_2 = V_q_2))) # label(fact_pCons__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.75 45 (all V_a all V_p all V_c all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (c_Polynomial_Osmult(T_a,V_c,V_p) = 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].
% 1.54/1.75 46 (all V_a all V_p all V_c all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),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].
% 1.54/1.75 47 (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].
% 1.54/1.75 48 (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,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = 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].
% 1.54/1.75 49 (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,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),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].
% 1.54/1.75 50 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 51 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 52 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 53 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 54 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 55 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 56 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 57 (all V_aa_2 all V_b_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 58 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)))) # label(fact_smult__add__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 59 (all V_pa_2 all T_a (class_Int_Oring__char__0(T_a) & class_Rings_Oidom(T_a) -> (c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_poly__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 60 (all V_r all V_q all V_c all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) = 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].
% 1.54/1.76 61 (all V_c all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = 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].
% 1.54/1.76 62 (all V_aa_2 all V_pa_2 all T_a (class_Rings_Oidom(T_a) -> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Polynomial_Oorder(T_a,V_aa_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_order__root) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 63 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 64 (all V_pa_2 all V_aa_2 all T_a all V_z_2 all V_f_2 all T_b (class_Groups_Ozero(T_b) -> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2 -> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))))) # label(fact_poly__rec__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 65 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),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].
% 1.54/1.76 66 (all V_pa_2 all V_aa_2 all V_f_2 all V_z_2 all T_a all T_b (class_Groups_Ozero(T_b) -> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))))) # label(fact_poly__rec_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 67 (all V_pa_2 all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)) <-> c_Polynomial_Opos__poly(T_a,V_pa_2) | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_pos__poly__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 68 (all V_q all V_a all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),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].
% 1.54/1.76 69 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),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].
% 1.54/1.76 70 (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,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = 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].
% 1.54/1.76 71 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),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].
% 1.54/1.76 72 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,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].
% 1.54/1.76 73 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,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].
% 1.54/1.76 74 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,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].
% 1.54/1.76 75 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,V_lx,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].
% 1.54/1.76 76 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,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].
% 1.54/1.76 77 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,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].
% 1.54/1.76 78 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,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].
% 1.54/1.76 79 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = 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].
% 1.54/1.76 80 (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_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = 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].
% 1.54/1.76 81 (all V_n all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)))) # label(fact_mult__monom) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 82 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.76 83 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.76 84 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 85 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 86 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 87 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 88 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 89 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 90 (all V_b_2 all V_c_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 91 (all V_z_2 all V_x_2 all V_y_2 all V_w_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2)) <-> V_w_2 = V_x_2 | V_y_2 = V_z_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 92 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 93 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),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].
% 1.54/1.76 94 (all V_d_2 all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_aa_2 != V_b_2 & V_c_2 != V_d_2 <-> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 95 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),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].
% 1.54/1.76 96 (all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> 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].
% 1.54/1.76 97 (all V_q all T_a (class_Rings_Ocomm__semiring__0(T_a) -> 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].
% 1.54/1.76 98 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 99 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p)) = c_Polynomial_Osmult(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_p))) # label(fact_smult__smult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 100 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q) = c_Polynomial_Osmult(T_a,V_a,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].
% 1.54/1.76 101 (all V_q all V_a all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,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].
% 1.54/1.76 102 (all V_r all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_r),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].
% 1.54/1.76 103 (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,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].
% 1.54/1.76 104 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 105 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 106 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 107 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 108 (all V_d all V_c all V_b all V_a all V_r all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_r != c_Groups_Ozero__class_Ozero(T_a) -> (V_a = V_b & V_c != V_d -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 109 (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].
% 1.54/1.76 110 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Polynomial_Osmult(T_a,V_a,V_p)))) # label(fact_smult__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 111 (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,c_Polynomial_Osmult(T_a,V_a,V_p)),V_n) = 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].
% 1.54/1.76 112 (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,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = 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].
% 1.54/1.76 113 (all V_n all V_b all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_n))) # label(fact_smult__monom) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 114 (all V_p all V_a all T_a (class_Groups_Ozero(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,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].
% 1.54/1.76 115 (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,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,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].
% 1.54/1.76 116 (all V_pa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_psize__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 117 (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)) = 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].
% 1.54/1.76 118 (all T_a all V_z_2 all V_f_2 all T_b (class_Groups_Ozero(T_b) -> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2 -> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2))) # label(fact_poly__rec__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 119 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 120 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),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].
% 1.54/1.76 121 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 122 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 123 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 124 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 125 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 126 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 127 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 128 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 129 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 130 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (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].
% 1.54/1.76 131 (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) -> 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].
% 1.54/1.76 132 (all V_b_2 all V_aa_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) | V_b_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 133 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> 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].
% 1.54/1.76 134 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> 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].
% 1.54/1.76 135 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 136 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 137 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,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].
% 1.54/1.76 138 (all V_b_2 all V_c_2 all V_aa_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 139 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) & c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 140 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 141 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 142 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,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].
% 1.54/1.76 143 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,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].
% 1.54/1.76 144 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 145 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 146 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 147 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,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].
% 1.54/1.76 148 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 149 (all V_n all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 150 (all V_n_2 all V_m_2 (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].
% 1.54/1.76 151 (all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 152 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 153 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 154 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 155 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 156 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 157 (all V_P_2 all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 158 (all V_t all V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 159 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 160 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 161 (all V_y all V_x (V_x != V_y -> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 162 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 163 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 164 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 165 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 166 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 167 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 168 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 169 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 170 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 171 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2) = 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].
% 1.54/1.76 172 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = 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].
% 1.54/1.76 173 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 174 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 175 (all V_n_2 all V_m_2 (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].
% 1.54/1.76 176 (all V_m 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].
% 1.54/1.76 177 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 178 (all V_n 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].
% 1.54/1.76 179 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = 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].
% 1.54/1.76 180 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = 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].
% 1.54/1.76 181 (all V_k all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 182 (all V_z all V_y all V_x c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 183 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 184 (all V_j all V_i -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)) # label(fact_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 185 (all V_i all V_j -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)) # label(fact_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 186 (all V_n all V_m all V_k c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 187 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 188 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 189 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.76 190 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 191 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 192 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 193 (all V_n all V_m all V_l all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 194 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 195 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> 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].
% 1.54/1.77 196 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> 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].
% 1.54/1.77 197 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> 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].
% 1.54/1.77 198 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> 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].
% 1.54/1.77 199 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 200 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 201 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 202 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 203 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = 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].
% 1.54/1.77 204 (all V_pa_2 all V_aa_2 all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)) = c_Nat_Onat_Onat__case(T_a,V_aa_2,c_Polynomial_Ocoeff(T_a,V_pa_2)))) # label(fact_coeff__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 205 (all V_pa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_pa_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2)))))) # label(fact_pos__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 206 (all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))) = c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))))) # label(fact_coeff__mult__degree__sum) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 207 (all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_k) & c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,B_k) = V_j)))) # label(fact_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 208 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 209 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 210 (all V_h all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)) = c_Polynomial_Odegree(T_a,V_p))) # label(fact_degree__offset__poly) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 211 (all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_degree__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 212 (all V_n all V_a all T_a (class_Groups_Ozero(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)) = V_n))) # label(fact_degree__monom__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 213 (all V_p all V_q all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p)) -> c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_p)))) # label(fact_degree__add__eq__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 214 (all V_q all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) -> c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_q)))) # label(fact_degree__add__eq__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 215 (all V_q all V_n all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n))))) # label(fact_degree__add__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 216 (all V_f2_2 all V_f1_2 all T_a hAPP(c_Nat_Onat_Onat__case(T_a,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].
% 1.54/1.77 217 (all V_p all V_a all T_a (class_Rings_Oidom(T_a) -> (V_a = c_Groups_Ozero__class_Ozero(T_a) -> c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)) = c_Polynomial_Odegree(T_a,V_p)))) # label(fact_degree__smult__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 218 (all V_n all V_p all T_a (class_Groups_Ozero(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) -> hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_coeff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 219 (all V_pa_2 all T_a (class_Groups_Ozero(T_a) -> (hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2)) = c_Groups_Ozero__class_Ozero(T_a) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_leading__coeff__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 220 (all V_p all T_a (class_Groups_Ozero(T_a) -> (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_leading__coeff__neq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 221 (all V_a all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_degree__pCons__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 222 (all V_q all V_p all T_a (class_Rings_Oidom(T_a) -> (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> (V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Odegree(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))))) # label(fact_degree__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 223 (all V_c_2 all V_pa_2 all T_a (class_Rings_Ocomm__semiring__0(T_a) -> (c_Polynomial_Osynthetic__div(T_a,V_pa_2,V_c_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> c_Polynomial_Odegree(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_synthetic__div__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 224 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = 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].
% 1.54/1.77 225 (all V_k all V_j all V_u all V_i c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_u),V_k)) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 226 (all V_r_2 all V_q_2 all V_y_2 all V_x_2 all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2) <-> V_x_2 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2) & (V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) & (V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2)))))) # label(fact_pdivmod__rel__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 227 (all V_n all V_p all T_a (class_Groups_Ozero(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) -> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a) -> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n))))) # label(fact_eq__zero__or__degree__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 228 (all V_pa_2 all V_aa_2 all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2) = c_Polynomial_OAbs__poly(T_a,c_Nat_Onat_Onat__case(T_a,V_aa_2,c_Polynomial_Ocoeff(T_a,V_pa_2))))) # label(fact_pCons__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 229 (all V_p all T_a (class_Groups_Ozero(T_a) -> (V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))))) # label(fact_psize__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 230 (all V_p all V_n all T_a (class_Groups_Ozero(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p)) -> (exists B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i) & hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) != c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_less__degree__imp) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 231 (all V_a all V_p all T_a (class_Groups_Ozero(T_a) -> (V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))))) # label(fact_degree__pCons__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 232 (all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))))) # label(fact_degree__pcompose__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 233 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 234 (all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 235 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_le0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 236 (all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 237 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)) <-> 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].
% 1.54/1.77 238 (all V_r2 all V_q2 all V_r1 all V_q1 all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2) -> V_q1 = V_q2 & V_r1 = V_r2)))) # label(fact_pdivmod__rel__unique) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 239 (all V_r2 all V_q2 all V_r1 all V_q1 all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2) -> V_r1 = V_r2)))) # label(fact_pdivmod__rel__unique__mod) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 240 (all V_r2 all V_q2 all V_r1 all V_q1 all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2) -> V_q1 = V_q2)))) # label(fact_pdivmod__rel__unique__div) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 241 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 242 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> 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].
% 1.54/1.77 243 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2) <-> 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].
% 1.54/1.77 244 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 245 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 246 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) <-> V_n_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 247 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 248 (all V_y all V_x (c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 249 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 250 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) -> (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> V_m = c_Nat_OSuc(V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 251 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 252 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 253 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 254 (all V_n all V_m (V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 255 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2)) <-> 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].
% 1.54/1.77 256 (all V_nat_H_2 all V_nat_2 (c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 257 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = c_Nat_OSuc(V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 258 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 259 (all V_n_2 all V_m_2 (-c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 260 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n)) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 261 (all V_n -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n)) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 262 (all V_n c_Nat_OSuc(V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 263 (all V_n V_n != c_Nat_OSuc(V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 264 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) # label(fact_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 265 (all V_p all V_a all T_a (class_Groups_Ozero(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))))) # label(fact_degree__pCons__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 266 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 267 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 268 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 269 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 270 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 271 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 272 (all V_b_2 all V_c_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 273 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 274 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 275 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 276 (all V_nat_H_1 c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 277 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 278 (all V_m c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 279 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 280 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 281 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) -> (-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].
% 1.54/1.77 282 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 283 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Nat_OSuc(V_m) != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 284 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 285 (all V_m all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m)) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 286 (all V_m_2 all V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) <-> V_n_2 = V_m_2))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 287 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2)) <-> 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].
% 1.54/1.77 288 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = V_n_2)) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 289 (all V_n_2 all V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 290 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 291 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 292 (all V_n all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 293 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 294 (all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 295 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 296 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) | V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 297 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (V_m != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 298 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 299 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 300 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 301 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 302 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 303 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 304 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 305 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 306 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 307 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 308 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 309 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 310 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 311 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 312 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 313 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 314 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 315 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 316 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 317 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 318 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 319 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 320 (all V_nat_2 all V_f2_2 all V_f1_2 all T_a hAPP(c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2),c_Nat_OSuc(V_nat_2)) = hAPP(V_f2_2,V_nat_2)) # label(fact_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 321 (all V_x all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x))) # label(fact_pdivmod__rel__by__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 322 (all V_y all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_pdivmod__rel__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 323 (all V_r_2 all V_q_2 all V_x_2 all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q_2,V_r_2) <-> V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_r_2 = V_x_2))) # label(fact_pdivmod__rel__by__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 324 (all V_r_2 all V_q_2 all V_y_2 all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_q_2,V_r_2) <-> V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_pdivmod__rel__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 325 (all V_a all V_r all V_q all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r) -> c_Polynomial_Opdivmod__rel(T_a,c_Polynomial_Osmult(T_a,V_a,V_x),V_y,c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_Osmult(T_a,V_a,V_r))))) # label(fact_pdivmod__rel__smult__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 326 (all V_x_2 all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_OAbs__poly(T_a,c_Polynomial_Ocoeff(T_a,V_x_2)) = V_x_2)) # label(fact_coeff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 327 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,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].
% 1.54/1.77 328 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 329 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 330 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 331 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 332 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 333 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 334 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 335 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 336 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 337 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,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].
% 1.54/1.77 338 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,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].
% 1.54/1.77 339 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,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].
% 1.54/1.77 340 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 341 (all V_b_2 all V_aa_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 342 (all V_b_2 all V_aa_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 343 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 344 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 345 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 346 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 347 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2) -> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 348 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 349 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 350 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 351 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 352 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 353 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) <-> (exists B_m V_n_2 = c_Nat_OSuc(B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 354 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 355 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = c_Nat_OSuc(B_j) & 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].
% 1.54/1.77 356 (all V_n_2 all V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 357 (all V_n_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 358 (all V_n_2 all V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 359 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Nat_OSuc(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].
% 1.54/1.77 360 (all V_m all V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i)))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 361 (all V_m all V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m)))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 362 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)) <-> 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].
% 1.54/1.77 363 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))) # label(fact_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 364 (all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))) # label(fact_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 365 (all V_n all V_p all V_a all T_a (class_Groups_Ozero(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),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].
% 1.54/1.77 366 (all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),c_Polynomial_Odegree(T_a,V_p)))) # label(fact_degree__smult__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 367 (all V_q all V_n all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n))))) # label(fact_degree__add__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 368 (all V_n all V_a all T_a (class_Groups_Ozero(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_n))) # label(fact_degree__monom__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 369 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b))))) # label(fact_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 370 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b))))) # label(fact_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 371 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 372 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.77 373 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 374 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 375 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 376 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 377 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 378 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 379 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 380 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 381 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 382 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 383 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 384 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 385 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 386 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 387 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a)) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) & V_y_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 388 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 389 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))))) # label(fact_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 390 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,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].
% 1.54/1.78 391 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,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].
% 1.54/1.78 392 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 393 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 394 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 395 (all V_r_H all V_q_H all V_z all V_r all V_q all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r) -> (c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H) -> c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_y,V_z),V_q_H,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_y,V_r_H),V_r)))))) # label(fact_pdivmod__rel__mult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 396 (all V_n all V_p all T_a (class_Groups_Ozero(T_a) -> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) != c_Groups_Ozero__class_Ozero(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))))) # label(fact_le__degree) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 397 (all V_a all V_p all T_a (class_Groups_Ozero(T_a) -> (V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))))) # label(fact_degree__pCons__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 398 (all V_n all V_a all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = 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].
% 1.54/1.78 399 (all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))))) # label(fact_degree__mult__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 400 (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)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(T_a,V_a,V_p),c_Polynomial_Odegree(T_a,V_p))))) # label(fact_order__degree) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 401 (all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) -> V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 402 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 403 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) <-> (exists B_n V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 404 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 405 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 406 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless(T_a,V_y,V_x))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 407 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 408 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 409 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 410 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 411 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 412 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 413 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 414 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 415 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 416 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 417 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 418 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 419 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 420 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 421 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 422 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 423 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> (all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 424 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (V_x != V_y -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 425 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 426 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 427 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 428 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 429 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless(T_a,V_a,V_c))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 430 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_c,V_a))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 431 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_c))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 432 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 433 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 434 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 435 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 436 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 437 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 438 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 439 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_y,V_x))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 440 (all V_x_2 all V_y_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 441 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_x = V_y | c_Orderings_Oord__class_Oless(T_a,V_y,V_x))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 442 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) | V_x_2 = V_y_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 443 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (V_x_2 != V_y_2 <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 444 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 445 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 446 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 447 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 448 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 449 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 450 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 451 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 452 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 453 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 454 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 455 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 456 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 457 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 458 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 459 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 460 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 461 (all V_y_2 all V_x_2 all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & -c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 462 (all V_p all V_n all T_a (class_Groups_Ozero(T_a) -> ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i) -> hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) = c_Groups_Ozero__class_Ozero(T_a))) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)))) # label(fact_degree__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 463 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v) -> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a)))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 464 (all V_nat c_Nat_Onat_Onat__size(c_Nat_OSuc(V_nat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(V_nat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 465 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2))))) # label(fact_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 466 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2)))) # label(fact_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 467 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) & -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 468 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 469 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 470 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oab__group__add(T_a) -> (V_aa_2 = V_b_2 <-> c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 471 (all V_b_2 all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 472 (all V_d_2 all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 473 (all V_d_2 all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 474 (all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = 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].
% 1.54/1.78 475 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 476 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)))) # label(fact_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 477 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)))) # label(fact_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 478 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)))) # label(fact_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 479 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 480 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,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].
% 1.54/1.78 481 (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].
% 1.54/1.78 482 (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].
% 1.54/1.78 483 (all V_n all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 484 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 485 (all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 486 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 487 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> 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].
% 1.54/1.78 488 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.78 489 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> 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].
% 1.54/1.78 490 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> 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].
% 1.54/1.78 491 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.78 492 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> 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].
% 1.54/1.78 493 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 494 (all V_k all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 495 (all V_n all V_k all V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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].
% 1.54/1.78 496 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 497 (all V_n all V_k all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 498 (all V_n all V_m all V_k c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 499 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))) # label(fact_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 500 (all V_m all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.54/1.78 501 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.54/1.78 502 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 503 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 504 (all V_l all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 505 (all V_n all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i)) # label(fact_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 506 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_m_2 = V_n_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 507 (all V_n all V_m all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 508 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) <-> 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].
% 1.54/1.78 509 (all V_n all V_m all V_k c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))) # label(fact_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 510 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 511 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)))) # label(fact_diff__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 512 (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,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = 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].
% 1.54/1.78 513 (all V_p all V_b all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)))) # label(fact_smult__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 514 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__diff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 515 (all V_b all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n))) # label(fact_diff__monom) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 516 (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].
% 1.54/1.78 517 (all V_d_2 all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Groups_Oab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) -> (V_aa_2 = V_b_2 <-> V_c_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 518 (all V_x_2 all T_a (class_Groups_Oone(T_a) -> (c_Groups_Oone__class_Oone(T_a) = V_x_2 <-> V_x_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 519 (all V_k all V_j all V_i c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 520 (all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 521 (all V_n all V_m c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 522 (all V_c all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_degree__synthetic__div) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 523 (all V_n_2 all V_m_2 (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].
% 1.54/1.78 524 (all V_n 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].
% 1.54/1.78 525 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = 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].
% 1.54/1.78 526 (all V_n 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].
% 1.54/1.78 527 (all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.78 528 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n)) # label(fact_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 529 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 530 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))))) # label(fact_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 531 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> 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) -> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))))) # label(fact_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 532 (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].
% 1.54/1.78 533 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 534 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 535 (all V_b all V_a all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))))) # label(fact_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 536 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_aa_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2) <-> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2) = V_d_2))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 537 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_aa_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2) <-> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 538 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 539 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 540 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 541 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 542 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 543 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 544 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 545 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 546 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 547 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)) <-> 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].
% 1.54/1.78 548 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 549 (all V_n all V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 550 (all V_m all V_n c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,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].
% 1.54/1.78 551 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 552 (all V_n_2 all V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> 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].
% 1.54/1.78 553 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 554 (all V_n all V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m)) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 555 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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].
% 1.54/1.78 556 (all V_c all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 557 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) <-> 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].
% 1.54/1.78 558 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 559 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.54/1.78 560 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 561 (all V_k_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2 <-> V_j_2 = 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].
% 1.54/1.78 562 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m)) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 563 (all V_i_2 all V_j_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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].
% 1.54/1.78 564 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.54/1.78 565 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m)) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 566 (all V_m all V_n all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.54/1.78 567 (all V_i_2 all V_k_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,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].
% 1.54/1.78 568 (all V_i all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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].
% 1.54/1.78 569 (all V_n c_Nat_OSuc(V_n) = 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].
% 1.54/1.78 570 (all V_n c_Nat_OSuc(V_n) = 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].
% 1.54/1.78 571 (all V_n all V_m (V_m = 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].
% 1.54/1.78 572 (all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_degree__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 573 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_aa_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2)))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 574 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_aa_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 575 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_aa_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2)))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 576 (all V_d_2 all V_b_2 all V_c_2 all V_e_2 all V_aa_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 577 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,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].
% 1.54/1.78 578 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,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].
% 1.54/1.78 579 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 580 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n)) # label(fact_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 581 (all V_i all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n))) # label(fact_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 582 (all V_b_2 all V_aa_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2))) <-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) & -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_d (V_aa_2 = 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].
% 1.54/1.78 583 (all V_b_2 all V_aa_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2))) <-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (all B_d (V_aa_2 = 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].
% 1.54/1.78 584 (all V_m all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)))) # label(fact_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 585 (all V_m all V_j all V_k (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 586 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2)))) # label(fact_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 587 (all V_n all V_m all V_u all V_i all V_j (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_u),V_m),V_n))) # label(fact_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 588 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2) <-> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2) = V_n_2))) # label(fact_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 589 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2))))) # label(fact_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 590 (all V_n all V_m all V_u all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i),V_u),V_n)))) # label(fact_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 591 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) -> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2) <-> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)))) # label(fact_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 592 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v) -> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a)))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.78 593 (all V_x all T_a (class_Rings_Oring__1(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))))) # label(fact_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 594 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 595 (all V_p all V_c all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),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)),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].
% 1.54/1.79 596 (all V_nat c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_OSuc(V_nat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 597 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))))) # label(fact_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 598 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2)))) # label(fact_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 599 (all V_aa_2 all V_b_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)))) # label(fact_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 600 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))))) # label(fact_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 601 (all V_p all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p)) # label(fact_diff__poly__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 602 (all V_q all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q))) # label(fact_diff__poly__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 603 (all V_n c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n) # label(fact_nat__size) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 604 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) # label(fact_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 605 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)))) # label(fact_smult__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 606 (all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)))) # label(fact_smult__minus__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 607 (all V_y_2 all V_x_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)))) # label(fact_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 608 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a)) # label(fact_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 609 (all V_b_2 all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 610 (all V_b_2 all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2 <-> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 611 (all V_b_2 all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> V_aa_2 = V_b_2))) # label(fact_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 612 (all V_n all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n))) # label(fact_minus__monom) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 613 (all V_x all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))) # label(fact_poly__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 614 (all V_p all V_a all T_a (class_Rings_Ocomm__ring(T_a) -> c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)))) # label(fact_smult__minus__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 615 (all V_n all V_p all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n) = 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].
% 1.54/1.79 616 (all V_p all V_a all T_b (class_Groups_Oab__group__add(T_b) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)))) # label(fact_minus__poly__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 617 (all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)))) # label(fact_minus__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 618 (all V_p all T_a (class_Groups_Oab__group__add(T_a) -> c_Polynomial_Odegree(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Polynomial_Odegree(T_a,V_p))) # label(fact_degree__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 619 (all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_minus__poly__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 620 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b)) # label(fact_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 621 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b)) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 622 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))) # label(fact_minus__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 623 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 624 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)))) # label(fact_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 625 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 626 (all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x)))) # label(fact_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 627 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 628 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 629 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 630 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 631 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))) # label(fact_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 632 (all V_b_2 all V_aa_2 all T_a (class_Rings_Oidom(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_aa_2) = c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2) <-> V_aa_2 = V_b_2 | V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 633 (all V_aa_2 all V_b_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)))) # label(fact_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 634 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2)))) # label(fact_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 635 (all V_b_2 all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))))) # label(fact_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 636 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2 <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 637 (all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 638 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 639 (all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) <-> c_Groups_Ozero__class_Ozero(T_a) = V_aa_2))) # label(fact_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 640 (all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_minus__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 641 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) <-> V_x_2 = V_y_2 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))))) # label(fact_less__eq__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 642 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) <-> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))))) # label(fact_less__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 643 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 644 (all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 645 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 646 (all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 647 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 648 (all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 649 (all V_aa_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 650 (all V_aa_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 651 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b))) # label(fact_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 652 (all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 653 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 654 (all V_b_2 all V_aa_2 all T_a (class_Groups_Ogroup__add(T_a) -> (V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) <-> c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 655 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_right__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 656 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a))) # label(fact_diff__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 657 (all V_x_2 all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2) = c_Groups_Oone__class_Oone(T_a) <-> V_x_2 = c_Groups_Oone__class_Oone(T_a) | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 658 (all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_x))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 659 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) # label(fact_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 660 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 661 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 662 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 663 (all V_q all V_n all V_p all T_a (class_Groups_Oab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n))))) # label(fact_degree__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 664 (all V_q all V_n all V_p all T_a (class_Groups_Oab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n))))) # label(fact_degree__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 665 (all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Polynomial_Opos__poly(T_a,V_p) | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)))) # label(fact_pos__poly__total) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 666 (all V_a all V_b all V_r all V_q all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r) -> (V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> (V_b = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_r)),c_Polynomial_Odegree(T_a,V_y)),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y))) -> c_Polynomial_Opdivmod__rel(T_a,c_Polynomial_OpCons(T_a,V_a,V_x),V_y,c_Polynomial_OpCons(T_a,V_b,V_q),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_r),c_Polynomial_Osmult(T_a,V_b,V_y)))))))) # label(fact_pdivmod__rel__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 667 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) # label(fact_Limits_Ominus__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 668 (all V_d all V_b all V_c all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)))) # label(fact_Deriv_Oadd__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 669 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))) # label(fact_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 670 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_divide__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 671 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)))) # label(fact_divide_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 672 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))) # label(fact_divide_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 673 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))) # label(fact_minus__divide__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 674 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 675 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 676 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 677 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c))) # label(fact_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 678 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 679 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)))) # label(fact_divide_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 680 (all V_b all V_a all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) = V_b -> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 681 (all V_a all V_b all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (V_b = c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) -> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 682 (all V_aa_2 all V_b_2 all V_c_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_aa_2 <-> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 683 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_aa_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) <-> c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2) = V_b_2)))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 684 (all V_h all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)),V_h) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h),V_d)))) # label(fact_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 685 (all V_aa_2 all V_b_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_b_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2) = c_Groups_Oone__class_Oone(T_a) <-> V_aa_2 = V_b_2)))) # label(fact_right__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 686 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__self) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 687 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (V_a = c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)) & (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__self__if) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 688 (all V_a all V_b all T_a (class_Rings_Odivision__ring(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 689 (all V_a all V_b all T_a (class_Rings_Odivision__ring(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))))) # label(fact_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 690 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 691 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 692 (all V_aa_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))))) # label(fact_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 693 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 694 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))) # label(fact_minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 695 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))) # label(fact_minus__divide__divide) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 696 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)))))) # label(fact_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 697 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 698 (all V_b_2 all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 699 (all V_b_2 all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 700 (all V_b_2 all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 701 (all V_b_2 all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 702 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 703 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 704 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 705 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 706 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 707 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 708 (all V_w_2 all V_x_2 all V_z_2 all V_y_2 all T_a (class_Fields_Ofield(T_a) -> (V_y_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_z_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2) <-> c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2) = c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 709 (all V_b all V_a all V_c all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 710 (all V_b all V_a all V_c all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 711 (all V_aa_2 all V_c_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_aa_2 <-> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 712 (all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_aa_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) <-> (V_c_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2) = V_b_2) & (V_c_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 713 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 714 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 715 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 716 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 717 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w) -> (c_Orderings_Oord__class_Oless(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__less2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 718 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 719 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 720 (all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 721 (all V_aa_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))))) # label(fact_divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 722 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 723 (all V_aa_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))))) # label(fact_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 724 (all V_z all V_x all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z))))) # label(fact_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 725 (all V_x all V_z all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x) -> c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 726 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))))) # label(fact_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 727 (all V_aa_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 728 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 729 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 730 (all V_x all V_z all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y)))) # label(fact_add__num__frac) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 731 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z)))) # label(fact_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 732 (all V_z all V_x all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y)))) # label(fact_add__frac__num) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 733 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z)))) # label(fact_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 734 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)))))) # label(fact_add__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 735 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z)))) # label(fact_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 736 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z)))) # label(fact_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 737 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)))))) # label(fact_diff__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 738 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b)))) # label(fact_gt__half__sum) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 739 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))))) # label(fact_less__half__sum) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 740 (all V_c_2 all V_b_2 all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 741 (all V_aa_2 all V_c_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)) & (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))))) # label(fact_divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 742 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 743 (all V_aa_2 all V_b_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))))) # label(fact_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 744 (all V_z all V_x all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z))))) # label(fact_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 745 (all V_x all V_z all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 746 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))))) # label(fact_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 747 (all V_x all V_a all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_x),V_y) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),c_Polynomial_Odegree(T_a,V_y)),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y))),V_y))))) # label(fact_mod__pCons) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 748 (all V_y_2 all V_x_2 all T_a (class_Lattices_Oboolean__algebra(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 749 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x))))) # label(fact_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 750 (all V_y all V_x all V_a all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_x),V_y) = c_Polynomial_Osmult(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_mod__smult__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 751 (all V_r all V_q all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_r))) # label(fact_mod__poly__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 752 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y)) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_x))) # label(fact_mod__poly__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 753 (all V_y all V_x all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Polynomial_Osmult(T_a,V_a,V_y)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_mod__smult__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 754 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_poly__mod__minus__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 755 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))) # label(fact_poly__mod__minus__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 756 (all V_x all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Odegree(T_a,V_y))))) # label(fact_degree__mod__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 757 (all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) = V_a)) # label(fact_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 758 (all V_x all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = V_x)) # label(fact_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 759 (all V_b all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))) # label(fact_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 760 (all V_x_2 all V_B_2 all V_A_2 all T_b all T_a (class_Groups_Ominus(T_a) -> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 761 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x)) # label(fact_double__compl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 762 (all V_x_2 all V_A_2 all T_b all T_a (class_Groups_Ouminus(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)))) # label(fact_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 763 (all V_y_2 all V_x_2 all T_a (class_Lattices_Oboolean__algebra(T_a) -> (c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 764 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 765 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 766 (all V_k all V_n all V_m c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))) # label(fact_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 767 (all V_n all V_m all V_k c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))) # label(fact_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 768 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) # label(fact_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 769 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) # label(fact_mod__mult__self3) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 770 (all V_d_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> (exists B_q V_m_2 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_d_2,B_q)))) # label(fact_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 771 (all V_n all V_m ((c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))))) # label(fact_mod__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 772 (all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mod__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 773 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)) # label(fact_mod__mult__self4) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 774 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_mod__le__divisor) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 775 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 776 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m)) # label(fact_mod__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 777 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_mod__less__divisor) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 778 (all V_n all V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_mod__geq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.79 779 (all V_n all V_m ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m) & (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)))) # label(fact_mod__if) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 780 (all V_m all V_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_le__mod__geq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 781 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(V_P_2,V_n_2))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) -> (V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,B_i),B_j) -> hBOOL(hAPP(V_P_2,B_j)))))))) # label(fact_split__mod) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 782 (all V_q all V_b all V_r all V_c (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_b,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_b,V_c))))) # label(fact_mod__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 783 (all V_m all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_k) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 784 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 785 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 786 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 787 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__self) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 788 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 789 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c))) # label(fact_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 790 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c))) # label(fact_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 791 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_c,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)))) # label(fact_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 792 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 793 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 794 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 795 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 796 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 797 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 798 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 799 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 800 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 801 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 802 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 803 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__diff__cong) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 804 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 805 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 806 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 807 (all V_a_H all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_H),V_b)))) # label(fact_mod__minus__cong) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 808 (all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b))) # label(fact_mod__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 809 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 810 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 811 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 812 (all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) & (V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) -> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) & (-c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) -> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))))))) # label(fact_sgn__poly__def) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 813 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Ozero__class_Ozero(T_a)) & (-(V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) -> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_poly__gcd__monic) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 814 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)))) # label(fact_sgn__minus) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 815 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) # label(fact_poly__gcd__minus__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 816 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) # label(fact_poly__gcd__minus__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 817 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_sgn__greater) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 818 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_sgn__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 819 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_sgn__one) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 820 (all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(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_poly__gcd__0__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 821 (all V_y_2 all V_x_2 all T_a (class_Fields_Ofield(T_a) -> (c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_poly__gcd__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 822 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a))) # label(fact_sgn__sgn) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 823 (all V_c all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)))) # label(fact_poly__gcd_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 824 (all V_c all V_a all V_b all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c)) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)))) # label(fact_poly__gcd_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 825 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,V_a,V_b) = c_Polynomial_Opoly__gcd(T_a,V_b,V_a))) # label(fact_poly__gcd_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 826 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a),c_Groups_Osgn__class_Osgn(T_a,V_b)))) # label(fact_sgn__times) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 827 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x),c_Groups_Osgn__class_Osgn(T_a,V_y)))) # label(fact_sgn__mult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 828 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sgn__0__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 829 (all T_a (class_Groups_Osgn__if(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 830 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 831 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 832 (all V_x all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))) # label(fact_poly__gcd__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 833 (all V_y all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))) # label(fact_poly__gcd__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 834 (all V_x all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))))) # label(fact_poly__gcd_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 835 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_sgn__1__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 836 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 837 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))) # label(fact_sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 838 (all V_aa_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_sgn__1__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 839 (all V_x all T_a (class_Groups_Osgn__if(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)) & (V_x != c_Groups_Ozero__class_Ozero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)) & (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))))) # label(fact_sgn__if) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 840 (all V_x all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x))),V_x)) & (V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))))) # label(fact_poly__gcd__code) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 841 (all V_n_2 all V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_P_2,V_n_2)) -> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) & (all B_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) -> -hBOOL(hAPP(V_P_2,B_i)))) & hBOOL(hAPP(V_P_2,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].
% 1.54/1.80 842 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a))) # label(fact_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 843 (all V_a all T_a (class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a))) # label(fact_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 844 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 845 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 846 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Oone__class_Oone(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b))) # label(fact_inverse__unique) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 847 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a)) # label(fact_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 848 (all V_b_2 all V_aa_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2) <-> V_aa_2 = V_b_2))) # label(fact_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 849 (all V_b all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b) -> V_a = V_b))) # label(fact_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 850 (all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 851 (all V_aa_2 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 852 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 853 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a))) # label(fact_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 854 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 855 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> V_a = V_b))))) # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 856 (all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_inverse__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 857 (all V_x_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a) <-> V_x_2 = c_Groups_Oone__class_Oone(T_a)))) # label(fact_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 858 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 859 (all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_field__inverse__zero) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 860 (all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 861 (all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 862 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a))) # label(fact_inverse__divide) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 863 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)))) # label(fact_field__divide__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 864 (all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)))) # label(fact_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 865 (all V_aa_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 866 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 867 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a))))) # label(fact_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 868 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 869 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 870 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 871 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 872 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 873 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 874 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))))) # label(fact_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 875 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)))) # label(fact_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 876 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 877 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 878 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a))))) # label(fact_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 879 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) -> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a))))) # label(fact_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 880 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)))) # label(fact_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 881 (all V_b all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_inverse__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 882 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 883 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 884 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_one__less__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 885 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))) # label(fact_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 886 (all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_field__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 887 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_left__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 888 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_right__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 889 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)))) # label(fact_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 890 (all V_r all V_q all V_y all V_x all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r) -> c_Polynomial_Opdivmod__rel(T_a,V_x,c_Polynomial_Osmult(T_a,V_a,V_y),c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_q),V_r))))) # label(fact_pdivmod__rel__smult__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 891 (all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))))) # label(fact_one__le__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 892 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)))) # label(fact_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 893 (all V_x_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))))) # label(fact_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 894 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))))) # label(fact_Deriv_Oinverse__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 895 (all V_h all V_b all V_a all T_a (class_RealVector_Oreal__normed__field(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),V_h) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_h)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))))) # label(fact_DERIV__inverse__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 896 (all V_x all T_a (class_Fields_Ofield(T_a) -> c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x))),V_x))) # label(fact_poly__gcd_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 897 (all V_y all V_x all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> ((all B_z (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z) -> (c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,B_z,V_x),V_y)))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 898 (all V_c_2 all V_pa_2 all T_a (class_Rings_Oidom(T_a) -> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_c_2) = c_Groups_Ozero__class_Ozero(T_a) <-> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)))) # label(fact_poly__eq__0__iff__dvd) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 899 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.80 900 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Opoly__gcd(T_a,V_x,V_y),V_x))) # label(fact_poly__gcd__dvd1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 901 (all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Opoly__gcd(T_a,V_x,V_y),V_y))) # label(fact_poly__gcd__dvd2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 902 (all V_y_2 all V_x_2 all T_a (class_Rings_Ocomm__ring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2)))) # label(fact_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 903 (all V_y_2 all V_x_2 all T_a (class_Rings_Ocomm__ring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2) <-> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2)))) # label(fact_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 904 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_z) -> c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)))))) # label(fact_dvd__diff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 905 (all V_q all V_p all T_a (class_Rings_Oidom(T_a) -> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) = hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q)) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_q,V_p) -> V_p = V_q))))) # label(fact_poly__dvd__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 906 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> 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].
% 1.54/1.80 907 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (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].
% 1.54/1.80 908 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)))) # label(fact_dvd__mult__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 909 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)))) # label(fact_dvd__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 910 (all V_k all V_b all V_a all T_a (class_Rings_Odvd(T_a) -> (V_a = c_Groups_Otimes__class_Otimes(T_a,V_b,V_k) -> c_Rings_Odvd__class_Odvd(T_a,V_b,V_a)))) # label(fact_dvdI) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 911 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_d) -> c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)))))) # label(fact_mult__dvd__mono) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 912 (all V_b all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))) # label(fact_dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 913 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))) # label(fact_dvd__mult2) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 914 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)))) # label(fact_dvd__triv__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 915 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))) # label(fact_dvd__triv__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 916 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))))) # label(fact_dvd__add) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 917 (all V_a all V_q all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))))) # label(fact_dvd__smult) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 918 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q) -> 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].
% 1.54/1.80 919 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,V_c))))) # label(fact_dvd__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 920 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,V_a))) # label(fact_dvd__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 921 (all V_q_2 all V_pa_2 all V_aa_2 all T_a (class_Fields_Ofield(T_a) -> (V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_aa_2,V_q_2)) <-> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2))))) # label(fact_dvd__smult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 922 (all V_a all V_q all V_p all T_a (class_Fields_Ofield(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q))))) # label(fact_smult__dvd) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 923 (all V_q all V_a all V_p all T_a (class_Fields_Ofield(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> 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].
% 1.54/1.80 924 (all V_b_2 all V_c_2 all V_aa_2 all T_a (class_Rings_Oidom(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)) <-> V_c_2 = c_Groups_Ozero__class_Ozero(T_a) | c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2)))) # label(fact_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 925 (all V_b_2 all V_aa_2 all V_c_2 all T_a (class_Rings_Oidom(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) <-> V_c_2 = c_Groups_Ozero__class_Ozero(T_a) | c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2)))) # label(fact_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 926 (all V_y_2 all V_x_2 all V_k_2 all T_a (class_Fields_Ofield(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)) <-> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_x_2) & c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_y_2)))) # label(fact_dvd__poly__gcd__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 927 (all V_y all V_x all V_k all T_a (class_Fields_Ofield(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,V_y) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))))) # label(fact_poly__gcd__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 928 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 929 (all V_b_2 all V_aa_2 all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2) <-> c_Divides_Odiv__class_Omod(T_a,V_b_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 930 (all V_n all V_m all V_k all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n)) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_n) -> c_Rings_Odvd__class_Odvd(T_a,V_k,V_m))))) # label(fact_dvd__mod__imp__dvd) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 931 (all V_n all V_m all V_k all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_m) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_n) -> c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))))) # label(fact_dvd__mod) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 932 (all V_a all V_b all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_b) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c)))) # label(fact_mod__mod__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 933 (all V_m_2 all V_n_2 all V_k_2 all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_n_2) -> (c_Rings_Odvd__class_Odvd(T_a,V_k_2,c_Divides_Odiv__class_Omod(T_a,V_m_2,V_n_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_m_2))))) # label(fact_dvd__mod__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 934 (all V_q_2 all V_pa_2 all V_aa_2 all T_a (class_Fields_Ofield(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2) <-> (V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) & (V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2))))) # label(fact_smult__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 935 (all V_q all V_p all T_a (class_Rings_Oidom(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) -> (V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))))) # label(fact_dvd__imp__degree__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 936 (all V_pa_2 all V_c_2 all T_a (class_Rings_Oidom(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) <-> hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2)) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__iff__poly__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 937 (all V_t_2 all V_D_2 all V_d_2 all T_a (class_Rings_Ocomm__ring(T_a) & class_Rings_Odvd(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2) -> (all B_x all B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2))))))) # label(fact_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 938 (all V_t_2 all V_D_2 all V_d_2 all T_a (class_Rings_Ocomm__ring(T_a) & class_Rings_Odvd(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2) -> (all B_x all B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2))))))) # label(fact_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 939 (all V_k c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) # label(fact_dvd__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 940 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))))) # label(fact_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 941 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m))))) # label(fact_dvd__diffD) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 942 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n))))) # label(fact_dvd__diffD1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 943 (all V_m_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 944 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)))) # label(fact_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 945 (all V_n_2 all V_m_2 all V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),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) | 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].
% 1.54/1.80 946 (all V_m_2 (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].
% 1.54/1.80 947 (all V_n_2 all V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2))) # label(fact_dvd__reduce) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 948 (all V_n all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)))) # label(fact_dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 949 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)))) # label(fact_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 950 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)) <-> 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].
% 1.54/1.80 951 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,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].
% 1.54/1.80 952 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,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].
% 1.54/1.80 953 (all V_l_2 all V_P_2 all T_a (class_Rings_Odvd(T_a) & class_Rings_Osemiring__0(T_a) -> ((exists B_x hBOOL(hAPP(V_P_2,c_Groups_Otimes__class_Otimes(T_a,V_l_2,B_x)))) <-> (exists B_x (c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(V_P_2,B_x))))))) # label(fact_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 954 (all V_y all V_x all V_d all T_a (class_Fields_Ofield(T_a) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y) -> ((all B_k (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),B_k,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),B_k,V_y) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),B_k,V_d)))) -> ((V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) -> hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) = c_Groups_Ozero__class_Ozero(T_a)) & (-(V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) -> hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) = c_Groups_Oone__class_Oone(T_a)) -> c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = V_d)))))) # label(fact_poly__gcd__unique) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 955 (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)) -> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),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) & -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)))) # label(fact_order) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 956 (all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x)) # label(fact_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 957 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)))) # label(fact_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 958 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)))) # label(fact_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 959 (all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)))) # label(fact_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 960 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)))) # label(fact_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 961 (all V_c all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) -> (V_b = V_c -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) & -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].
% 1.54/1.80 962 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -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].
% 1.54/1.80 963 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -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].
% 1.54/1.80 964 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) & -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].
% 1.54/1.80 965 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))) # label(fact_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 966 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)))) # label(fact_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 967 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -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].
% 1.54/1.80 968 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)))) # label(fact_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 969 (all V_c all V_b all V_a (V_a = V_b -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) & -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].
% 1.54/1.80 970 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)))) # label(fact_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 971 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> (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].
% 1.54/1.80 972 (all V_n all V_m (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) -> (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].
% 1.54/1.80 973 (all V_c all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) -> (V_b = V_c -> 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].
% 1.54/1.80 974 (all V_c all V_b all V_a (V_a = V_b -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c) -> 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].
% 1.54/1.80 975 (all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) -> (V_a != V_b -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)))) # label(fact_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 976 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -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].
% 1.54/1.80 977 (all V_x_2 all V_y_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 978 (all V_y all V_x (V_x = V_y -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))) # label(fact_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 979 (all V_b all V_a (V_a != V_b -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)))) # label(fact_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 980 (all V_y_2 all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & V_x_2 != V_y_2)) # label(fact_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 981 (all V_y_2 all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) | V_x_2 = V_y_2)) # label(fact_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 982 (all V_y_2 all V_x_2 (V_x_2 = V_y_2 <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2))) # label(fact_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 983 (all V_n all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)))) # label(fact_degree__power__le) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 984 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 985 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 986 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q) = c_Power_Opower__class_Opower(T_a,V_x,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].
% 1.54/1.80 987 (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,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),V_x) = 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].
% 1.54/1.80 988 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 989 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 990 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 991 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.80 992 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) = c_Groups_Otimes__class_Otimes(T_a,V_x,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].
% 1.54/1.80 993 (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].
% 1.54/1.81 994 (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].
% 1.54/1.81 995 (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].
% 1.54/1.81 996 (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].
% 1.54/1.81 997 (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].
% 1.54/1.81 998 (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].
% 1.54/1.81 999 (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].
% 1.54/1.81 1000 (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].
% 1.54/1.81 1001 (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].
% 1.54/1.81 1002 (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].
% 1.54/1.81 1003 (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].
% 1.54/1.81 1004 (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].
% 1.54/1.81 1005 (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].
% 1.54/1.81 1006 (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].
% 1.54/1.81 1007 (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].
% 1.54/1.81 1008 (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].
% 1.54/1.81 1009 (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].
% 1.54/1.81 1010 (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].
% 1.54/1.81 1011 (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].
% 1.54/1.81 1012 (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].
% 1.54/1.81 1013 (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].
% 1.54/1.81 1014 (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].
% 1.54/1.81 1015 (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].
% 1.54/1.81 1016 (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].
% 1.54/1.81 1017 (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].
% 1.54/1.81 1018 (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].
% 1.54/1.81 1019 (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].
% 1.54/1.81 1020 (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].
% 1.54/1.81 1021 (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].
% 1.54/1.81 1022 (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].
% 1.54/1.81 1023 (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].
% 1.54/1.81 1024 (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].
% 1.54/1.81 1025 (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].
% 1.54/1.81 1026 (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].
% 1.54/1.81 1027 (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].
% 1.54/1.81 1028 (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].
% 1.54/1.81 1029 (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].
% 1.54/1.81 1030 (all T_1 (class_Fields_Ofield(T_1) -> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 1031 (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].
% 1.54/1.81 1032 (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].
% 1.54/1.81 1033 (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].
% 1.54/1.81 1034 (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].
% 1.54/1.81 1035 (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].
% 1.54/1.81 1036 (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].
% 1.54/1.81 1037 (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].
% 1.54/1.81 1038 (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].
% 1.54/1.81 1039 (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].
% 1.54/1.81 1040 (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].
% 1.54/1.81 1041 (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].
% 1.54/1.81 1042 (all T_1 (class_Fields_Ofield(T_1) -> class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Divides_Oring__div) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 1043 (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].
% 1.54/1.81 1044 (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].
% 1.54/1.81 1045 (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].
% 1.54/1.81 1046 (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].
% 1.54/1.81 1047 (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].
% 1.54/1.81 1048 (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].
% 1.64/1.90 1049 (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].
% 1.64/1.90 1050 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Osgn__if) # label(axiom) # label(non_clause). [assumption].
% 1.64/1.90 1051 (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].
% 1.64/1.90 1052 (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].
% 1.64/1.90 1053 (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].
% 1.64/1.90 1054 (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].
% 1.64/1.90 1055 (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].
% 1.64/1.90 1056 (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].
% 1.64/1.90 1057 (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].
% 1.64/1.90 1058 (all V_y_2 all V_x_2 (-hBOOL(c_fequal(V_x_2,V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause). [assumption].
% 1.64/1.90 1059 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(c_fequal(V_x_2,V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption].
% 1.64/1.90 1060 -(exists B_q (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p) & (all B_x hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,B_x))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.64/1.90
% 1.64/1.90 ============================== end of process non-clausal formulas ===
% 1.64/1.90
% 1.64/1.90 ============================== PROCESS INITIAL CLAUSES ===============
% 1.64/1.90
% 1.64/1.90 ============================== PREDICATE ELIMINATION =================
% 1.64/1.90 1061 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 1.64/1.90 1062 -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(4)].
% 1.64/1.90 1063 -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(4)].
% 1.64/1.90 1064 -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(59)].
% 1.64/1.90 1065 -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(59)].
% 1.64/1.90 Derived: -class_Rings_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(tc_Complex_Ocomplex,A) != c_Polynomial_Opoly(tc_Complex_Ocomplex,B) | A = B. [resolve(1061,a,1062,a)].
% 1.64/1.90 Derived: -class_Rings_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(tc_Complex_Ocomplex,A) = c_Polynomial_Opoly(tc_Complex_Ocomplex,B) | A != B. [resolve(1061,a,1063,a)].
% 1.90/2.13 1066 -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(1046)].
% 1.90/2.13 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(1066,b,1062,a)].
% 1.90/2.13 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(1066,b,1063,a)].
% 1.90/2.13 1067 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 1.90/2.13 1068 -class_Groups_Oab__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(9)].
% 1.90/2.13 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). [resolve(1067,a,1068,a)].
% 1.90/2.13 1069 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 1.90/2.13 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)). [resolve(1069,a,1068,a)].
% 1.90/2.13 1070 -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(1022)].
% 1.90/2.13 Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,D)). [resolve(1070,b,1068,a)].
% 1.90/2.13 1071 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.90/2.13 1072 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(11)].
% 1.90/2.13 1073 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,B,D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(11)].
% 1.90/2.13 1074 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__cancel) # label(axiom). [clausify(12)].
% 1.90/2.13 1075 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,D,C) | B != D # label(fact_add__right__cancel) # label(axiom). [clausify(12)].
% 1.90/2.13 1076 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__imp__eq) # label(axiom). [clausify(14)].
% 1.90/2.13 1077 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__imp__eq) # label(axiom). [clausify(16)].
% 1.90/2.13 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B = C. [resolve(1071,a,1072,a)].
% 1.90/2.13 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B != C. [resolve(1071,a,1073,a)].
% 1.90/2.13 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A = C. [resolve(1071,a,1074,a)].
% 1.90/2.13 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A != C. [resolve(1071,a,1075,a)].
% 1.90/2.13 1078 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B = C. [resolve(1078,a,1072,a)].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B != C. [resolve(1078,a,1073,a)].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,B) | A = C. [resolve(1078,a,1074,a)].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,B) | A != C. [resolve(1078,a,1075,a)].
% 2.24/2.47 1079 -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(1017)].
% 2.24/2.47 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D) | C = D. [resolve(1079,b,1072,a)].
% 2.24/2.47 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D) | C != D. [resolve(1079,b,1073,a)].
% 2.24/2.47 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C) | B = D. [resolve(1079,b,1074,a)].
% 2.24/2.47 Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C) | B != D. [resolve(1079,b,1075,a)].
% 2.24/2.47 1080 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.24/2.47 1081 -class_Groups_Ocancel__ab__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__imp__eq) # label(axiom). [clausify(15)].
% 2.24/2.47 1082 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.24/2.47 1083 -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(1009)].
% 2.24/2.47 1084 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.24/2.47 1085 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B) = B # label(fact_add__0__left) # label(axiom). [clausify(50)].
% 2.24/2.47 1086 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(54)].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = A. [resolve(1084,a,1085,a)].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1084,a,1086,a)].
% 2.24/2.47 1087 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom). [assumption].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = A. [resolve(1087,a,1085,a)].
% 2.24/2.47 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1087,a,1086,a)].
% 2.24/2.47 1088 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom). [clausify(1039)].
% 2.24/2.47 Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = B. [resolve(1088,b,1085,a)].
% 2.24/2.47 Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1088,b,1086,a)].
% 2.24/2.54 1089 -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(1008)].
% 2.24/2.54 1090 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom). [clausify(53)].
% 2.24/2.54 1091 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom). [clausify(53)].
% 2.24/2.54 1092 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom). [clausify(63)].
% 2.24/2.54 1093 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom). [clausify(63)].
% 2.24/2.54 1094 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(104)].
% 2.24/2.54 1095 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(104)].
% 2.24/2.54 1096 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(105)].
% 2.24/2.54 1097 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(105)].
% 2.24/2.54 1098 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(344)].
% 2.24/2.54 1099 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(344)].
% 2.24/2.54 1100 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(345)].
% 2.24/2.54 1101 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(345)].
% 2.24/2.54 1102 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__zero) # label(axiom). [clausify(636)].
% 2.24/2.54 1103 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__zero) # label(axiom). [clausify(636)].
% 2.24/2.55 1104 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_equal__neg__zero) # label(axiom). [clausify(638)].
% 2.24/2.55 1105 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_equal__neg__zero) # label(axiom). [clausify(638)].
% 2.24/2.55 1106 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_minus__le__self__iff) # label(axiom). [clausify(643)].
% 2.24/2.55 1107 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_minus__le__self__iff) # label(axiom). [clausify(643)].
% 2.24/2.55 1108 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__minus__self__iff) # label(axiom). [clausify(645)].
% 2.24/2.55 1109 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__minus__self__iff) # label(axiom). [clausify(645)].
% 2.24/2.55 1110 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__nonneg) # label(axiom). [clausify(650)].
% 2.24/2.55 1111 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__nonneg) # label(axiom). [clausify(650)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1089,b,1090,a)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1089,b,1091,a)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1094,a)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1095,a)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1089,b,1096,a)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1089,b,1097,a)].
% 2.24/2.55 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1098,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1099,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1089,b,1100,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1089,b,1101,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1089,b,1102,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1089,b,1103,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1106,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1107,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1089,b,1108,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1089,b,1109,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1110,a)].
% 2.39/2.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1089,b,1111,a)].
% 2.39/2.63 1112 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].
% 2.39/2.63 1113 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom). [clausify(57)].
% 2.39/2.63 1114 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom). [clausify(57)].
% 2.39/2.63 1115 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom). [clausify(91)].
% 2.39/2.63 1116 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C)) | B != D # label(fact_crossproduct__eq) # label(axiom). [clausify(91)].
% 2.39/2.63 1117 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C)) | C != E # label(fact_crossproduct__eq) # label(axiom). [clausify(91)].
% 2.39/2.63 1118 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(94)].
% 2.39/2.63 1119 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(94)].
% 2.39/2.63 1120 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,E,C)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(94)].
% 2.39/2.63 1121 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Ozero__class_Ozero(A) = B | C != D | E = F | c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,B,E)) != c_Groups_Oplus__class_Oplus(A,D,c_Groups_Otimes__class_Otimes(A,B,F)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(108)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1112,a,1113,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(1112,a,1114,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | A = C | B = D. [resolve(1112,a,1115,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | A != C. [resolve(1112,a,1116,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | B != D. [resolve(1112,a,1117,a)].
% 2.39/2.63 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,E)). [resolve(1112,a,1121,a)].
% 2.39/2.63 1122 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1122,a,1113,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1122,a,1114,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,D),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B)) | A = C | B = D. [resolve(1122,a,1115,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,D),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B)) | A != C. [resolve(1122,a,1116,a)].
% 2.39/2.63 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,D),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B)) | B != D. [resolve(1122,a,1117,a)].
% 2.39/2.63 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,D)) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,E)). [resolve(1122,a,1121,a)].
% 2.39/2.63 1123 -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(1000)].
% 2.39/2.63 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1123,b,1113,a)].
% 2.39/2.63 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1123,b,1114,a)].
% 2.39/2.63 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,E)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,E),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | B = D | C = E. [resolve(1123,b,1115,a)].
% 2.39/2.63 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,E)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,E),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | B != D. [resolve(1123,b,1116,a)].
% 2.39/2.63 Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,E)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,E),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | C != E. [resolve(1123,b,1117,a)].
% 2.39/2.63 Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | C != D | E = F | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,E)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,F)). [resolve(1123,b,1121,a)].
% 2.57/2.79 1124 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.57/2.79 1125 -class_Groups_Oab__semigroup__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(76)].
% 2.57/2.79 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1124,a,1125,a)].
% 2.57/2.79 1126 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.57/2.79 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C)). [resolve(1126,a,1125,a)].
% 2.57/2.79 1127 -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(1020)].
% 2.57/2.79 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)). [resolve(1127,b,1125,a)].
% 2.57/2.79 1128 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].
% 2.57/2.79 1129 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__imp__less__left) # label(axiom). [clausify(84)].
% 2.57/2.79 1130 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__imp__less__right) # label(axiom). [clausify(85)].
% 2.57/2.79 1131 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__cancel__left) # label(axiom). [clausify(89)].
% 2.57/2.79 1132 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_add__less__cancel__left) # label(axiom). [clausify(89)].
% 2.57/2.79 1133 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(90)].
% 2.57/2.79 1134 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless(A,B,D) # label(fact_add__less__cancel__right) # label(axiom). [clausify(90)].
% 2.57/2.79 1135 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__imp__le__left) # label(axiom). [clausify(266)].
% 2.57/2.79 1136 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__imp__le__right) # label(axiom). [clausify(267)].
% 2.57/2.79 1137 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom). [clausify(271)].
% 2.57/2.80 1138 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom). [clausify(271)].
% 2.57/2.80 1139 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(272)].
% 2.57/2.80 1140 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom). [clausify(272)].
% 2.57/2.80 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1128,a,1129,a)].
% 2.57/2.80 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1128,a,1130,a)].
% 2.57/2.80 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1128,a,1132,a)].
% 2.57/2.80 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1128,a,1134,a)].
% 2.57/2.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1128,a,1135,a)].
% 2.57/2.80 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1128,a,1136,a)].
% 2.57/2.80 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1128,a,1138,a)].
% 2.57/2.80 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1128,a,1140,a)].
% 2.57/2.80 1141 -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(1002)].
% 2.57/2.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1141,b,1129,a)].
% 2.57/2.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1141,b,1130,a)].
% 2.57/2.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1141,b,1132,a)].
% 2.57/2.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1141,b,1134,a)].
% 2.67/2.88 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1141,b,1135,a)].
% 2.67/2.88 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1141,b,1136,a)].
% 2.67/2.88 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1141,b,1138,a)].
% 2.67/2.88 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1141,b,1140,a)].
% 2.67/2.88 1142 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.67/2.88 1143 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__strict__mono) # label(axiom). [clausify(86)].
% 2.67/2.88 1144 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__strict__left__mono) # label(axiom). [clausify(87)].
% 2.67/2.88 1145 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__strict__right__mono) # label(axiom). [clausify(88)].
% 2.67/2.88 1146 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__less__le__mono) # label(axiom). [clausify(351)].
% 2.67/2.88 1147 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__le__less__mono) # label(axiom). [clausify(352)].
% 2.67/2.88 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1142,a,1143,a)].
% 2.67/2.88 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1142,a,1146,a)].
% 2.67/2.88 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1142,a,1147,a)].
% 2.67/2.88 1148 -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(1001)].
% 2.67/2.88 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1148,b,1143,a)].
% 2.72/2.96 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1148,b,1146,a)].
% 2.72/2.96 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1148,b,1147,a)].
% 2.72/2.96 1149 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 2.72/2.96 1150 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__pos__pos) # label(axiom). [clausify(106)].
% 2.72/2.96 1151 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__neg) # label(axiom). [clausify(107)].
% 2.72/2.96 1152 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__nonneg) # label(axiom). [clausify(346)].
% 2.72/2.96 1153 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) != 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(347)].
% 2.72/2.96 1154 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) != 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(347)].
% 2.72/2.96 1155 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) = 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(347)].
% 2.72/2.96 1156 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__increasing) # label(axiom). [clausify(348)].
% 2.72/2.96 1157 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,D,B)) # label(fact_add__increasing2) # label(axiom). [clausify(349)].
% 2.72/2.96 1158 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__nonpos) # label(axiom). [clausify(350)].
% 2.72/2.96 1159 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__neg) # label(axiom). [clausify(381)].
% 2.72/2.96 1160 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__neg__nonpos) # label(axiom). [clausify(382)].
% 2.72/2.96 1161 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing2) # label(axiom). [clausify(383)].
% 2.72/2.96 1162 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing) # label(axiom). [clausify(384)].
% 2.72/2.96 1163 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__pos) # label(axiom). [clausify(385)].
% 2.72/2.96 1164 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__pos__nonneg) # label(axiom). [clausify(386)].
% 2.72/2.96 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)). [resolve(1149,a,1150,a)].
% 2.72/2.96 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1149,a,1151,a)].
% 2.72/2.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)). [resolve(1149,a,1152,a)].
% 2.72/2.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(1149,a,1153,a)].
% 2.72/2.96 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1149,a,1154,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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(1149,a,1155,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1149,a,1156,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A)). [resolve(1149,a,1157,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1149,a,1158,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1149,a,1159,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1149,a,1160,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1149,a,1161,a)].
% 2.72/2.97 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1149,a,1162,a)].
% 2.72/2.97 1165 -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(1007)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)). [resolve(1165,b,1150,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1165,b,1151,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)). [resolve(1165,b,1152,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1165,b,1153,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1165,b,1154,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = 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(1165,b,1155,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1165,b,1156,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,B)). [resolve(1165,b,1157,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1165,b,1158,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1165,b,1159,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1165,b,1160,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1165,b,1161,a)].
% 2.72/2.97 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1165,b,1162,a)].
% 2.80/3.05 1166 -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(1012)].
% 2.80/3.05 1167 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(119)].
% 2.80/3.05 1168 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(119)].
% 2.80/3.05 1169 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(119)].
% 2.80/3.05 1170 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(121)].
% 2.80/3.05 1171 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(121)].
% 2.80/3.05 1172 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(121)].
% 2.80/3.05 1173 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(123)].
% 2.80/3.05 1174 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(124)].
% 2.80/3.05 1175 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__neg__neg) # label(axiom). [clausify(128)].
% 2.80/3.05 1176 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(138)].
% 2.80/3.05 1177 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,D,B) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(138)].
% 2.80/3.05 1178 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(138)].
% 2.80/3.05 1179 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | c_Orderings_Oord__class_Oless(A,B,D) | c_Orderings_Oord__class_Oless(A,D,B) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(138)].
% 2.80/3.05 1180 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(138)].
% 2.80/3.05 1181 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,B) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(138)].
% 2.80/3.05 1182 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(139)].
% 2.80/3.05 1183 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(139)].
% 2.80/3.05 1184 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(139)].
% 2.80/3.05 1185 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(139)].
% 2.80/3.05 1186 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(139)].
% 2.80/3.05 1187 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(139)].
% 2.80/3.05 1188 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(140)].
% 2.80/3.05 1189 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(140)].
% 2.80/3.05 1190 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(146)].
% 2.80/3.05 1191 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(146)].
% 2.80/3.05 1192 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(341)].
% 2.80/3.05 1193 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom). [clausify(341)].
% 2.80/3.05 1194 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(341)].
% 2.80/3.05 1195 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom). [clausify(341)].
% 2.80/3.05 1196 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(341)].
% 2.80/3.05 1197 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom). [clausify(341)].
% 2.80/3.05 1198 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(342)].
% 2.80/3.05 1199 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(342)].
% 2.80/3.05 1200 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(342)].
% 2.80/3.05 1201 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(342)].
% 2.80/3.05 1202 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(342)].
% 2.80/3.05 1203 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(342)].
% 2.80/3.05 1204 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(379)].
% 2.80/3.05 1205 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(379)].
% 2.80/3.05 1206 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(380)].
% 2.80/3.05 1207 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(380)].
% 2.80/3.05 1208 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(387)].
% 2.80/3.05 1209 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(387)].
% 2.80/3.05 1210 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),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(387)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),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(1166,b,1167,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1166,b,1168,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1166,b,1169,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1166,b,1170,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C. [resolve(1166,b,1171,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),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(1166,b,1172,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,B)). [resolve(1166,b,1173,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)). [resolve(1166,b,1174,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)). [resolve(1166,b,1175,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1176,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B). [resolve(1166,b,1177,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1178,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B). [resolve(1166,b,1179,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1166,b,1180,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1182,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1166,b,1183,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1184,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1166,b,1185,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1166,b,1186,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1166,b,1188,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C). [resolve(1166,b,1190,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1192,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1166,b,1193,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1194,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1166,b,1195,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1196,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1166,b,1197,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1198,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1199,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1200,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1201,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1166,b,1202,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1166,b,1203,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C). [resolve(1166,b,1204,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C). [resolve(1166,b,1205,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1166,b,1206,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D). [resolve(1166,b,1207,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),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(1166,b,1208,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),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(1166,b,1209,a)].
% 2.80/3.05 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),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(1166,b,1210,a)].
% 2.99/3.22 1211 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom). [clausify(1026)].
% 2.99/3.22 1212 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__sum__squares__lt__zero) # label(axiom). [clausify(120)].
% 2.99/3.22 1213 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__square__less__zero) # label(axiom). [clausify(137)].
% 2.99/3.22 1214 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,B)) # label(fact_zero__le__square) # label(axiom). [clausify(343)].
% 2.99/3.22 1215 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))) # label(fact_sum__squares__ge__zero) # label(axiom). [clausify(388)].
% 2.99/3.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1211,b,1212,a)].
% 2.99/3.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1211,b,1213,a)].
% 2.99/3.22 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B)). [resolve(1211,b,1214,a)].
% 2.99/3.22 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,C))). [resolve(1211,b,1215,a)].
% 2.99/3.22 1216 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 2.99/3.22 1217 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_pos__add__strict) # label(axiom). [clausify(122)].
% 2.99/3.22 1218 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__le__one) # label(axiom). [clausify(538)].
% 2.99/3.22 1219 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__le__zero) # label(axiom). [clausify(539)].
% 2.99/3.22 1220 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__less__one) # label(axiom). [clausify(540)].
% 2.99/3.22 1221 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__less__zero) # label(axiom). [clausify(541)].
% 2.99/3.22 1222 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_less__1__mult) # label(axiom). [clausify(542)].
% 3.01/3.22 1223 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_less__add__one) # label(axiom). [clausify(543)].
% 3.01/3.22 1224 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))) # label(fact_zero__less__two) # label(axiom). [clausify(579)].
% 3.01/3.22 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)). [resolve(1216,a,1217,a)].
% 3.01/3.22 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1216,a,1218,a)].
% 3.01/3.22 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1216,a,1219,a)].
% 3.01/3.22 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(1216,a,1220,a)].
% 3.01/3.22 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1216,a,1221,a)].
% 3.01/3.22 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1216,a,1222,a)].
% 3.01/3.22 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1216,a,1223,a)].
% 3.01/3.22 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(1216,a,1224,a)].
% 3.01/3.22 1225 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom). [clausify(1019)].
% 3.01/3.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)). [resolve(1225,b,1217,a)].
% 3.01/3.22 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1225,b,1218,a)].
% 3.01/3.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1225,b,1219,a)].
% 3.01/3.22 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1225,b,1220,a)].
% 3.01/3.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1225,b,1221,a)].
% 3.01/3.22 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)). [resolve(1225,b,1222,a)].
% 3.11/3.38 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1225,b,1223,a)].
% 3.11/3.38 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_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(1225,b,1224,a)].
% 3.11/3.38 1226 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.11/3.38 1227 -class_Rings_Olinordered__comm__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(125)].
% 3.11/3.38 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)). [resolve(1226,a,1227,a)].
% 3.11/3.38 1228 -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(1003)].
% 3.11/3.38 1229 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 3.11/3.38 1230 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(126)].
% 3.11/3.38 1231 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(127)].
% 3.11/3.38 1232 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__pos__pos) # label(axiom). [clausify(141)].
% 3.11/3.38 1233 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg) # label(axiom). [clausify(142)].
% 3.11/3.38 1234 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg2) # label(axiom). [clausify(143)].
% 3.11/3.38 1235 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__less__mult__pos) # label(axiom). [clausify(144)].
% 3.11/3.38 1236 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__less__mult__pos2) # label(axiom). [clausify(145)].
% 3.11/3.38 1237 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__neg__pos) # label(axiom). [clausify(147)].
% 3.11/3.38 1238 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__left__le__imp__le) # label(axiom). [clausify(369)].
% 3.11/3.38 1239 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_mult__right__le__imp__le) # label(axiom). [clausify(370)].
% 3.11/3.38 1240 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__imp__less__left) # label(axiom). [clausify(371)].
% 3.11/3.38 1241 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__less__imp__less__right) # label(axiom). [clausify(373)].
% 3.11/3.38 1242 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__le__less__imp__less) # label(axiom). [clausify(375)].
% 3.11/3.38 1243 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__less__le__imp__less) # label(axiom). [clausify(376)].
% 3.11/3.38 1244 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__strict__mono_H) # label(axiom). [clausify(377)].
% 3.11/3.38 1245 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__strict__mono) # label(axiom). [clausify(378)].
% 3.11/3.38 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1229,a,1231,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1229,a,1232,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1229,a,1233,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1229,a,1234,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). [resolve(1229,a,1235,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). [resolve(1229,a,1236,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C). [resolve(1229,a,1238,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C). [resolve(1229,a,1239,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). [resolve(1229,a,1240,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). [resolve(1229,a,1241,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1229,a,1242,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1229,a,1243,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1229,a,1244,a)].
% 3.11/3.39 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1229,a,1245,a)].
% 3.11/3.39 1246 -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(1005)].
% 3.11/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)). [resolve(1246,b,1232,a)].
% 3.11/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1246,b,1233,a)].
% 3.11/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1246,b,1234,a)].
% 3.11/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C). [resolve(1246,b,1235,a)].
% 3.11/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1246,b,1236,a)].
% 3.19/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D). [resolve(1246,b,1239,a)].
% 3.19/3.39 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D). [resolve(1246,b,1240,a)].
% 3.27/3.48 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D). [resolve(1246,b,1241,a)].
% 3.27/3.48 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,E)). [resolve(1246,b,1242,a)].
% 3.27/3.48 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,E)). [resolve(1246,b,1243,a)].
% 3.27/3.48 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,E)). [resolve(1246,b,1244,a)].
% 3.27/3.48 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,E)). [resolve(1246,b,1245,a)].
% 3.27/3.48 1247 class_Rings_Ono__zero__divisors(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 3.27/3.48 1248 -class_Rings_Ono__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divisors__zero) # label(axiom). [clausify(130)].
% 3.27/3.48 1249 -class_Rings_Ono__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) # label(fact_no__zero__divisors) # label(axiom). [clausify(131)].
% 3.27/3.48 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(1247,a,1248,a)].
% 3.27/3.48 1250 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 3.27/3.48 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B. [resolve(1250,a,1248,a)].
% 3.41/3.65 1251 -class_Rings_Oidom(A) | class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom). [clausify(1024)].
% 3.41/3.65 Derived: -class_Rings_Oidom(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,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(1251,b,1248,a)].
% 3.41/3.65 1252 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 3.41/3.65 1253 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(132)].
% 3.41/3.65 1254 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(132)].
% 3.41/3.65 1255 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Otimes__class_Otimes(A,B,C) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(132)].
% 3.41/3.65 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1252,a,1254,a)].
% 3.41/3.65 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B. [resolve(1252,a,1255,a)].
% 3.41/3.65 1256 -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(1013)].
% 3.41/3.65 Derived: -class_Rings_Oidom(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1256,b,1254,a)].
% 3.41/3.65 Derived: -class_Rings_Oidom(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C. [resolve(1256,b,1255,a)].
% 3.41/3.65 1257 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom). [assumption].
% 3.41/3.65 1258 -class_Rings_Omult__zero(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__zero__right) # label(axiom). [clausify(133)].
% 3.41/3.65 1259 -class_Rings_Omult__zero(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__zero__left) # label(axiom). [clausify(134)].
% 3.41/3.65 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1257,a,1258,a)].
% 3.41/3.65 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1257,a,1259,a)].
% 3.41/3.65 1260 class_Rings_Omult__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Omult__zero) # label(axiom). [assumption].
% 3.41/3.65 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1260,a,1258,a)].
% 3.41/3.65 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1260,a,1259,a)].
% 3.41/3.65 1261 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Omult__zero) # label(axiom). [clausify(1043)].
% 3.41/3.65 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1261,b,1258,a)].
% 3.63/3.90 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1261,b,1259,a)].
% 3.63/3.90 1262 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.63/3.90 1263 -class_Rings_Ocomm__semiring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(135)].
% 3.63/3.90 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1262,a,1263,a)].
% 3.63/3.90 1264 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.63/3.90 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C)). [resolve(1264,a,1263,a)].
% 3.63/3.90 1265 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom). [clausify(1031)].
% 3.63/3.90 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)). [resolve(1265,b,1263,a)].
% 3.63/3.90 1266 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 3.63/3.90 1267 -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D),E) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),E)) # label(fact_combine__common__factor) # label(axiom). [clausify(136)].
% 3.63/3.90 Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C),D) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D)). [resolve(1266,a,1267,a)].
% 3.63/3.90 1268 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom). [assumption].
% 3.63/3.90 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C),D) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C),D)). [resolve(1268,a,1267,a)].
% 3.63/3.90 1269 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom). [clausify(1047)].
% 3.63/3.90 Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D),E) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D),E)). [resolve(1269,b,1267,a)].
% 3.63/3.90 1270 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.63/3.90 1271 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult_Oadd__right) # label(axiom). [clausify(154)].
% 3.63/3.90 1272 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__right_Oadd) # label(axiom). [clausify(155)].
% 3.63/3.90 1273 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult_Oadd__left) # label(axiom). [clausify(156)].
% 3.63/3.90 1274 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult_Ozero__left) # label(axiom). [clausify(195)].
% 3.63/3.90 1275 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__left_Ozero) # label(axiom). [clausify(196)].
% 3.63/3.90 1276 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult_Ozero__right) # label(axiom). [clausify(197)].
% 3.63/3.90 1277 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mult__right_Ozero) # label(axiom). [clausify(198)].
% 3.63/3.90 1278 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__left_Oadd) # label(axiom). [clausify(199)].
% 3.63/3.90 1279 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult_Odiff__right) # label(axiom). [clausify(475)].
% 3.63/3.90 1280 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult__right_Odiff) # label(axiom). [clausify(476)].
% 3.63/3.90 1281 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mult_Odiff__left) # label(axiom). [clausify(477)].
% 3.63/3.90 1282 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mult__left_Odiff) # label(axiom). [clausify(478)].
% 3.63/3.90 1283 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),c_Groups_Ominus__class_Ominus(A,C,E)),c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),E)),c_Groups_Otimes__class_Otimes(A,D,c_Groups_Ominus__class_Ominus(A,C,E))) # label(fact_mult_Oprod__diff__prod) # label(axiom). [clausify(535)].
% 3.63/3.90 1284 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_mult__left_Ominus) # label(axiom). [clausify(624)].
% 3.73/3.98 1285 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_mult_Ominus__left) # label(axiom). [clausify(625)].
% 3.73/3.98 1286 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_mult__right_Ominus) # label(axiom). [clausify(626)].
% 3.73/3.98 1287 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_mult_Ominus__right) # label(axiom). [clausify(627)].
% 3.73/3.98 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)). [resolve(1270,a,1271,a)].
% 3.73/3.98 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C)). [resolve(1270,a,1279,a)].
% 3.73/3.98 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),B). [resolve(1270,a,1281,a)].
% 3.73/3.98 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),D)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D))). [resolve(1270,a,1283,a)].
% 3.73/3.98 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B). [resolve(1270,a,1284,a)].
% 3.73/3.98 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1270,a,1286,a)].
% 3.73/3.98 1288 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom). [assumption].
% 3.73/3.98 1289 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E) = B # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1290 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = D # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1291 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = E | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,E),c_Polynomial_Odegree(A,C)) # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1292 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != E # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1293 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,E),c_Polynomial_Odegree(A,C)) # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1294 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1295 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != E # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1296 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,E),c_Polynomial_Odegree(A,C)) # label(fact_pdivmod__rel__def) # label(axiom). [clausify(226)].
% 3.73/3.98 1297 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | -c_Polynomial_Opdivmod__rel(A,B,C,F,V6) | D = F # label(fact_pdivmod__rel__unique) # label(axiom). [clausify(238)].
% 3.73/3.98 1298 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | -c_Polynomial_Opdivmod__rel(A,B,C,F,V6) | E = V6 # label(fact_pdivmod__rel__unique) # label(axiom). [clausify(238)].
% 3.73/3.98 1299 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | -c_Polynomial_Opdivmod__rel(A,B,C,F,V6) | E = V6 # label(fact_pdivmod__rel__unique__mod) # label(axiom). [clausify(239)].
% 3.73/3.98 1300 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | -c_Polynomial_Opdivmod__rel(A,B,C,F,V6) | D = F # label(fact_pdivmod__rel__unique__div) # label(axiom). [clausify(240)].
% 3.73/3.98 1301 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) # label(fact_pdivmod__rel__by__0) # label(axiom). [clausify(321)].
% 3.73/3.98 1302 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) # label(fact_pdivmod__rel__0) # label(axiom). [clausify(322)].
% 3.73/3.98 1303 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C # label(fact_pdivmod__rel__by__0__iff) # label(axiom). [clausify(323)].
% 3.73/3.98 1304 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D) | D = B # label(fact_pdivmod__rel__by__0__iff) # label(axiom). [clausify(323)].
% 3.73/3.98 1305 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | D != B # label(fact_pdivmod__rel__by__0__iff) # label(axiom). [clausify(323)].
% 3.73/3.98 1306 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C # label(fact_pdivmod__rel__0__iff) # label(axiom). [clausify(324)].
% 3.73/3.98 1307 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = D # label(fact_pdivmod__rel__0__iff) # label(axiom). [clausify(324)].
% 3.73/3.98 1308 -class_Fields_Ofield(A) | c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D # label(fact_pdivmod__rel__0__iff) # label(axiom). [clausify(324)].
% 3.73/3.98 1309 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Polynomial_Opdivmod__rel(A,c_Polynomial_Osmult(A,F,B),C,c_Polynomial_Osmult(A,F,D),c_Polynomial_Osmult(A,F,E)) # label(fact_pdivmod__rel__smult__left) # label(axiom). [clausify(325)].
% 3.73/3.98 1310 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | -c_Polynomial_Opdivmod__rel(A,D,F,V6,V7) | c_Polynomial_Opdivmod__rel(A,B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,F),V6,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,V7),E)) # label(fact_pdivmod__rel__mult) # label(axiom). [clausify(395)].
% 3.73/3.98 1311 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | c_Rings_Oinverse__class_Odivide(A,hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_OpCons(A,F,E)),c_Polynomial_Odegree(A,C)),hAPP(c_Polynomial_Ocoeff(A,C),c_Polynomial_Odegree(A,C))) != V6 | c_Polynomial_Opdivmod__rel(A,c_Polynomial_OpCons(A,F,B),C,c_Polynomial_OpCons(A,V6,D),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,F,E),c_Polynomial_Osmult(A,V6,C))) # label(fact_pdivmod__rel__pCons) # label(axiom). [clausify(666)].
% 3.73/3.98 1312 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) != c_Rings_Oinverse__class_Odivide(A,E,B) | c_Groups_Otimes__class_Otimes(A,D,B) = c_Groups_Otimes__class_Otimes(A,E,C) # label(fact_frac__eq__eq) # label(axiom). [clausify(708)].
% 3.73/3.98 1313 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) = c_Rings_Oinverse__class_Odivide(A,E,B) | c_Groups_Otimes__class_Otimes(A,D,B) != c_Groups_Otimes__class_Otimes(A,E,C) # label(fact_frac__eq__eq) # label(axiom). [clausify(708)].
% 3.73/3.98 1314 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),B) = c_Groups_Oplus__class_Oplus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_add__divide__eq__iff) # label(axiom). [clausify(731)].
% 3.73/3.98 1315 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,B,D)),B) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_divide__add__eq__iff) # label(axiom). [clausify(733)].
% 3.73/3.98 1316 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)),c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)) # label(fact_add__frac__eq) # label(axiom). [clausify(734)].
% 3.73/3.98 1317 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),B) = c_Groups_Ominus__class_Ominus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_diff__divide__eq__iff) # label(axiom). [clausify(735)].
% 3.73/3.98 1318 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,C,c_Groups_Otimes__class_Otimes(A,B,D)),B) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_divide__diff__eq__iff) # label(axiom). [clausify(736)].
% 3.73/3.98 1319 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)),c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)) # label(fact_diff__frac__eq) # label(axiom). [clausify(737)].
% 3.73/3.98 1320 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,C,D),B) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,C,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),D,B)),c_Polynomial_Osmult(A,c_Rings_Oinverse__class_Odivide(A,hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_OpCons(A,C,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),D,B))),c_Polynomial_Odegree(A,B)),hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))),B)) # label(fact_mod__pCons) # label(axiom). [clausify(747)].
% 3.73/3.98 1321 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) = c_Polynomial_Osmult(A,B,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,D)) # label(fact_mod__smult__left) # label(axiom). [clausify(750)].
% 3.73/3.98 1322 -class_Fields_Ofield(A) | -c_Polynomial_Opdivmod__rel(A,B,C,D,E) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,C) = E # label(fact_mod__poly__eq) # label(axiom). [clausify(751)].
% 3.73/3.98 1323 -class_Fields_Ofield(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C)) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,C) = B # label(fact_mod__poly__less) # label(axiom). [clausify(752)].
% 3.73/3.98 1324 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,c_Polynomial_Osmult(A,B,D)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,D) # label(fact_mod__smult__right) # label(axiom). [clausify(753)].
% 3.73/3.98 1325 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,C)) # label(fact_poly__mod__minus__left) # label(axiom). [clausify(754)].
% 3.73/3.98 1326 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,C) # label(fact_poly__mod__minus__right) # label(axiom). [clausify(755)].
% 3.73/3.98 1327 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,B)),c_Polynomial_Odegree(A,B)) # label(fact_degree__mod__less) # label(axiom). [clausify(756)].
% 3.73/3.98 1328 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Opoly__gcd(A,B,C)),c_Polynomial_Odegree(A,c_Polynomial_Opoly__gcd(A,B,C))) # label(fact_poly__gcd__monic) # label(axiom). [clausify(813)].
% 3.73/3.98 1329 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Oone__class_Oone(A) = hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Opoly__gcd(A,B,C)),c_Polynomial_Odegree(A,c_Polynomial_Opoly__gcd(A,B,C))) # label(fact_poly__gcd__monic) # label(axiom). [clausify(813)].
% 3.73/3.98 1330 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Oone__class_Oone(A) = hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Opoly__gcd(A,C,B)),c_Polynomial_Odegree(A,c_Polynomial_Opoly__gcd(A,C,B))) # label(fact_poly__gcd__monic) # label(axiom). [clausify(813)].
% 3.73/3.98 1331 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) = c_Polynomial_Opoly__gcd(A,B,C) # label(fact_poly__gcd__minus__right) # label(axiom). [clausify(815)].
% 3.73/3.98 1332 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C) = c_Polynomial_Opoly__gcd(A,B,C) # label(fact_poly__gcd__minus__left) # label(axiom). [clausify(816)].
% 3.73/3.98 1333 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(fact_poly__gcd__0__0) # label(axiom). [clausify(820)].
% 3.73/3.98 1334 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B # label(fact_poly__gcd__zero__iff) # label(axiom). [clausify(821)].
% 3.73/3.98 1335 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C # label(fact_poly__gcd__zero__iff) # label(axiom). [clausify(821)].
% 3.73/3.98 1336 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,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 # label(fact_poly__gcd__zero__iff) # label(axiom). [clausify(821)].
% 3.73/3.98 1337 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,c_Polynomial_Opoly__gcd(A,B,C),D) = c_Polynomial_Opoly__gcd(A,B,c_Polynomial_Opoly__gcd(A,C,D)) # label(fact_poly__gcd_Oassoc) # label(axiom). [clausify(823)].
% 3.73/3.98 1338 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,c_Polynomial_Opoly__gcd(A,C,D)) = c_Polynomial_Opoly__gcd(A,C,c_Polynomial_Opoly__gcd(A,B,D)) # label(fact_poly__gcd_Oleft__commute) # label(axiom). [clausify(824)].
% 3.73/3.98 1339 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,C) = c_Polynomial_Opoly__gcd(A,C,B) # label(fact_poly__gcd_Ocommute) # label(axiom). [clausify(825)].
% 3.73/3.98 1340 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) # label(fact_poly__gcd__1__right) # label(axiom). [clausify(832)].
% 3.73/3.98 1341 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) # label(fact_poly__gcd__1__left) # label(axiom). [clausify(833)].
% 3.73/3.98 1342 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Polynomial_Opoly__gcd(A,B,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,B)) = c_Polynomial_Opoly__gcd(A,C,B) # label(fact_poly__gcd_Osimps_I2_J) # label(axiom). [clausify(834)].
% 3.73/3.98 1343 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Polynomial_Opoly__gcd(A,C,B) = c_Polynomial_Osmult(A,c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Polynomial_Ocoeff(A,C),c_Polynomial_Odegree(A,C))),C) # label(fact_poly__gcd__code) # label(axiom). [clausify(840)].
% 3.73/3.98 1344 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Polynomial_Opoly__gcd(A,B,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),C,B)) = c_Polynomial_Opoly__gcd(A,C,B) # label(fact_poly__gcd__code) # label(axiom). [clausify(840)].
% 3.73/3.98 1345 -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_field__class_Onormalizing__field__rules_I2_J) # label(axiom). [clausify(843)].
% 3.73/3.98 1346 -class_Fields_Ofield(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_field__divide__inverse) # label(axiom). [clausify(863)].
% 3.73/3.98 1347 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C)) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_inverse__add) # label(axiom). [clausify(881)].
% 3.73/3.98 1348 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),B) # label(fact_field__inverse) # label(axiom). [clausify(886)].
% 3.73/3.98 1349 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Polynomial_Opdivmod__rel(A,C,D,E,F) | c_Polynomial_Opdivmod__rel(A,C,c_Polynomial_Osmult(A,B,D),c_Polynomial_Osmult(A,c_Rings_Oinverse__class_Oinverse(A,B),E),F) # label(fact_pdivmod__rel__smult__right) # label(axiom). [clausify(890)].
% 3.73/3.98 1350 -class_Fields_Ofield(A) | c_Polynomial_Opoly__gcd(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Polynomial_Osmult(A,c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))),B) # label(fact_poly__gcd_Osimps_I1_J) # label(axiom). [clausify(896)].
% 3.73/3.98 1351 -class_Fields_Ofield(A) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Opoly__gcd(A,B,C),B) # label(fact_poly__gcd__dvd1) # label(axiom). [clausify(900)].
% 3.73/3.98 1352 -class_Fields_Ofield(A) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Opoly__gcd(A,B,C),C) # label(fact_poly__gcd__dvd2) # label(axiom). [clausify(901)].
% 3.73/3.98 1353 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Polynomial_Osmult(A,B,D)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D) # label(fact_dvd__smult__iff) # label(axiom). [clausify(921)].
% 3.73/3.98 1354 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Polynomial_Osmult(A,B,D)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D) # label(fact_dvd__smult__iff) # label(axiom). [clausify(921)].
% 3.73/3.98 1355 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ozero__class_Ozero(A) = D | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,D,B),C) # label(fact_smult__dvd) # label(axiom). [clausify(922)].
% 3.73/3.98 1356 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Osmult(A,C,D)) | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) # label(fact_dvd__smult__cancel) # label(axiom). [clausify(923)].
% 3.73/3.98 1357 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) # label(fact_dvd__poly__gcd__iff) # label(axiom). [clausify(926)].
% 3.73/3.98 1358 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) # label(fact_dvd__poly__gcd__iff) # label(axiom). [clausify(926)].
% 3.73/3.98 1359 -class_Fields_Ofield(A) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) # label(fact_dvd__poly__gcd__iff) # label(axiom). [clausify(926)].
% 3.73/3.98 1360 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D)) # label(fact_poly__gcd__greatest) # label(axiom). [clausify(927)].
% 3.73/3.98 1361 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = D # label(fact_smult__dvd__iff) # label(axiom). [clausify(934)].
% 3.73/3.98 1362 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D) # label(fact_smult__dvd__iff) # label(axiom). [clausify(934)].
% 3.73/3.98 1363 -class_Fields_Ofield(A) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) | c_Groups_Ozero__class_Ozero(A) = B | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D) # label(fact_smult__dvd__iff) # label(axiom). [clausify(934)].
% 3.73/3.98 1364 -class_Fields_Ofield(A) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | c_Groups_Ozero__class_Ozero(A) != B # label(fact_smult__dvd__iff) # label(axiom). [clausify(934)].
% 3.73/3.98 1365 -class_Fields_Ofield(A) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D) # label(fact_smult__dvd__iff) # label(axiom). [clausify(934)].
% 3.73/3.98 1366 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1367 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = D | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1368 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),C) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1369 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),C) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1370 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1371 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = D | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1372 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),D) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1373 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),D) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1374 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1375 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = D | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1376 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),B) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != D | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 1377 -class_Fields_Ofield(A) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),f21(D,C,B,A),B) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Groups_Oone__class_Oone(A) != hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)) | c_Polynomial_Opoly__gcd(A,C,D) = B # label(fact_poly__gcd__unique) # label(axiom). [clausify(954)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),D) = A. [resolve(1288,a,1289,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C. [resolve(1288,a,1290,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = D | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,D),c_Polynomial_Odegree(tc_Complex_Ocomplex,B)). [resolve(1288,a,1291,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != D. [resolve(1288,a,1292,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,D),c_Polynomial_Odegree(tc_Complex_Ocomplex,B)). [resolve(1288,a,1293,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B. [resolve(1288,a,1294,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != D. [resolve(1288,a,1295,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),D) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,D),c_Polynomial_Odegree(tc_Complex_Ocomplex,B)). [resolve(1288,a,1296,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,E,F) | C = E. [resolve(1288,a,1297,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,E,F) | D = F. [resolve(1288,a,1298,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A). [resolve(1288,a,1301,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(1288,a,1302,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B. [resolve(1288,a,1303,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,C) | C = A. [resolve(1288,a,1304,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | C != A. [resolve(1288,a,1305,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B. [resolve(1288,a,1306,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C. [resolve(1288,a,1307,a)].
% 3.73/3.98 Derived: c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C. [resolve(1288,a,1308,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,E,A),B,c_Polynomial_Osmult(tc_Complex_Ocomplex,E,C),c_Polynomial_Osmult(tc_Complex_Ocomplex,E,D)). [resolve(1288,a,1309,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,C,E,F,V6) | c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,E),F,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,V6),D)). [resolve(1288,a,1310,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,E,D)),c_Polynomial_Odegree(tc_Complex_Ocomplex,B)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,B),c_Polynomial_Odegree(tc_Complex_Ocomplex,B))) != F | c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,E,A),B,c_Polynomial_OpCons(tc_Complex_Ocomplex,F,C),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,E,D),c_Polynomial_Osmult(tc_Complex_Ocomplex,F,B))). [resolve(1288,a,1311,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,A) | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,A) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,B). [resolve(1288,a,1312,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,A) | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,A) != c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,B). [resolve(1288,a,1313,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)). [resolve(1288,a,1314,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C). [resolve(1288,a,1315,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,A)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)). [resolve(1288,a,1316,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C),A) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)). [resolve(1288,a,1317,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)),A) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C). [resolve(1288,a,1318,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,A)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)). [resolve(1288,a,1319,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,B,C),A) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,B,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A)),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,B,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A))),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)),hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A))),A)). [resolve(1288,a,1320,a)].
% 3.73/3.98 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,A,B),C) = c_Polynomial_Osmult(tc_Complex_Ocomplex,A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)). [resolve(1288,a,1321,a)].
% 3.73/3.98 Derived: -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,A,B,C,D) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) = D. [resolve(1288,a,1322,a)].
% 3.73/3.98 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,B)) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) = A. [resolve(1288,a,1323,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,c_Polynomial_Osmult(tc_Complex_Ocomplex,A,C)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1288,a,1324,a)].
% 3.73/3.98 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A),B) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)). [resolve(1288,a,1325,a)].
% 3.73/3.98 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B). [resolve(1288,a,1326,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)). [resolve(1288,a,1327,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B)),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B))). [resolve(1288,a,1328,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B)),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B))). [resolve(1288,a,1329,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,A)),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,A))). [resolve(1288,a,1330,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B)) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B). [resolve(1288,a,1331,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A),B) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B). [resolve(1288,a,1332,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1288,a,1333,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(1288,a,1334,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B. [resolve(1288,a,1335,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B. [resolve(1288,a,1336,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B),C) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C)). [resolve(1288,a,1337,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C)) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,C)). [resolve(1288,a,1338,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,A). [resolve(1288,a,1339,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1288,a,1340,a)].
% 3.73/3.98 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1288,a,1341,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)) = c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,A). [resolve(1288,a,1342,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != A | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,A) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,B),c_Polynomial_Odegree(tc_Complex_Ocomplex,B))),B). [resolve(1288,a,1343,a)].
% 3.73/3.98 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A). [resolve(1288,a,1345,a)].
% 3.73/3.98 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1288,a,1346,a)].
% 3.73/3.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1288,a,1347,a)].
% 3.73/3.99 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),A). [resolve(1288,a,1348,a)].
% 3.73/3.99 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | -c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,B,C,D,E) | c_Polynomial_Opdivmod__rel(tc_Complex_Ocomplex,B,c_Polynomial_Osmult(tc_Complex_Ocomplex,A,C),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),D),E). [resolve(1288,a,1349,a)].
% 3.73/3.99 Derived: c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A))),A). [resolve(1288,a,1350,a)].
% 3.73/3.99 Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B),A). [resolve(1288,a,1351,a)].
% 3.73/3.99 Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,A,B),B). [resolve(1288,a,1352,a)].
% 3.73/3.99 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,c_Polynomial_Osmult(tc_Complex_Ocomplex,A,C)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1288,a,1353,a)].
% 3.73/3.99 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,c_Polynomial_Osmult(tc_Complex_Ocomplex,A,C)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1288,a,1354,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,C,A),B). [resolve(1288,a,1355,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B). [resolve(1288,a,1357,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C). [resolve(1288,a,1358,a)].
% 3.73/3.99 Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C). [resolve(1288,a,1359,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,A,B),C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C. [resolve(1288,a,1361,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,A,B),C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1288,a,1362,a)].
% 3.73/3.99 Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,A,B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1288,a,1364,a)].
% 3.73/3.99 Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,A,B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C). [resolve(1288,a,1365,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1366,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1367,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1368,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1369,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1370,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1371,a)].
% 3.73/3.99 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1372,a)].
% 3.86/4.07 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),C) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1373,a)].
% 3.86/4.07 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1374,a)].
% 3.86/4.07 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1375,a)].
% 3.86/4.07 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != C | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1376,a)].
% 3.86/4.07 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),f21(C,B,A,tc_Complex_Ocomplex),A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,A),c_Polynomial_Odegree(tc_Complex_Ocomplex,A)) | c_Polynomial_Opoly__gcd(tc_Complex_Ocomplex,B,C) = A. [resolve(1288,a,1377,a)].
% 3.86/4.07 1378 -class_Fields_Ofield(A) | class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [clausify(1030)].
% 3.86/4.07 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1378,a,1288,a)].
% 3.86/4.07 1379 -class_Fields_Ofield(A) | class_Divides_Oring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Oring__div) # label(axiom). [clausify(1042)].
% 3.86/4.07 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1379,a,1288,a)].
% 3.86/4.07 1380 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.86/4.07 1381 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__mono) # label(axiom). [clausify(268)].
% 3.93/4.15 1382 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__left__mono) # label(axiom). [clausify(269)].
% 3.93/4.15 1383 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__right__mono) # label(axiom). [clausify(270)].
% 3.93/4.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). [resolve(1380,a,1381,a)].
% 3.93/4.15 1384 -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(1006)].
% 3.93/4.15 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)). [resolve(1384,b,1381,a)].
% 3.93/4.15 1385 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 3.93/4.15 1386 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(327)].
% 3.93/4.15 1387 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom). [clausify(327)].
% 3.93/4.15 1388 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonpos__nonneg) # label(axiom). [clausify(337)].
% 3.93/4.15 1389 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos2) # label(axiom). [clausify(338)].
% 3.93/4.15 1390 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos) # label(axiom). [clausify(339)].
% 3.93/4.15 1391 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__nonneg__nonneg) # label(axiom). [clausify(340)].
% 3.93/4.15 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1385,a,1386,a)].
% 3.93/4.23 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(1385,a,1387,a)].
% 3.93/4.23 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)). [resolve(1385,a,1391,a)].
% 3.93/4.23 1392 -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(1011)].
% 3.93/4.23 1393 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom). [clausify(1034)].
% 3.93/4.23 1394 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(328)].
% 3.93/4.23 1395 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_split__mult__pos__le) # label(axiom). [clausify(328)].
% 3.93/4.23 1396 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)) # label(fact_mult__left__mono__neg) # label(axiom). [clausify(331)].
% 3.93/4.23 1397 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)) # label(fact_mult__right__mono__neg) # label(axiom). [clausify(332)].
% 3.93/4.23 1398 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)) # label(fact_mult__nonpos__nonpos) # label(axiom). [clausify(336)].
% 3.93/4.23 1399 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F) # label(fact_le__add__iff1) # label(axiom). [clausify(573)].
% 3.93/4.23 1400 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F) # label(fact_le__add__iff1) # label(axiom). [clausify(573)].
% 3.93/4.23 1401 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)) # label(fact_le__add__iff2) # label(axiom). [clausify(574)].
% 4.03/4.23 1402 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)) # label(fact_le__add__iff2) # label(axiom). [clausify(574)].
% 4.03/4.23 1403 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F) # label(fact_less__add__iff1) # label(axiom). [clausify(575)].
% 4.03/4.23 1404 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F) # label(fact_less__add__iff1) # label(axiom). [clausify(575)].
% 4.03/4.23 1405 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)) # label(fact_less__add__iff2) # label(axiom). [clausify(576)].
% 4.03/4.23 1406 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)) # label(fact_less__add__iff2) # label(axiom). [clausify(576)].
% 4.03/4.23 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,B)). [resolve(1393,b,1396,a)].
% 4.03/4.23 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D)). [resolve(1393,b,1397,a)].
% 4.03/4.23 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E),C),D),F). [resolve(1393,b,1399,a)].
% 4.03/4.23 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E),C),D),F). [resolve(1393,b,1400,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B),C),F)). [resolve(1393,b,1401,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B),C),F)). [resolve(1393,b,1402,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E),C),D),F). [resolve(1393,b,1403,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E),C),D),F). [resolve(1393,b,1404,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B),C),F)). [resolve(1393,b,1405,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B),C),F)). [resolve(1393,b,1406,a)].
% 4.08/4.31 1407 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 4.08/4.31 1408 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__mono) # label(axiom). [clausify(329)].
% 4.08/4.31 1409 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)) # label(fact_mult__mono_H) # label(axiom). [clausify(330)].
% 4.08/4.31 1410 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_mult__left__mono) # label(axiom). [clausify(334)].
% 4.08/4.31 1411 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)) # label(fact_mult__right__mono) # label(axiom). [clausify(335)].
% 4.08/4.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1407,a,1408,a)].
% 4.08/4.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)). [resolve(1407,a,1409,a)].
% 4.08/4.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)). [resolve(1407,a,1410,a)].
% 4.08/4.31 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)). [resolve(1407,a,1411,a)].
% 4.08/4.31 1412 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom). [clausify(1023)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,E)). [resolve(1412,b,1408,a)].
% 4.08/4.31 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,E)). [resolve(1412,b,1409,a)].
% 4.33/4.55 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C)). [resolve(1412,b,1410,a)].
% 4.33/4.55 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)). [resolve(1412,b,1411,a)].
% 4.33/4.55 1413 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 4.33/4.55 1414 -class_Rings_Oordered__comm__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)) # label(fact_comm__mult__left__mono) # label(axiom). [clausify(333)].
% 4.33/4.55 1415 -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(1014)].
% 4.33/4.55 1416 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 4.33/4.55 1417 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__left__less__imp__less) # label(axiom). [clausify(372)].
% 4.33/4.55 1418 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__right__less__imp__less) # label(axiom). [clausify(374)].
% 4.33/4.55 1419 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom). [clausify(1018)].
% 4.33/4.55 1420 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 4.33/4.55 1421 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(404)].
% 4.33/4.55 1422 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom). [clausify(404)].
% 4.33/4.55 1423 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(405)].
% 4.33/4.55 1424 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom). [clausify(405)].
% 4.33/4.55 1425 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(406)].
% 4.33/4.55 1426 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__cases) # label(axiom). [clausify(408)].
% 4.33/4.55 1427 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__linear) # label(axiom). [clausify(422)].
% 4.33/4.55 1428 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__cases) # label(axiom). [clausify(424)].
% 4.33/4.55 1429 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neqE) # label(axiom). [clausify(439)].
% 4.33/4.55 1430 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | B = C # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(440)].
% 4.33/4.55 1431 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) | B != C # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(440)].
% 4.33/4.55 1432 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | C = B | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__less__linear) # label(axiom). [clausify(441)].
% 4.33/4.55 1433 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | C = B # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(442)].
% 4.33/4.55 1434 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(442)].
% 4.33/4.55 1435 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(442)].
% 4.33/4.55 1436 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom). [clausify(443)].
% 4.33/4.55 1437 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom). [clausify(443)].
% 4.33/4.55 1438 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom). [clausify(443)].
% 4.33/4.55 1439 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,B,C) | C = B # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(452)].
% 4.33/4.55 1440 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(452)].
% 4.33/4.55 1441 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_leD) # label(axiom). [clausify(454)].
% 4.33/4.55 1442 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | C = B # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(457)].
% 4.33/4.55 1443 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,C) | C != B # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(457)].
% 4.33/4.55 1444 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__leE) # label(axiom). [clausify(458)].
% 4.33/4.55 1445 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_leI) # label(axiom). [clausify(459)].
% 4.33/4.55 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1420,a,1421,a)].
% 4.33/4.55 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1420,a,1422,a)].
% 4.33/4.55 Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A). [resolve(1420,a,1426,a)].
% 4.33/4.55 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B = A | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1420,a,1428,a)].
% 4.33/4.55 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A) | A != B. [resolve(1420,a,1431,a)].
% 4.37/4.63 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). [resolve(1420,a,1434,a)].
% 4.37/4.63 Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B != A. [resolve(1420,a,1435,a)].
% 4.37/4.63 Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). [resolve(1420,a,1438,a)].
% 4.37/4.63 Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B = A. [resolve(1420,a,1439,a)].
% 4.37/4.63 Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | B != A. [resolve(1420,a,1443,a)].
% 4.37/4.63 1446 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [clausify(1036)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1446,b,1421,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1446,b,1422,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1446,b,1426,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C = B | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1446,b,1428,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B) | B != C. [resolve(1446,b,1431,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1446,b,1434,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C != B. [resolve(1446,b,1435,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | B != C | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C). [resolve(1446,b,1438,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C = B. [resolve(1446,b,1439,a)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | C != B. [resolve(1446,b,1443,a)].
% 4.37/4.63 1447 -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(1004)].
% 4.37/4.63 1448 -class_Rings_Olinordered__semiring__1__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oone__class_Oone(A) != c_Groups_Oplus__class_Oplus(A,E,F) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C) # label(fact_convex__bound__lt) # label(axiom). [clausify(463)].
% 4.37/4.63 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),E,F) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),F,D)),C). [resolve(1447,b,1448,a)].
% 4.46/4.71 1449 class_Groups_Ogroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ogroup__add) # label(axiom). [assumption].
% 4.46/4.71 1450 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(468)].
% 4.46/4.71 1451 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_diff__self) # label(axiom). [clausify(469)].
% 4.46/4.71 1452 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | B = C # label(fact_right__minus__eq) # label(axiom). [clausify(471)].
% 4.46/4.71 1453 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | B != C # label(fact_right__minus__eq) # label(axiom). [clausify(471)].
% 4.46/4.71 1454 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(479)].
% 4.46/4.71 1455 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = B # label(fact_add__diff__cancel) # label(axiom). [clausify(480)].
% 4.46/4.71 1456 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,C) | c_Groups_Ouminus__class_Ouminus(A,B) = C # label(fact_add__eq__0__iff) # label(axiom). [clausify(607)].
% 4.46/4.71 1457 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,C) | c_Groups_Ouminus__class_Ouminus(A,B) != C # label(fact_add__eq__0__iff) # label(axiom). [clausify(607)].
% 4.46/4.71 1458 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B)) = B # label(fact_minus__minus) # label(axiom). [clausify(608)].
% 4.46/4.71 1459 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_equation__minus__iff) # label(axiom). [clausify(609)].
% 4.46/4.71 1460 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_equation__minus__iff) # label(axiom). [clausify(609)].
% 4.46/4.71 1461 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ouminus__class_Ouminus(A,C) = B # label(fact_minus__equation__iff) # label(axiom). [clausify(610)].
% 4.46/4.71 1462 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ouminus__class_Ouminus(A,C) != B # label(fact_minus__equation__iff) # label(axiom). [clausify(610)].
% 4.46/4.71 1463 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ouminus__class_Ouminus(A,C) | B = C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(611)].
% 4.46/4.71 1464 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ouminus__class_Ouminus(A,C) | B != C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(611)].
% 4.46/4.71 1465 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oplus__class_Oplus(A,B,C)) = C # label(fact_minus__add__cancel) # label(axiom). [clausify(620)].
% 4.46/4.71 1466 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),C)) = C # label(fact_add__minus__cancel) # label(axiom). [clausify(621)].
% 4.46/4.71 1467 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_minus__add) # label(axiom). [clausify(622)].
% 4.46/4.71 1468 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(637)].
% 4.46/4.71 1469 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(637)].
% 4.46/4.71 1470 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(639)].
% 4.46/4.71 1471 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(639)].
% 4.46/4.71 1472 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_minus__zero) # label(axiom). [clausify(640)].
% 4.46/4.71 1473 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,C) | c_Groups_Ouminus__class_Ouminus(A,B) = C # label(fact_minus__unique) # label(axiom). [clausify(651)].
% 4.46/4.71 1474 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B) # label(fact_left__minus) # label(axiom). [clausify(653)].
% 4.46/4.71 1475 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) != C | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,C,B) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(654)].
% 4.46/4.71 1476 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = C | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,C,B) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(654)].
% 4.46/4.71 1477 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_right__minus) # label(axiom). [clausify(655)].
% 4.46/4.71 1478 -class_Groups_Ogroup__add(A) | c_Groups_Ouminus__class_Ouminus(A,B) = c_Groups_Ominus__class_Ominus(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_diff__0) # label(axiom). [clausify(656)].
% 4.46/4.71 1479 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Oplus__class_Oplus(A,B,C) # label(fact_diff__minus__eq__add) # label(axiom). [clausify(659)].
% 4.46/4.71 1480 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_diff__def) # label(axiom). [clausify(662)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(1449,a,1450,a)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1449,a,1451,a)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(1449,a,1452,a)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | A != B. [resolve(1449,a,1453,a)].
% 4.46/4.71 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),B) = A. [resolve(1449,a,1454,a)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),B) = A. [resolve(1449,a,1455,a)].
% 4.46/4.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = B. [resolve(1449,a,1456,a)].
% 4.46/4.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B. [resolve(1449,a,1457,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = A. [resolve(1449,a,1458,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) = A. [resolve(1449,a,1459,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) | A = B. [resolve(1449,a,1463,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B) | A != B. [resolve(1449,a,1464,a)].
% 4.46/4.71 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = B. [resolve(1449,a,1465,a)].
% 4.46/4.71 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B)) = B. [resolve(1449,a,1466,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1449,a,1467,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1449,a,1468,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1449,a,1469,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1449,a,1472,a)].
% 4.46/4.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),A). [resolve(1449,a,1474,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A). [resolve(1449,a,1475,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,A). [resolve(1449,a,1476,a)].
% 4.46/4.71 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)). [resolve(1449,a,1477,a)].
% 4.46/4.71 Derived: c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A). [resolve(1449,a,1478,a)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B). [resolve(1449,a,1479,a)].
% 4.46/4.71 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1449,a,1480,a)].
% 4.46/4.71 1481 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom). [clausify(1041)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(1481,b,1450,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1481,b,1451,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = C. [resolve(1481,b,1452,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B != C. [resolve(1481,b,1453,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),C) = B. [resolve(1481,b,1454,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),C) = B. [resolve(1481,b,1455,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = C. [resolve(1481,b,1456,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != C. [resolve(1481,b,1457,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) = B. [resolve(1481,b,1458,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != C | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C) = B. [resolve(1481,b,1459,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C) | B = C. [resolve(1481,b,1463,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C) | B != C. [resolve(1481,b,1464,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)) = C. [resolve(1481,b,1465,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C)) = C. [resolve(1481,b,1466,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)). [resolve(1481,b,1467,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(1481,b,1468,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B. [resolve(1481,b,1469,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1481,b,1472,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),B). [resolve(1481,b,1474,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) != C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,B). [resolve(1481,b,1475,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = C | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,B). [resolve(1481,b,1476,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)). [resolve(1481,b,1477,a)].
% 4.46/4.71 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1481,b,1478,a)].
% 4.55/4.79 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C). [resolve(1481,b,1479,a)].
% 4.55/4.79 Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)). [resolve(1481,b,1480,a)].
% 4.55/4.79 1482 -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(1016)].
% 4.55/4.79 1483 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,D,E) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(472)].
% 4.55/4.79 1484 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(472)].
% 4.55/4.79 1485 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(473)].
% 4.55/4.79 1486 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(473)].
% 4.55/4.79 1487 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(533)].
% 4.55/4.79 1488 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(533)].
% 4.55/4.79 1489 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(534)].
% 4.55/4.79 1490 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(534)].
% 4.55/4.79 1491 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__minus__iff) # label(axiom). [clausify(597)].
% 4.55/4.79 1492 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__minus__iff) # label(axiom). [clausify(597)].
% 4.55/4.79 1493 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__le__iff) # label(axiom). [clausify(598)].
% 4.55/4.79 1494 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__le__iff) # label(axiom). [clausify(598)].
% 4.55/4.79 1495 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_neg__le__iff__le) # label(axiom). [clausify(599)].
% 4.55/4.79 1496 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_neg__le__iff__le) # label(axiom). [clausify(599)].
% 4.55/4.79 1497 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_le__imp__neg__le) # label(axiom). [clausify(600)].
% 4.55/4.79 1498 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_neg__less__iff__less) # label(axiom). [clausify(633)].
% 4.55/4.79 1499 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_neg__less__iff__less) # label(axiom). [clausify(633)].
% 4.55/4.79 1500 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__less__iff) # label(axiom). [clausify(634)].
% 4.55/4.79 1501 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B) # label(fact_minus__less__iff) # label(axiom). [clausify(634)].
% 4.55/4.79 1502 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_less__minus__iff) # label(axiom). [clausify(635)].
% 4.55/4.79 1503 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) # label(fact_less__minus__iff) # label(axiom). [clausify(635)].
% 4.55/4.79 1504 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(644)].
% 4.55/4.79 1505 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(644)].
% 4.55/4.79 1506 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(646)].
% 4.55/4.79 1507 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(646)].
% 4.55/4.79 1508 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(648)].
% 4.55/4.79 1509 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(648)].
% 4.55/4.79 1510 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(649)].
% 4.55/4.80 1511 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(649)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E). [resolve(1482,b,1483,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E). [resolve(1482,b,1484,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E). [resolve(1482,b,1485,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E). [resolve(1482,b,1486,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1487,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1488,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1489,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1490,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)). [resolve(1482,b,1491,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C),B). [resolve(1482,b,1493,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1482,b,1495,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B). [resolve(1482,b,1496,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1482,b,1498,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B). [resolve(1482,b,1499,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C),B). [resolve(1482,b,1500,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)). [resolve(1482,b,1502,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1482,b,1504,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1482,b,1505,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1506,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1507,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1508,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(1482,b,1509,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1482,b,1510,a)].
% 4.55/4.80 Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B). [resolve(1482,b,1511,a)].
% 4.85/5.11 1512 class_Rings_Ozero__neq__one(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.85/5.11 1513 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_zero__neq__one) # label(axiom). [clausify(481)].
% 4.85/5.11 1514 -class_Rings_Ozero__neq__one(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Ozero__class_Ozero(A) # label(fact_one__neq__zero) # label(axiom). [clausify(482)].
% 4.85/5.11 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1512,a,1513,a)].
% 4.85/5.11 1515 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ozero__neq__one) # label(axiom). [assumption].
% 4.85/5.11 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1515,a,1513,a)].
% 4.85/5.11 1516 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom). [clausify(1033)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1516,b,1513,a)].
% 4.85/5.11 1517 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 4.85/5.11 1518 -class_Groups_Omonoid__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(487)].
% 4.85/5.11 1519 -class_Groups_Omonoid__mult(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(490)].
% 4.85/5.11 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) = A. [resolve(1517,a,1518,a)].
% 4.85/5.11 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(1517,a,1519,a)].
% 4.85/5.11 1520 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom). [assumption].
% 4.85/5.11 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A) = A. [resolve(1520,a,1518,a)].
% 4.85/5.11 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1520,a,1519,a)].
% 4.85/5.11 1521 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom). [clausify(1037)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) = B. [resolve(1521,b,1518,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1521,b,1519,a)].
% 4.85/5.11 1522 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.85/5.11 1523 -class_Groups_Ocomm__monoid__mult(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B) = B # label(fact_mult__1) # label(axiom). [clausify(489)].
% 4.85/5.11 1524 -class_Groups_Ocomm__monoid__mult(A) | c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom). [clausify(492)].
% 4.85/5.11 1525 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.85/5.11 1526 -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(1021)].
% 4.85/5.11 1527 class_Rings_Oring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring) # label(axiom). [assumption].
% 4.85/5.11 1528 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D) = F # label(fact_eq__add__iff1) # label(axiom). [clausify(536)].
% 4.85/5.11 1529 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D) != F # label(fact_eq__add__iff1) # label(axiom). [clausify(536)].
% 4.85/5.11 1530 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D) != c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F) = D # label(fact_eq__add__iff2) # label(axiom). [clausify(537)].
% 4.85/5.11 1531 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F) | c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F) != D # label(fact_eq__add__iff2) # label(axiom). [clausify(537)].
% 4.85/5.11 1532 -class_Rings_Oring(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,E)),c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,D),E)) # label(fact_mult__diff__mult) # label(axiom). [clausify(594)].
% 4.85/5.11 1533 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__right) # label(axiom). [clausify(628)].
% 4.85/5.11 1534 -class_Rings_Oring(A) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_minus__mult__left) # label(axiom). [clausify(629)].
% 4.85/5.11 1535 -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) # label(fact_minus__mult__commute) # label(axiom). [clausify(630)].
% 4.85/5.11 1536 -class_Rings_Oring(A) | c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Otimes__class_Otimes(A,B,C) # label(fact_minus__mult__minus) # label(axiom). [clausify(631)].
% 4.85/5.11 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D),B),C) = E. [resolve(1527,a,1528,a)].
% 4.85/5.11 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D),B),C) != E. [resolve(1527,a,1529,a)].
% 4.85/5.11 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,D,A),B),E) = C. [resolve(1527,a,1530,a)].
% 4.85/5.11 Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,D,B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,D,A),B),E) != C. [resolve(1527,a,1531,a)].
% 4.85/5.11 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),D)). [resolve(1527,a,1532,a)].
% 4.85/5.11 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)). [resolve(1527,a,1535,a)].
% 4.85/5.11 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B). [resolve(1527,a,1536,a)].
% 4.85/5.11 1537 -class_Rings_Ocomm__ring(A) | class_Rings_Oring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom). [clausify(1054)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E),C),D) = F. [resolve(1537,b,1528,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E),C),D) != F. [resolve(1537,b,1529,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B),C),F) = D. [resolve(1537,b,1530,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B),C),F) != D. [resolve(1537,b,1531,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,E)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,E)),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,D),E)). [resolve(1537,b,1532,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)). [resolve(1537,b,1533,a)].
% 4.85/5.11 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C). [resolve(1537,b,1534,a)].
% 5.13/5.35 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)). [resolve(1537,b,1535,a)].
% 5.13/5.35 Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C). [resolve(1537,b,1536,a)].
% 5.13/5.35 1538 -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(1015)].
% 5.13/5.35 1539 -class_Rings_Olinordered__semiring__1(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oone__class_Oone(A) != c_Groups_Oplus__class_Oplus(A,E,F) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C) # label(fact_convex__bound__le) # label(axiom). [clausify(592)].
% 5.13/5.35 Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),E,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),F,D)),C). [resolve(1538,b,1539,a)].
% 5.13/5.35 1540 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom). [assumption].
% 5.13/5.35 1541 -class_Rings_Oring__1(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Oone__class_Oone(A)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A)),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_real__squared__diff__one__factored) # label(axiom). [clausify(593)].
% 5.13/5.35 Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))). [resolve(1540,a,1541,a)].
% 5.13/5.35 1542 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom). [clausify(1051)].
% 5.13/5.35 Derived: -class_Rings_Ocomm__ring__1(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))). [resolve(1542,b,1541,a)].
% 5.13/5.35 1543 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 5.13/5.35 1544 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Otimes__class_Otimes(A,B,B) | c_Groups_Oone__class_Oone(A) = B | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) = B # label(fact_square__eq__1__iff) # label(axiom). [clausify(657)].
% 5.21/5.42 1545 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = c_Groups_Otimes__class_Otimes(A,B,B) | c_Groups_Oone__class_Oone(A) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(657)].
% 5.21/5.42 1546 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = c_Groups_Otimes__class_Otimes(A,B,B) | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(657)].
% 5.21/5.42 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1543,a,1544,a)].
% 5.21/5.42 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1543,a,1545,a)].
% 5.21/5.42 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,A) | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) != A. [resolve(1543,a,1546,a)].
% 5.21/5.42 1547 -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(1010)].
% 5.21/5.42 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = B | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(1547,b,1544,a)].
% 5.21/5.42 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != B. [resolve(1547,b,1545,a)].
% 5.21/5.42 Derived: -class_Rings_Oidom(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,B) | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) != B. [resolve(1547,b,1546,a)].
% 5.21/5.42 1548 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom). [assumption].
% 5.21/5.42 1549 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_diff__divide__distrib) # label(axiom). [clausify(669)].
% 5.21/5.42 1550 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_divide__1) # label(axiom). [clausify(670)].
% 5.21/5.42 1551 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_minus__divide__left) # label(axiom). [clausify(673)].
% 5.21/5.42 1552 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__zero__left) # label(axiom). [clausify(675)].
% 5.21/5.42 1553 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Otimes__class_Otimes(A,B,C),D) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_times__divide__eq__right) # label(axiom). [clausify(677)].
% 5.21/5.42 1554 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_add__divide__distrib) # label(axiom). [clausify(678)].
% 5.21/5.43 1555 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_eq__divide__imp) # label(axiom). [clausify(680)].
% 5.21/5.43 1556 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Otimes__class_Otimes(A,C,B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_divide__eq__imp) # label(axiom). [clausify(681)].
% 5.21/5.43 1557 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | c_Groups_Otimes__class_Otimes(A,D,B) = C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(682)].
% 5.21/5.43 1558 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | c_Groups_Otimes__class_Otimes(A,D,B) != C # label(fact_nonzero__divide__eq__eq) # label(axiom). [clausify(682)].
% 5.21/5.43 1559 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | c_Groups_Otimes__class_Otimes(A,D,B) = C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(683)].
% 5.21/5.43 1560 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | c_Groups_Otimes__class_Otimes(A,D,B) != C # label(fact_nonzero__eq__divide__eq) # label(axiom). [clausify(683)].
% 5.21/5.43 1561 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != c_Groups_Oone__class_Oone(A) | C = B # label(fact_right__inverse__eq) # label(axiom). [clausify(685)].
% 5.21/5.43 1562 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = c_Groups_Oone__class_Oone(A) | C != B # label(fact_right__inverse__eq) # label(axiom). [clausify(685)].
% 5.21/5.43 1563 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_divide__self) # label(axiom). [clausify(686)].
% 5.21/5.43 1564 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)) = c_Rings_Oinverse__class_Odivide(A,C,B) # label(fact_nonzero__minus__divide__divide) # label(axiom). [clausify(688)].
% 5.21/5.43 1565 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_nonzero__minus__divide__right) # label(axiom). [clausify(689)].
% 5.21/5.43 1566 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_inverse__eq__divide) # label(axiom). [clausify(842)].
% 5.21/5.43 1567 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_divide__inverse) # label(axiom). [clausify(844)].
% 5.21/5.43 1568 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_nonzero__inverse__mult__distrib) # label(axiom). [clausify(845)].
% 5.21/5.43 1569 -class_Rings_Odivision__ring(A) | c_Groups_Oone__class_Oone(A) != c_Groups_Otimes__class_Otimes(A,B,C) | c_Rings_Oinverse__class_Oinverse(A,B) = C # label(fact_inverse__unique) # label(axiom). [clausify(846)].
% 5.21/5.43 1570 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_nonzero__imp__inverse__nonzero) # label(axiom). [clausify(852)].
% 5.21/5.43 1571 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B)) = B # label(fact_nonzero__inverse__inverse__eq) # label(axiom). [clausify(853)].
% 5.21/5.43 1572 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__zero__imp__zero) # label(axiom). [clausify(854)].
% 5.21/5.43 1573 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ozero__class_Ozero(A) = B | B = C # label(fact_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(855)].
% 5.21/5.43 1574 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_inverse__1) # label(axiom). [clausify(856)].
% 5.21/5.43 1575 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_nonzero__inverse__minus__eq) # label(axiom). [clausify(874)].
% 5.21/5.43 1576 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oplus__class_Oplus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,C)) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__add) # label(axiom). [clausify(882)].
% 5.21/5.43 1577 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ominus__class_Ominus(A,C,B)),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_division__ring__inverse__diff) # label(axiom). [clausify(885)].
% 5.21/5.43 1578 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),B) # label(fact_left__inverse) # label(axiom). [clausify(887)].
% 5.21/5.43 1579 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_right__inverse) # label(axiom). [clausify(888)].
% 5.21/5.43 1580 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B) # label(fact_nonzero__inverse__eq__divide) # label(axiom). [clausify(889)].
% 5.21/5.43 1581 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ominus__class_Ominus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,C))) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_Deriv_Oinverse__diff__inverse) # label(axiom). [clausify(894)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)). [resolve(1548,a,1549,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(1548,a,1550,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),B) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)). [resolve(1548,a,1551,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1548,a,1552,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),C) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)). [resolve(1548,a,1553,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)). [resolve(1548,a,1554,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,A) != C | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A) = B. [resolve(1548,a,1555,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) != C | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,A) = B. [resolve(1548,a,1557,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | B = A. [resolve(1548,a,1561,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | B != A. [resolve(1548,a,1562,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1548,a,1563,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A). [resolve(1548,a,1564,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A)). [resolve(1548,a,1565,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1548,a,1568,a)].
% 5.21/5.43 Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = B. [resolve(1548,a,1569,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1548,a,1570,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1548,a,1571,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | A = B. [resolve(1548,a,1573,a)].
% 5.21/5.43 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1548,a,1574,a)].
% 5.21/5.43 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1548,a,1575,a)].
% 5.26/5.51 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1548,a,1576,a)].
% 5.26/5.51 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,A)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1548,a,1577,a)].
% 5.26/5.51 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1548,a,1579,a)].
% 5.26/5.51 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B))) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1548,a,1581,a)].
% 5.26/5.51 1582 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 5.26/5.51 1583 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D) = c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide_Odiff) # label(axiom). [clausify(671)].
% 5.26/5.51 1584 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide_Ominus) # label(axiom). [clausify(672)].
% 5.26/5.51 1585 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide_Ozero) # label(axiom). [clausify(676)].
% 5.26/5.51 1586 -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),D) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide_Oadd) # label(axiom). [clausify(679)].
% 5.26/5.51 1587 -class_RealVector_Oreal__normed__field(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)),D) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D)),c_Rings_Oinverse__class_Oinverse(A,C))) # label(fact_DERIV__inverse__lemma) # label(axiom). [clausify(895)].
% 5.26/5.51 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)),C) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),C)),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B))). [resolve(1582,a,1587,a)].
% 5.35/5.58 1588 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) # label(axiom). [assumption].
% 5.35/5.58 1589 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__zero) # label(axiom). [clausify(674)].
% 5.35/5.58 1590 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__self__if) # label(axiom). [clausify(687)].
% 5.35/5.58 1591 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_divide__self__if) # label(axiom). [clausify(687)].
% 5.35/5.58 1592 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B)) = B # label(fact_inverse__inverse__eq) # label(axiom). [clausify(847)].
% 5.35/5.58 1593 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | B = C # label(fact_inverse__eq__iff__eq) # label(axiom). [clausify(848)].
% 5.35/5.58 1594 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Rings_Oinverse__class_Oinverse(A,C) | B != C # label(fact_inverse__eq__iff__eq) # label(axiom). [clausify(848)].
% 5.35/5.58 1595 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Rings_Oinverse__class_Oinverse(A,C) | B = C # label(fact_inverse__eq__imp__eq) # label(axiom). [clausify(849)].
% 5.35/5.58 1596 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_inverse__zero) # label(axiom). [clausify(850)].
% 5.35/5.58 1597 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(851)].
% 5.35/5.58 1598 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_inverse__nonzero__iff__nonzero) # label(axiom). [clausify(851)].
% 5.35/5.58 1599 -class_Rings_Odivision__ring__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)) # label(fact_inverse__minus__eq) # label(axiom). [clausify(875)].
% 5.35/5.58 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1588,a,1589,a)].
% 5.35/5.58 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1588,a,1590,a)].
% 5.35/5.58 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)) = A. [resolve(1588,a,1592,a)].
% 5.35/5.58 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | A = B. [resolve(1588,a,1593,a)].
% 5.35/5.58 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B) | A != B. [resolve(1588,a,1594,a)].
% 5.35/5.58 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1588,a,1596,a)].
% 5.65/5.86 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1588,a,1598,a)].
% 5.65/5.86 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A)). [resolve(1588,a,1599,a)].
% 5.65/5.86 1600 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 5.65/5.86 1601 -class_RealVector_Oreal__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)),F) = c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,C,E),F)),c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,D),F),E)) # label(fact_DERIV__mult__lemma) # label(axiom). [clausify(684)].
% 5.65/5.86 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)),E) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D),E)),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),E),D)). [resolve(1600,a,1601,a)].
% 5.65/5.86 1602 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) # label(axiom). [assumption].
% 5.65/5.86 1603 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E)) = c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,E)) # label(fact_times__divide__times__eq) # label(axiom). [clausify(693)].
% 5.65/5.86 1604 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ouminus__class_Ouminus(A,C)) = c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_minus__divide__right) # label(axiom). [clausify(694)].
% 5.65/5.86 1605 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)) = c_Rings_Oinverse__class_Odivide(A,B,C) # label(fact_minus__divide__divide) # label(axiom). [clausify(695)].
% 5.65/5.86 1606 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Rings_Oinverse__class_Odivide(A,C,D) # label(fact_mult__divide__mult__cancel__left) # label(axiom). [clausify(709)].
% 5.65/5.86 1607 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Otimes__class_Otimes(A,D,B)) = c_Rings_Oinverse__class_Odivide(A,C,D) # label(fact_mult__divide__mult__cancel__right) # label(axiom). [clausify(710)].
% 5.65/5.86 1608 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,D,C) = B # label(fact_divide__eq__eq) # label(axiom). [clausify(711)].
% 5.65/5.86 1609 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_divide__eq__eq) # label(axiom). [clausify(711)].
% 5.65/5.86 1610 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq) # label(axiom). [clausify(711)].
% 5.65/5.86 1611 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Otimes__class_Otimes(A,D,C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divide__eq__eq) # label(axiom). [clausify(711)].
% 5.65/5.86 1612 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Otimes__class_Otimes(A,D,C) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq) # label(axiom). [clausify(711)].
% 5.65/5.86 1613 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Otimes__class_Otimes(A,D,C) = B # label(fact_eq__divide__eq) # label(axiom). [clausify(712)].
% 5.65/5.86 1614 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_eq__divide__eq) # label(axiom). [clausify(712)].
% 5.65/5.86 1615 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq) # label(axiom). [clausify(712)].
% 5.65/5.86 1616 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Otimes__class_Otimes(A,D,C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_eq__divide__eq) # label(axiom). [clausify(712)].
% 5.65/5.86 1617 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Otimes__class_Otimes(A,D,C) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq) # label(axiom). [clausify(712)].
% 5.65/5.86 1618 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,D,B)),B) = c_Groups_Oplus__class_Oplus(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_add__num__frac) # label(axiom). [clausify(730)].
% 5.65/5.86 1619 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,D,B)),B) = c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_add__frac__num) # label(axiom). [clausify(732)].
% 5.65/5.86 1620 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) != c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) = B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(857)].
% 5.65/5.86 1621 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,B) = c_Groups_Oone__class_Oone(A) | c_Groups_Oone__class_Oone(A) != B # label(fact_inverse__eq__1__iff) # label(axiom). [clausify(857)].
% 5.65/5.86 1622 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)) # label(fact_inverse__mult__distrib) # label(axiom). [clausify(858)].
% 5.65/5.86 1623 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_field__inverse__zero) # label(axiom). [clausify(859)].
% 5.65/5.86 1624 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Odivide(A,B,C)) = c_Rings_Oinverse__class_Odivide(A,C,B) # label(fact_inverse__divide) # label(axiom). [clausify(862)].
% 5.65/5.86 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,D)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,D)). [resolve(1602,a,1603,a)].
% 5.65/5.86 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)). [resolve(1602,a,1604,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B). [resolve(1602,a,1605,a)].
% 5.73/5.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,C)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C). [resolve(1602,a,1606,a)].
% 5.73/5.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,A),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C). [resolve(1602,a,1607,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C. [resolve(1602,a,1609,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C. [resolve(1602,a,1610,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C. [resolve(1602,a,1612,a)].
% 5.73/5.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,A)),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A)). [resolve(1602,a,1618,a)].
% 5.73/5.98 Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,C,A)),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C). [resolve(1602,a,1619,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = A. [resolve(1602,a,1620,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != A. [resolve(1602,a,1621,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,A),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,B)). [resolve(1602,a,1622,a)].
% 5.73/5.98 Derived: c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A). [resolve(1602,a,1624,a)].
% 5.73/5.98 1625 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption].
% 5.73/5.98 1626 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Otimes__class_Otimes(A,C,D)),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mult__self2) # label(axiom). [clausify(764)].
% 5.73/5.98 1627 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Otimes__class_Otimes(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,B,D) # label(fact_mod__mult__self1) # label(axiom). [clausify(765)].
% 5.73/5.98 1628 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mod__trivial) # label(axiom). [clausify(784)].
% 5.73/5.98 1629 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__0) # label(axiom). [clausify(785)].
% 5.73/5.98 1630 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_mod__by__0) # label(axiom). [clausify(786)].
% 5.73/5.98 1631 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__self) # label(axiom). [clausify(787)].
% 5.73/5.98 1632 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,E),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,D,F),C) # label(fact_mod__mult__cong) # label(axiom). [clausify(788)].
% 5.73/5.98 1633 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_zmod__simps_I4_J) # label(axiom). [clausify(789)].
% 5.73/5.98 1634 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)) = c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,D),C) # label(fact_mod__mult__mult2) # label(axiom). [clausify(790)].
% 5.73/5.98 1635 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)) = c_Groups_Otimes__class_Otimes(A,B,c_Divides_Odiv__class_Omod(A,C,D)) # label(fact_mod__mult__mult1) # label(axiom). [clausify(791)].
% 5.73/5.98 1636 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_mod__mult__eq) # label(axiom). [clausify(792)].
% 5.73/5.98 1637 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C) # label(fact_mod__mult__left__eq) # label(axiom). [clausify(793)].
% 5.73/5.98 1638 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),D) # label(fact_mod__mult__right__eq) # label(axiom). [clausify(794)].
% 5.73/5.98 1639 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,E),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,D,F),C) # label(fact_mod__add__cong) # label(axiom). [clausify(795)].
% 5.73/5.98 1640 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_zmod__simps_I1_J) # label(axiom). [clausify(796)].
% 5.73/5.98 1641 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D) # label(fact_zmod__simps_I2_J) # label(axiom). [clausify(797)].
% 5.73/5.98 1642 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mod__add__eq) # label(axiom). [clausify(798)].
% 5.73/5.98 1643 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mod__add__left__eq) # label(axiom). [clausify(799)].
% 5.73/5.98 1644 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D) # label(fact_mod__add__right__eq) # label(axiom). [clausify(800)].
% 5.73/5.98 1645 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),B) = c_Divides_Odiv__class_Omod(A,C,B) # label(fact_mod__add__self1) # label(axiom). [clausify(801)].
% 5.73/5.98 1646 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__add__self2) # label(axiom). [clausify(802)].
% 5.73/5.98 1647 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self1__is__0) # label(axiom). [clausify(809)].
% 5.73/5.98 1648 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self2__is__0) # label(axiom). [clausify(810)].
% 5.73/5.98 1649 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Oone__class_Oone(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__by__1) # label(axiom). [clausify(811)].
% 5.73/5.98 1650 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__imp__mod__0) # label(axiom). [clausify(928)].
% 5.73/5.98 1651 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom). [clausify(929)].
% 5.73/5.98 1652 -class_Divides_Osemiring__div(A) | c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,C,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom). [clausify(929)].
% 5.73/5.98 1653 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,C,D)) | -c_Rings_Odvd__class_Odvd(A,B,D) | c_Rings_Odvd__class_Odvd(A,B,C) # label(fact_dvd__mod__imp__dvd) # label(axiom). [clausify(930)].
% 5.73/5.98 1654 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,D) | c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,C,D)) # label(fact_dvd__mod) # label(axiom). [clausify(931)].
% 5.73/5.98 1655 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,D,C),B) = c_Divides_Odiv__class_Omod(A,D,B) # label(fact_mod__mod__cancel) # label(axiom). [clausify(932)].
% 5.73/5.98 1656 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,D,C)) | c_Rings_Odvd__class_Odvd(A,B,D) # label(fact_dvd__mod__iff) # label(axiom). [clausify(933)].
% 5.73/5.98 1657 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,D,C)) | -c_Rings_Odvd__class_Odvd(A,B,D) # label(fact_dvd__mod__iff) # label(axiom). [clausify(933)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1625,a,1626,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C). [resolve(1625,a,1627,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1625,a,1628,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1629,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(1625,a,1630,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1631,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,E),B). [resolve(1625,a,1632,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),B). [resolve(1625,a,1633,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C),B). [resolve(1625,a,1634,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)). [resolve(1625,a,1635,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),B). [resolve(1625,a,1636,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),C). [resolve(1625,a,1638,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E),B). [resolve(1625,a,1639,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). [resolve(1625,a,1640,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C). [resolve(1625,a,1641,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). [resolve(1625,a,1642,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A). [resolve(1625,a,1645,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(1625,a,1646,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1647,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1648,a)].
% 5.73/5.98 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1649,a)].
% 5.73/5.98 Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1650,a)].
% 5.73/5.98 Derived: c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(1625,a,1652,a)].
% 5.73/6.00 Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B). [resolve(1625,a,1653,a)].
% 5.73/6.00 Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)). [resolve(1625,a,1654,a)].
% 5.73/6.00 Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,A). [resolve(1625,a,1655,a)].
% 5.73/6.00 1658 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1378,a,1288,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B). [resolve(1658,a,1626,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C). [resolve(1658,a,1627,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B). [resolve(1658,a,1628,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1629,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = A. [resolve(1658,a,1630,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1631,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,D),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,E),B). [resolve(1658,a,1632,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1658,a,1633,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1658,a,1634,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C)) = c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)). [resolve(1658,a,1635,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1658,a,1636,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C). [resolve(1658,a,1638,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,D),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,E),B). [resolve(1658,a,1639,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1658,a,1640,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C). [resolve(1658,a,1641,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1658,a,1642,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A). [resolve(1658,a,1645,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B). [resolve(1658,a,1646,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1647,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1648,a)].
% 5.73/6.00 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1649,a)].
% 5.81/6.06 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1650,a)].
% 5.81/6.06 Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1658,a,1652,a)].
% 5.81/6.06 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B). [resolve(1658,a,1653,a)].
% 5.81/6.06 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)). [resolve(1658,a,1654,a)].
% 5.81/6.06 Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A). [resolve(1658,a,1655,a)].
% 5.81/6.06 1659 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(1379,a,1288,a)].
% 5.81/6.06 1660 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,E),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,D,F),C) # label(fact_mod__diff__cong) # label(axiom). [clausify(803)].
% 5.81/6.06 1661 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mod__diff__eq) # label(axiom). [clausify(804)].
% 5.81/6.06 1662 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mod__diff__left__eq) # label(axiom). [clausify(805)].
% 5.81/6.06 1663 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,C),D) # label(fact_mod__diff__right__eq) # label(axiom). [clausify(806)].
% 5.81/6.06 1664 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,B),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,D),C) # label(fact_mod__minus__cong) # label(axiom). [clausify(807)].
% 5.81/6.06 1665 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,c_Divides_Odiv__class_Omod(A,B,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ouminus__class_Ouminus(A,B),C) # label(fact_mod__minus__eq) # label(axiom). [clausify(808)].
% 5.81/6.06 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,D),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,E),B). [resolve(1659,a,1660,a)].
% 5.87/6.10 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1659,a,1661,a)].
% 5.87/6.10 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B). [resolve(1659,a,1662,a)].
% 5.87/6.10 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C). [resolve(1659,a,1663,a)].
% 5.87/6.10 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C),B). [resolve(1659,a,1664,a)].
% 5.87/6.10 Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A),B). [resolve(1659,a,1665,a)].
% 5.87/6.10 1666 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 5.87/6.10 1667 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ouminus__class_Ouminus(A,B)) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Osgn__class_Osgn(A,B)) # label(fact_sgn__minus) # label(axiom). [clausify(814)].
% 5.87/6.10 1668 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sgn__zero__iff) # label(axiom). [clausify(830)].
% 5.87/6.10 1669 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sgn__zero__iff) # label(axiom). [clausify(830)].
% 5.87/6.10 1670 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__zero) # label(axiom). [clausify(831)].
% 5.87/6.10 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,A)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A)). [resolve(1666,a,1667,a)].
% 5.87/6.10 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(1666,a,1668,a)].
% 5.87/6.10 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A. [resolve(1666,a,1669,a)].
% 5.87/6.10 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1666,a,1670,a)].
% 6.09/6.33 1671 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 6.09/6.33 1672 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Oone__class_Oone(A)) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__one) # label(axiom). [clausify(819)].
% 6.09/6.33 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1671,a,1672,a)].
% 6.09/6.33 1673 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 6.09/6.33 1674 -class_RealVector_Oreal__normed__div__algebra(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Otimes__class_Otimes(A,B,C)) = c_Groups_Otimes__class_Otimes(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Osgn__class_Osgn(A,C)) # label(fact_sgn__mult) # label(axiom). [clausify(827)].
% 6.09/6.33 Derived: c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B)) = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,A),c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,B)). [resolve(1673,a,1674,a)].
% 6.09/6.33 1675 -class_Rings_Olinordered__idom(A) | class_Groups_Osgn__if(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Osgn__if) # label(axiom). [clausify(1050)].
% 6.09/6.33 1676 -class_Groups_Osgn__if(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn0) # label(axiom). [clausify(829)].
% 6.09/6.33 1677 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__if) # label(axiom). [clausify(839)].
% 6.09/6.33 1678 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__if) # label(axiom). [clausify(839)].
% 6.09/6.33 1679 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)) # label(fact_sgn__if) # label(axiom). [clausify(839)].
% 6.09/6.33 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1675,b,1676,a)].
% 6.09/6.33 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(1675,b,1677,a)].
% 6.09/6.33 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(1675,b,1678,a)].
% 6.09/6.34 Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))). [resolve(1675,b,1679,a)].
% 6.09/6.34 1680 class_Rings_Odvd(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Odvd) # label(axiom). [assumption].
% 6.09/6.34 1681 -class_Rings_Odvd(A) | c_Groups_Otimes__class_Otimes(A,B,C) != D | c_Rings_Odvd__class_Odvd(A,B,D) # label(fact_dvdI) # label(axiom). [clausify(910)].
% 6.09/6.34 1682 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,D,E)) | c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,D,c_Groups_Otimes__class_Otimes(A,F,C)),E)) # label(fact_inf__period_I3_J) # label(axiom). [clausify(937)].
% 6.09/6.34 1683 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,D,E)) | -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,D,c_Groups_Otimes__class_Otimes(A,F,C)),E)) # label(fact_inf__period_I3_J) # label(axiom). [clausify(937)].
% 6.09/6.34 1684 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,D,E)) | c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,D,c_Groups_Otimes__class_Otimes(A,F,C)),E)) # label(fact_inf__period_I4_J) # label(axiom). [clausify(938)].
% 6.09/6.34 1685 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,D,E)) | -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,D,c_Groups_Otimes__class_Otimes(A,F,C)),E)) # label(fact_inf__period_I4_J) # label(axiom). [clausify(938)].
% 6.09/6.34 1686 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,c_Groups_Otimes__class_Otimes(A,C,D))) | c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,f19(C,B,A),c_Groups_Ozero__class_Ozero(A))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(953)].
% 6.09/6.34 1687 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,c_Groups_Otimes__class_Otimes(A,C,D))) | hBOOL(hAPP(B,f19(C,B,A))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(953)].
% 6.09/6.34 1688 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,c_Groups_Otimes__class_Otimes(A,C,f20(C,B,A)))) | -c_Rings_Odvd__class_Odvd(A,C,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(953)].
% 6.09/6.34 Derived: c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B) != C | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C). [resolve(1680,a,1681,a)].
% 6.09/6.34 Derived: -class_Rings_Ocomm__ring(tc_Nat_Onat) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,E,B)),D)). [resolve(1680,a,1682,b)].
% 6.09/6.34 Derived: -class_Rings_Ocomm__ring(tc_Nat_Onat) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,E,B)),D)). [resolve(1680,a,1683,b)].
% 6.09/6.34 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | -hBOOL(hAPP(A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C))) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,f19(B,A,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(1680,a,1686,a)].
% 6.09/6.34 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | -hBOOL(hAPP(A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C))) | hBOOL(hAPP(A,f19(B,A,tc_Nat_Onat))). [resolve(1680,a,1687,a)].
% 6.09/6.34 Derived: -class_Rings_Osemiring__0(tc_Nat_Onat) | hBOOL(hAPP(A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,f20(B,A,tc_Nat_Onat)))) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(A,C)). [resolve(1680,a,1688,a)].
% 6.09/6.34 1689 class_Rings_Odvd(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odvd) # label(axiom). [assumption].
% 6.09/6.34 Derived: c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,A,B) != C | c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,C). [resolve(1689,a,1681,a)].
% 6.09/6.34 Derived: -class_Rings_Ocomm__ring(tc_Complex_Ocomplex) | -c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,B) | -c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,D)) | c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,E,B)),D)). [resolve(1689,a,1682,b)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__ring(tc_Complex_Ocomplex) | -c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,B) | c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,D)) | -c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,C,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,E,B)),D)). [resolve(1689,a,1683,b)].
% 6.17/6.44 Derived: -class_Rings_Osemiring__0(tc_Complex_Ocomplex) | -hBOOL(hAPP(A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C))) | c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,B,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,f19(B,A,tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))). [resolve(1689,a,1686,a)].
% 6.17/6.44 Derived: -class_Rings_Osemiring__0(tc_Complex_Ocomplex) | -hBOOL(hAPP(A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,C))) | hBOOL(hAPP(A,f19(B,A,tc_Complex_Ocomplex))). [resolve(1689,a,1687,a)].
% 6.17/6.44 Derived: -class_Rings_Osemiring__0(tc_Complex_Ocomplex) | hBOOL(hAPP(A,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,B,f20(B,A,tc_Complex_Ocomplex)))) | -c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,B,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | -hBOOL(hAPP(A,C)). [resolve(1689,a,1688,a)].
% 6.17/6.44 1690 -class_Rings_Ocomm__semiring__1(A) | class_Rings_Odvd(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Odvd) # label(axiom). [clausify(1057)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C) != D | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D). [resolve(1690,b,1681,a)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ocomm__ring(tc_Polynomial_Opoly(A)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,E)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),F,C)),E)). [resolve(1690,b,1682,b)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ocomm__ring(tc_Polynomial_Opoly(A)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,E)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),F,C)),E)). [resolve(1690,b,1683,b)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D))) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),f19(C,B,tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))). [resolve(1690,b,1686,a)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D))) | hBOOL(hAPP(B,f19(C,B,tc_Polynomial_Opoly(A)))). [resolve(1690,b,1687,a)].
% 6.17/6.44 Derived: -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) | hBOOL(hAPP(B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,f20(C,B,tc_Polynomial_Opoly(A))))) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(B,D)). [resolve(1690,b,1688,a)].
% 6.17/6.44
% 6.17/6.44 ============================== end predicate elimination =============
% 11.58/11.81
% 11.58/11.81 Auto_denials: (non-Horn, no changes).
% 11.58/11.81
% 11.58/11.81 Term ordering decisions:
% 11.58/11.81 Function symbol KB weights: tc_Nat_Onat=1. tc_Complex_Ocomplex=1. tc_HOL_Obool=1. v_a=1. v_p=1. c_Groups_Ouminus__class_Ouminus=1. hAPP=1. c_Polynomial_Odegree=1. c_Polynomial_Ocoeff=1. c_Rings_Oinverse__class_Oinverse=1. c_Polynomial_Opoly=1. c_Groups_Osgn__class_Osgn=1. tc_fun=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_Nat_Osize__class_Osize=1. c_fequal=1. c_Polynomial_OAbs__poly=1. f1=1. f3=1. f5=1. f7=1. f8=1. f9=1. f14=1. f17=1. tc_Polynomial_Opoly=1. c_Groups_Ozero__class_Ozero=1. c_Nat_OSuc=1. c_Groups_Oone__class_Oone=1. c_Nat_Onat_Onat__size=1. f6=1. f22=1. c_Groups_Otimes__class_Otimes=1. c_Groups_Oplus__class_Oplus=1. c_Groups_Ominus__class_Ominus=1. c_Divides_Odiv__class_Omod=1. c_Polynomial_OpCons=1. c_Rings_Oinverse__class_Odivide=1. c_Polynomial_Osmult=1. c_Polynomial_Opoly__gcd=1. c_Polynomial_Omonom=1. c_Power_Opower__class_Opower=1. c_Polynomial_Osynthetic__div=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. c_Polynomial_Oorder=1. c_Polynomial_Opcompose=1. c_Nat_Onat_Onat__case=1. f2=1. f4=1. f11=1. f12=1. f13=1. f15=1. f16=1. f19=1. f20=1. c_If=1. f10=1. f21=1. c_Polynomial_Opoly__rec=1.
% 11.58/11.81
% 11.58/11.81 ============================== end of process initial clauses ========
% 11.58/11.81
% 11.58/11.81 ============================== CLAUSES FOR SEARCH ====================
% 11.58/11.81
% 11.58/11.81 ============================== end of clauses for search =============
% 11.58/11.81
% 11.58/11.81 ============================== SEARCH ================================
% 11.58/11.81
% 11.58/11.81 % Starting search at 4.95 seconds.
% 11.58/11.81
% 11.58/11.81 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 5.10 sec).
% 11.58/11.81
% 11.58/11.81 Low Water (keep): wt=42.000, iters=3451
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% 11.58/11.81 Low Water (keep): wt=39.000, iters=3343
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% 11.58/11.81 Low Water (keep): wt=38.000, iters=3374
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% 11.58/11.81 Low Water (keep): wt=36.000, iters=3354
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% 11.58/11.81 Low Water (keep): wt=35.000, iters=3340
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% 11.58/11.81 Low Water (keep): wt=34.000, iters=3359
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% 11.58/11.81 Low Water (keep): wt=33.000, iters=3366
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% 11.58/11.81 Low Water (keep): wt=31.000, iters=3354
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% 11.58/11.81 Low Water (keep): wt=30.000, iters=3335
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% 11.58/11.81 Low Water (keep): wt=29.000, iters=3484
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% 11.58/11.81 Low Water (keep): wt=28.000, iters=3350
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% 11.58/11.81 Low Water (keep): wt=27.000, iters=3337
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% 11.58/11.81 Low Water (keep): wt=24.000, iters=3342
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% 11.58/11.81 Low Water (keep): wt=23.000, iters=3341
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% 11.58/11.81 Low Water (keep): wt=22.000, iters=3399
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% 11.58/11.81 Low Water (keep): wt=21.000, iters=3353
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% 11.58/11.81 Low Water (keep): wt=20.000, iters=3334
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% 11.58/11.81 Low Water (keep): wt=19.000, iters=3358
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% 11.58/11.81 Low Water (keep): wt=18.000, iters=3359
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% 11.58/11.81 Low Water (keep): wt=17.000, iters=3337
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% 11.58/11.81 Low Water (keep): wt=16.000, iters=3340
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% 11.58/11.81 Low Water (displace): id=5347, wt=112.000
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% 11.58/11.81 Low Water (displace): id=6054, wt=95.000
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% 11.58/11.81 Low Water (displace): id=6798, wt=87.000
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% 11.58/11.81 Low Water (displace): id=5353, wt=83.000
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% 11.58/11.81 Low Water (displace): id=5377, wt=76.000
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% 11.58/11.81 Low Water (displace): id=6885, wt=69.000
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% 11.58/11.81 Low Water (displace): id=6811, wt=67.000
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% 11.58/11.81 Low Water (displace): id=6032, wt=66.000
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% 11.58/11.81 Low Water (displace): id=6804, wt=65.000
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% 11.58/11.81 Low Water (displace): id=6147, wt=61.000
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% 11.58/11.81 Low Water (displace): id=6856, wt=60.000
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% 11.58/11.81 Low Water (displace): id=6697, wt=59.000
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% 11.58/11.81 Low Water (displace): id=5856, wt=58.000
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% 11.58/11.81 Low Water (displace): id=5972, wt=57.000
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% 11.58/11.81 Low Water (displace): id=5391, wt=56.000
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% 11.58/11.81 Low Water (displace): id=6711, wt=55.000
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% 11.58/11.81 Low Water (displace): id=6578, wt=54.000
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% 11.58/11.81 Low Water (displace): id=4512, wt=53.000
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% 11.58/11.81 Low Water (displace): id=14717, wt=51.000
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% 11.58/11.81 Low Water (displace): id=14688, wt=48.000
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% 11.58/11.81 Low Water (displace): id=14779, wt=46.000
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% 11.58/11.81 Low Water (displace): id=14984, wt=43.000
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% 11.58/11.81 Low Water (displace): id=14985, wt=40.000
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% 11.58/11.81 Low Water (displace): id=14467, wt=39.000
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% 11.58/11.81 Low Water (displace): id=15007, wt=37.000
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% 11.58/11.81 Low Water (displace): id=14687, wt=36.000
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% 11.58/11.81 Low Water (displace): id=14716, wt=35.000
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% 11.58/11.81 Low Water (displace): id=15638, wt=34.000
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% 11.58/11.81 Low Water (displace): id=14700, wt=33.000
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% 11.58/11.81 Low Water (displace): id=14705, wt=32.000
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% 11.58/11.81 Low Water (displace): id=15637, wt=31.000
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% 11.58/11.81 Low Water (displace): id=16057, wt=15.000
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% 11.58/11.81 Low Water (keep): wt=15.000, iters=3354
% 11.58/11.81
% 11.58/11.81 Low Water (displace): id=18490, wt=14.000
% 11.58/11.81
% 11.58/11.81 Low Water (keep): wt=14.000, iteCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------